101.yaml

usual:
  usualTime: "13:00"
  usualDay: "Monday"
  usualRoom: "LT1414a"
  usualBuilding: "Livingstone Tower"

talks:
- tag: Talk
  date: '2026-02-12T16:00:00Z'
  speaker: Shriram Krishnamurthi
  speakerurl: https://cs.brown.edu/~sk/
  institute: Brown University
  insturl: https://cs.brown.edu
  title: "Resugaring: Lifting Semantic Features through Syntactic Sugar"
  abstract: |
    Syntactic sugar is pervasive in language technology. It is used to shrink the size of a core language; to define domain-specific languages; and even to let programmers extend their language. Unfortunately, syntactic sugar is eliminated by transformation, so when the system provides feedback, it is in terms of a program that is unfamiliar to the authors. Thus, tool authors are forced to choose between their convenience and that of the programmer.

    We address this conflict by showing how to lift core language features to present them in terms of the surface syntax. We have performed this research over three different features: execution traces, binding, and type rules. In each case we identify properties expected of the lifting and prove that our techniques satisfy these.

    More broadly, though syntactic sugar is a central area of programming languages, it remains under-represented in the research literature. We briefly examine some other elements of a research agenda for this area.
  location: LT1414a
  material: []
- tag: Talk
  date: '2026-03-30T13:00:00Z'
  speaker: Sam Fish
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Categorical Quantum Nonlocality
  abstract: |
    After decades of being embroiled in political skirmishes, quantum physicists find themselves presented with a mathematical framework which predicts behaviour contrary to our reasonable intuitive leaning towards locality. Despite powerful attempts to quell the movement ensuing upon this realisation and to force it into irrelevance - even in the face of an incredibly successful experimental verification which no campaign can possibly diminish or sugar-coat - researchers now see no option but to accept the findings and to seek to understand their far reaches, along with anything they might reveal about quantum theory's relationship with relativity via Einstein's requirement of local causality. 
    
    On Monday I intend to present this timeline of escalation as faithfully as I can, along with some investigative findings, and some underlying categorical actors.
  location: LT711
  material: []
- tag: Talk
  date: '2026-03-23T13:00:00Z'
  speaker: Emma Tye
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: (A very belated) Advert for POPL'26
  abstract: |
    So POPL'26 was 2 months ago. I went as a student volunteer, with my attendance funded by SIGPLAN and my travel funded by MSP. But what do I actually remember from it? What stood out? Did I see anything I think my fellow PhDs and professors would like?

    I plan to give an overview of my first experience at a major conference as a student, as well as a whirlwind tour of some papers that caught my interest, or I think might catch yours!
  location: LT711
  material: []
- tag: Talk
  date: '2026-03-16T13:00:00Z'
  speaker: Clemens Kupke
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Thin behaviours, (co)algebraically (Part I)
  abstract: |
    In this talk I'll provide an update on our project on thin structures. Thin trees as introduced by Bojanczyk, Idziaszek and Skrzypczak are infinite trees with at most countably many infinite paths. While the theory of (top-down) automata operating on infinite trees is considerably less well-behaved than the one of automata on infinite words, thin trees provide a convenient setting where one can study tree-shaped data that behaves in some ways like words. In this talk I will recall the notion of a thin tree. I will then explain how thin trees generalise to the level of coalgebras for an analytic functor and how those thin "behaviours" can be seen as the quotient of an initial algebra of representants (terms of finite depth, but involving an infinitary operation). We axiomatize that quotient with a single equation. Underlying our result is a normal form theorem for thin behaviours. I will then sketch how thin behaviours might be useful in verification and/or model learning. The details of the latter will, however, most likely be the content for another 101.

    This is joint work with Anton Chernev, Corina Cirstea and Helle Hvid Hansen.
  location: LT711
  material: []
- tag: CancelledTalk
  date: '2026-03-09T13:00:00Z'
  speaker: Fiona Blackett
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: TBC
  abstract: ''
  location: LT711
  material: []
- tag: Talk
  date: '2026-03-02T13:00:00Z'
  speaker: Vikraman Choudhury
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Inceptions
  abstract: |
    We can program with continuations using the continuation monad, which gives us control operators, control effects, and classical logic. But, it is not an algebraic effect, and corresponds to a large algebraic theory. Is there a monad for non-local control effects, which is still algebraic?

    This is work-in-progress, and based on joint work with Gregor Feierabend and Marcelo Fiore.
  location: LT711
  material: []
- tag: Talk
  date: '2026-02-23T13:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Introduction to setoids
  abstract: |
    A setoid is a type X together with an equivalence relation ≅_X : X → X → Prop, i.e. ≅_X is reflexive, symmetric, and transitive. Setoids are widely used in (pre-HoTT) type theory based approaches to constructive mathematics, where quotients might not be available, or better avoided for computational reasons. Even though setoids have a bad reputation ("setoid hell") due to a quickly leading to a lot of boilerplate, I'll argue that they are quite nice to work with as a model construction, as setoids validate many convenient axioms such as function extensionality and countable choice.
  location: LT711
  material: []
- tag: Talk
  date: '2026-02-16T13:00:00Z'
  speaker: Conor McBride
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Finitary testing
  abstract: ''
  location: LT307
  material: []
- tag: Talk
  date: '2026-02-09T13:00:00Z'
  speaker: Rin Liu
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Structural Set Theory
  abstract: |
    Suppose you were asked, "is 3 ∈ ℕ?" Being a natural number, 3 is indeed a member of ℕ, so the answer is “yes”. On the other hand, the question, “is π ∈ ℚ?”, would quickly receive an answer of “no”. Now, suppose you were then asked, “is π ∈ log?”

    You’d might pause for a moment, before again answering in the negative, but for a different reason than before. After all, π is a number, and log is a function, so π being a member of log -- whatever that means -- would be ridiculous! A better answer might be to declare the question as meaningless.

    As computer scientists and/or type theorists, the problem here is obvious. But in the foundations used in most mathematics outside of (higher) category theory, the issue is less clear-cut. In most common presentations of set-theoretic foundations -- for our purposes, ZFC; Zermelo–Fraenkel set theory with Choice -- everything is a set, so the question “is π ∈ log?” should have a yes-or-no answer.

    Many of these kinds of quirks arise from the "global" nature of the set membership relation: it is always valid to compare any two arbitrary sets for membership and equality. However, in most practical contexts, sets are often stratified, in the sense that we usually don’t have very long chains of membership containment, and sets from different strata are very rarely compared or combined. This talk aims to present the structuralist's approach to this problem: a categorical way of constructing "structural" sets connected together via only local set membership relations between them that avoids these kinds of problems. This talk is intended to be accessible and expository, and requires only basic exposure to category theory.
  location: LT209
  material: []
- tag: Talk
  date: '2026-02-02T13:00:00Z'
  speaker: Guillaume Allais
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Trees for Concurrency
  abstract: |
    Looking at Claessen's 1999 functional pearl "A poor man's concurrency monad", we will see how we can simulate a limited form of concurrency in purely functional terms. We will then go on to see how to modify the setup to return a value from that computation as well as introduce join points.
  location: LT209
  material: []
- tag: Talk
  date: '2026-01-26T13:00:00Z'
  speaker: Ezra Schoen
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Species of Trees
  abstract: |
    Mathematicians and computer scientists both enjoy trees very much. I know I certainly do, and I wish to share my enthusiasm. This talk will be a theory-light tour of various interesting phenomena relating to species of trees. We will discuss what makes a species, what makes a tree, and look at a range of particularly interesting examples of species of trees. In the interest of managing expectations: you're not likely to learn all that much about combinatorial species from this talk. It's more of an excuse to have a fun and relaxed time exploring ways trees can occur 'in the wild'.
  location: LT209
  material: []
- tag: Talk
  date: '2026-01-19T13:00:00Z'
  speaker: Conor McBride
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Wiggle It (Just a Little Bit)
  abstract: |
    Testing can reveal the absence of bugs in situations where we can show that the test data expose all the possible variations. This is straightforward when the domain is finite, but one can also achieve test coverage for large domains by restricting the ways in which the program may process its input. For example, the fact that the sum of the numbers less than n is n choose 2 can be proven by testing for n in {0, 1, 2} because both calculations are inherently quadratic. I have, on and off, been thinking about how to deliver similar results for other inductive data structures. For example, one can generate particularly well behaved folds on unlabelled binary trees by giving (i) the tree which is the image of the leaf, and (ii) a tree with two variables showing how the ouptut for a node is computed from the outputs for its two subtrees. I claim that if two such folds agree at the four smallest trees, then they agree for all trees. Clearly, we recover (i) by testing at a leaf. We recover (ii) by testing at a node with leaves for subtrees, then perturbing each of those subtrees in turn, to see where the output changes. That is to say, we use perturbation to recover abstraction. I am currently working on a proof of this claim in Agda and will share my progress (and my prospectus) in this talk.
  location: LT210
  material: []
- tag: Talk
  date: '2025-12-15T13:00:00Z'
  speaker: Ezra Schoen
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Duality
  abstract: ''
  location: TBD
  material: []
- tag: Talk
  date: '2025-12-11T15:00:00Z'
  speaker: Noam Zeilberger
  speakerurl: 'https://noamz.org/'
  institute: Laboratoire d'informatique de l'École Polytechnique
  insturl: ''
  title: The free bifibration on a functor
  abstract: |
    Joint work with Bryce Clarke and Gabriel Scherer.

    Preprint: https://arxiv.org/abs/2511.07314

    A functor p : D → C is a bifibration if, loosely speaking, one can push and pull objects of D along arrows of C. The talk will begin by recalling the formal definition together with some motivation, and then explain how the free bifibration generated by a functor p may be constructed using a simple sequent calculus. This sequent calculus is closely related to a certain "zigzag double category" ℤC constructed as the free bifibration on the identity functor id : C → C, and which is also the free fibrant double category on C. The double category perspective leads to a nice string diagram calculus, while proof-theoretic techniques allow us to derive a canonicity result for free bifibrations, and to analyze some examples of a combinatorial nature.
  location: LT310 and online
  material: []
- tag: CancelledTalk
  date: '2025-12-08T13:00:00Z'
  speaker: Guillaume Allais
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: TBD
  abstract: ''
  location: TBD
  material: []
- tag: Talk
  date: '2025-12-09T14:00:00Z'
  speaker: Jan de Muijnck-Hughes
  speakerurl: ''
  institute: MSP/StrathCyber
  insturl: ''
  title: An Introduction to Design-by-Contract with Dafny
  abstract: |
    Dafny is a multi-paradigm language with deep integration of <strong>design-by-contract</strong> style verification: Hoare Triples.  What makes Dafny interesting from a language design perspective is that, although, there is a clear separation between a specification and the code it reasons about, specifications are nonetheless made from code.  For this 101, I am going to introduce everyone to Dafny and show how one can write and reason about simple imperative and object-oriented programs and their behaviour.

    What excites me about Dafny is its potential to act as a <em>bridging language</em> that guides students, who are ostensibly rooted in imperative programming, through to the world of verification without having to introduce them to the world of dependently-typed functional programming.  I hope you will be excited about Dafny too.
  location: LT1414a
  material: []
- tag: Talk
  date: '2025-11-24T13:00:00Z'
  speaker: Vikraman Choudhury
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Semantic analysis of Polarization
  abstract:  Polarization is a proof-theoretic technique used to study various kinds of logics with classical dualities. I will give a model-theoretic explanation of polarization in the context of classical logic and classical linear logic (Girard and Laurent). Finally, I will show a higher-dimensional generalisation of these ideas to generalised species.
  location: LT310 and online
  material: []
- tag: Talk
  date: '2025-11-17T13:00:00Z'
  speaker: Clemens Kupke
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Graph Games with Infinite Plays
  abstract: In this 101 I am planning to discuss 2-player graph games with infinite plays. At first we will focus on games with "trivial" acceptance conditions where a player either loses or wins all infinite plays. As motivating example I will present the games that characterize least and greatest fixpoints of monotone operators. After that we will explore why those games are too simple for reasoning about alternating fixpoints and move to parity games, a type of graph game that captures the full expressive power of the modal mu calculus. Time permitting I will explain how to prove that parity games are (memoryless) determined and how one can compute winning regions of a given parity game.
  location: LT1414a and Online
  material: []
- tag: Talk
  date: '2025-11-10T13:00:00Z'
  speaker: Ohad Kammar
  speakerurl: https://denotational.co.uk/
  institute: University of Edinburgh
  insturl: ''
  title: Modular abstract syntax trees (MAST) – substitution tensors with second-class sorts
  abstract: |
    We adapt Fiore, Plotkin, and Turi's treatment of abstract syntax with binding, substitution, and holes to account for languages with second-class sorts. These situations include programming calculi such as the Call-by-Value λ-calculus (CBV) and Levy's Call-by-Push-Value (CBPV). Prohibiting second-class sorts from appearing in variable contexts means the presheaf of variables is no longer a left-unit for Fiore et al's substitution tensor product. We generalised their development to associative and right-unital skew monoidal categories. We reuse much of the development through skew bicategorical arguments. In ongoing work, we replace the skew monoidal structure with ordinary monoidal structure by recourse to substitution modules instead of substitution monoids.

    We apply the resulting theory in two scenarios. We employ the mathematical theory to circumvent the expression problem when proving substitution lemmata for varieties of CBV denotational semantics modularly. We employ a computational implementation of the theory to circumvent the expression problem when implementing intrinsically-typed foreign-function interfaces for the 29 theories of SMTLIB.

    Joint work with Marcelo Fiore, Kajetan Granops, Mihail-Codrin Iftode, Georg Moser, and Sam Staton.
  location: LT1414a and Online
  material: []
- tag: Talk
  date: '2025-11-04T16:00:00Z'
  speaker: Georgi Nakov
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Matrix Type Theory
  abstract: |
    What is an appropriate type for a matrix, and what are the accompanying typing rules? Depending on your mileage, the answer might seem obvious or dull &mdash; can't we start with a humble <tt>Matrix A m n</tt>? I would argue that better candidates exist, and that suitable typing rules are far from obvious, at least if we aim at actually implementing the said rules. In this talk, I will embark on the long journey of turning something that looks good on paper into something that works in code. We try to abolish any implicit assumptions, hidden computation and blind guessing from the initial typing rules, and refine them until they can guide a precise implementation. With guest occurrences of the usual suspects &mdash; bidirectional typing, thinnings, and typecheckers-that-get-to-know-monoid-laws.
  location: LT1414a and Online
  material: []
- tag: Talk
  date: '2025-10-27T13:00:00Z'
  speaker: Sean Watters
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: What I did in my PhD
  abstract:
    The modal μ-calculus is a modal logic that type theorists don't usually spare much thought for; it's usually treated classically, and its main application is as a specification language for model checking, where it subsumes weaker but more commonly used logics like LTL, CTL, and PDL. Meanwhile, modal logicians study the μ-calculus using very "1930s" concepts like explicitly named variables. Most of my efforts during my PhD have been spent trying to pull the theory of the modal μ-calculus into this century (AKA into Agda) using the tools of type theory, but my real interest is in what we type theorists might glean from the exchange. For example, the modal μ-calculus is a fixpoint logic, with a very mature account of fixpoint alternation - something that every proof assistant (to my knowledge) is lacking.

    In this talk, I'll be using the μ-calculus and some of my recent work on it as a motivating example to give a slightly non-standard introduction to some important MSP ideas - syntaxes with binding, and data types as fixpoints. I'll cover the least fixpoint (which computer scientists love), the greatest fixpoint (which we sometimes tolerate), and the rational fixpoint (which many forget exists, but plays a key role in my work). If time permits, I'd also like to open the door to the terrifying world of arbitrary fixpoint alternation, and some (very very early) ideas for taming it.
  location: LT310 and Online
  material: []
- tag: Talk
  date: '2025-10-20T13:00:00Z'
  speaker: Bob Atkey
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Capucci Logic
  abstract: |
    For some applications, it is useful for the truth of a logical statement to be approximate instead of merely true or false. Fuzzy Logics are a famous example of such logics, where statements are valued in the interval [0,1], where 1 represents "definitely true" and 0 represents "definitely false".

    In this talk, I'll talk about a logic which is valued in [0,∞] where implication is interpreted as a ratio between premises and conclusion. The main feature of this logic is that we can formulate a logic where the "sharp" lattice connectives are replaced by smooth ones. Our hope is that this will allow such logics to be used in situations where satisfiability can be learned, or where non-satisfaction is treated as a cost during training.
  location: LT310 and online
  material: []
- tag: Talk
  date: '2025-10-13T13:00:00Z'
  speaker: Fiona Blackett
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Introduction to Persistent Homology
  abstract: ''
  location: LT1414a and Online
  material: []
- tag: Talk
  date: '2025-10-10T16:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: An introduction to constructive logic
  abstract: Constructive logic (also known as intuitionistic logic) is logic without
    the Law of the Excluded Middle, which states that P or ¬ P holds for every proposition
    P. Hilbert famously said that denying mathematicians the use of the Law of the
    Excluded Middle is "the same as denying the boxer the use of his fists". I will
    try to convince you that there sometimes is merit in not trying to punch people
    in the head. For example, constructive logic is the internal logic of toposes,
    and so a constructive proof can often be reinterpreted to show a much stronger
    result than a classical one, e.g., a constructed proof of the existence of a function
    might in fact automatically yield the existence of a <em>continuous</em> or <em>computable</em>
    function. Constructive logic often leads to interesting mathematics, as it allows
    for finer distinctions than classical logic. I will also discuss how and when,
    despite appearances, constructive logic can be seen as an extension of classical
    logic, rather than as a restriction.
  location: LT210 and online
  material: []
- tag: Talk
  date: '2025-10-03T16:00:00Z'
  speaker: Jeremy Singer
  speakerurl: https://www.dcs.gla.ac.uk/~jsinger/
  institute: University of Glasgow
  insturl: https://www.gla.ac.uk/schools/computing/
  title: Let's Take Esoteric Programming Languages Seriously
  abstract: Esoteric programming languages are challenging to learn, but their unusual
    features and constraints may serve to improve programming ability. From languages
    designed to be intentionally obtuse (e.g. INTERCAL) to others targeting artistic
    expression (e.g. Piet) or exploring the nature of computation (e.g. Fractan),
    there is rich variety in the realm of esoteric programming languages. This essay
    examines the counterintuitive appeal of esoteric languages and seeks to analyse
    reasons for this popularity. We will explore why people are attracted to esoteric
    languages in terms of (a) program comprehension and construction, as well as (b)
    language design and implementation. Our assertion is that esoteric languages can
    improve general PL awareness, at the same time as enabling the esoteric programmer
    to impress their peers with obscure knowledge. We will also consider pedagogic
    principles and the use of AI, in relation to esoteric languages. Emerging from
    the specific discussion, we identify a general set of "good" reasons for designing
    new programming languages. It may not be possible to be exhaustive on this topic,
    and it is certain we have not achieved that goal here. However we believe our
    most important contribution is to draw attention to the varied and often implicit
    motivations involved in programming language design.
  location: LT1414a and Online
  material: []
- tag: Talk
  date: '2025-09-22T13:00:00Z'
  speaker: Conor Mc Bride
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: 'Leftovers, Rightunders: Typechecking Thinnings Compositionally'
  abstract: |-
    In the interests of sharing MSP lore, I came up with a way to talk about both the "Input Subject Output" approach to typechecking and the Category of Thinnings in the same talk, making the latter an interesting example of the former.

    The Input Subject Output approach, like most bidirectional approaches to problem decomposition, tracks whether signals go from parent to child or vice versa, but it also acknowledges a signal has a guarantor as well as a sender, responsible for the meaningfulness of the signal. Meanwhile, thinnings are order-preserving embeddings between ordered sequences, or dually, selections of elements from sequences (their resemblance to binomial coffecients is no accident), and are thus a fine example of a monoidal category.

    I won't assume that any of you know know any of this: many of us do; more of us should. And I'll try to tell the story with pictures, drawn on a whiteboard, rather than jargon.

    I often use thinnings to talk about embeddings between scopes, the latter seen as sequences which grow on the right (because of prejudices about time). A compositional way to typecheck a thinning is to start with the available stuff "over" the thinning, together with a thinning that will start choosing from the newest stuff on the right. If all is well, we shall learn which "leftovers" have not yet been considered, and which "rightunders" have been not only considered but also selected. There is a healthy story about both the monoidal/parallel/spatial/tensor structure of thinnings and their categorical/sequential/temporal/composition structure, yielding an algorithm which never has to guess where to chop sequences in two.
  location: LT1310 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=BABpO4epxOo
    linkDescription: Video
- tag: SpecialEvent
  date: '2025-09-18T16:05:00Z'
  endDate: '2025-09-18T17:00:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: LT1414a and Online
  locationurl: ''
  description: ''
- tag: Talk
  date: '2025-05-30T14:00:00Z'
  speaker: Liang-Ting Chen
  speakerurl: https://l-tchen.github.io/
  institute: Institute of Information Science, Academia Sinica, Taiwan
  insturl: https://www.iis.sinica.edu.tw/en/index.html
  title: A formal treatment of bidirectional typing
  abstract: 'In this talks, we consider a general and formal theory of bidirectional
    typing for simply typed languages: for every signature that specifies a mode-correct
    bidirectionally typed language, there exists a proof-relevant type synthesiser
    which, given an input abstract syntax tree, constructs a typing derivation if
    any, gives its refutation if not, or reports that the input does not have enough
    type annotations.<br>Sufficient conditions for deriving a type synthesiser such
    as soundness, completeness, and mode-correctness are established for all signatures.
    We propose a preprocessing step, which helps the user to deal with missing type
    annotations. The entire theory is implemented in Agda, serving as a verified generator
    of proof-relevant type synthesisers as a by-product.'
  location: LT210 and Online
  material: []
- tag: SpecialEvent
  date: '2025-05-28T11:00:00Z'
  endDate: '2025-05-28T12:00:00Z'
  title: ADR/Promotion Information Meeting
  url: ''
  location: LT1414a
  locationurl: ''
  description: ''
- tag: Talk
  date: '2025-03-19T16:00:00Z'
  speaker: Petar Veličković
  speakerurl: https://petar-v.com/
  institute: Google DeepMind
  insturl: https://deepmind.google/
  title: Generalisation in LLMs
  abstract: A general talk about our recent works on generalisation in llms
  location: LT210 and Online
  material:
  - tag: Link
    address: https://youtu.be/7Z144Ymohd0
    linkDescription: Video
- tag: CancelledTalk
  date: '2025-03-19T11:00:00Z'
  speaker: Matthew Cartmell
  speakerurl: https://www.strath.ac.uk/staff/cartmellmatthewprofessor/
  institute: Department of Mechanical and Aerospace Engineering
  insturl: ''
  title: Symbolic Computational Dynamics
  abstract: |-
    The term 'symbolic computational dynamics' has evolved over time and has been promoted by ourselves over the years to describe our interdisciplinary research in engineering dynamics, applied mathematics, and symbolic computation and has now gained recognition and some acceptance in the nonlinear dynamics community. This research has been based on a combination of the modelling of time-variant mechanical systems (mostly) using classical equation derivation techniques such as Newton-Euler and Lagrange, the approximate analytical solution of the ODEs, PDEs / BCs, or DAEs that have been derived using appropriate asymptotic methods, and finally the symbolic computation needed to make this whole process as automated and scalable as possible.

    Symbolic Computational Dynamics has its roots in the 1970s when early codes such as MACSYMA emerged, and then gained further traction in the later 1980s with the advent of codes such as Maple and Mathematica. It has evolved into a more structured research activity in recent years and this seminar will attempt to summarise some of the principal milestones along the way. The mathematical challenges posed by vibration theory have been exceptionally useful for developing practical algorithmic structures for various asymptotic mathematical methods for approximate solution, notably methods such as Lindstedt-Poincaré, Poincaré-Lighthill, Krylov-Bogoliubov, general averaging, and the method of multiple scales. These experiments with manual analysis started in the early 1980s and eventually led to the development of precursor codes in Mathematica. We started to adopt this code quite early on in our research due to its robustness and powerful functionality. This decision has affected our work significantly, in ways that have continued to work reasonably to our advantage, and we have developed several prototype solvers, mostly exploiting the powerful and adaptable method of multiple scales over the alternatives.

    EPSRC funding was first awarded in 1997 and several grants followed, enabling a small research team to be sustained for the following fifteen years. The findings of that period enabled several specialised studies to follow and further PhDs focusing on solver refinements and some initial work on symbolic code for the semi-automated derivation of differential equation models for low dimensional systems.

    In 2020 the start-up company Symbolic Computational Dynamics Ltd (SCD Ltd) was founded, and sufficient private investment was obtained for the co-funding of a further PhD. In 2024 SCD Ltd was proposed for possible spin-out conversion through the University of Strathclyde’s Stage Gate company development programme. This has led to highly significant business development support for a focused programme of product development, with the intention to enter a high growth phase so that SCD software products can be brought to the market within 12 to 15 months.

    This seminar will outline some of the contributions that we have made to the field of symbolic computational dynamics, and the development of our software to the point where commercial products can be planned.
  location: LT? and Online
  material: []
- tag: CancelledTalk
  date: '2025-04-28T15:00:00Z'
  speaker: Justus Matthiesen
  speakerurl: ''
  institute: University of Edinburgh
  insturl: ''
  title: TBD
  abstract: ''
  location: LT412 and Online
  material: []
- tag: Talk
  date: '2025-04-22T15:00:00Z'
  speaker: April Gonçalves
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: A quick & dirty look at at abstract syntax with binders and metavariables
  abstract: In this talk, I will show the (categorical) semantics of Fiore and collaborators’
    “Second-Order Abstract Syntax with Binders” and of McBride and collaborators’
    “Universe of Syntaxes with Bindings”. I will also compare them under multiple
    criteria (literature, usage, meta theory and implementation/formalisation), with
    special focus on how both approaches handle metavariables by using System F as
    our main example. (Please beware it’s a work in progress, and many details haven’t
    been worked out yet
  location: LT210 and Online
  material:
  - tag: Link
    address: https://youtu.be/kwSeO50FBFE
    linkDescription: Video
- tag: Talk
  date: '2025-04-07T15:00:00Z'
  speaker: Aven Dauz
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Modelling cybersecurity games with compositional game theory
  abstract: Compositional game theory and its corresponding Haskell DSL <q>open-games-engine</q>,
    have been used for modelling microeconomic games, auctions, and smart contracts.
    Some advantages of this compositional approach are leveraging modularity and code-reuse
    to construct larger games. Incidentally, game theory has been used to model complex
    attack-defense scenarios in cybersecurity, with the simplest case modelling the
    strategic interaction between a single attacker and defender. Scaling these models
    to accurately reflect real-world attacks and extrapolate data to improve the performance
    of systems remains an active area of research. In this talk I'll present a honeypot
    allocation game and design choices that allow a modeller to easily extend the
    construction to represent defensive strategies such as deception.
  location: LT412 and Online
  material:
  - tag: Link
    address: https://youtu.be/JBOcJW_kxy8
    linkDescription: Video
- tag: CancelledTalk
  date: '2025-03-31T15:00:00Z'
  speaker: Philippa Cowderoy
  speakerurl: ''
  institute: ''
  insturl: ''
  title: TBD
  abstract: ''
  location: LT412 and Online
  material: []
- tag: Talk
  date: '2025-03-17T15:00:00Z'
  speaker: Ross Horne
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Additives without Weakening
  abstract: As we know, in linear logic, conjunction and disjunction decompose into
    separate multiplicative and additive forms. Only additives are idempotent in general
    (A + A --o A). The additives also have some properties such as weakening (A &
    B --o A). By dropping weakening, the additives further decompose into infinitely
    many <q>sub-additive</q> operators. <p>I explain how I spotted these sub-additive
    operators when studying nominal quantifiers that can similarly be decomposed into
    new nominal quantifiers. I found these new additives curious since the resulting
    operators have properties that are sound with respect to probability distributions,
    effectively internalising probability distributions in logic. I end by giving
    a taste of the proof theory of the sub-additives. A novelty is that, due to how
    sub-additives control certain distributivity properties that play an essential
    role in established cut elimination techniques, a new proof technique must be
    invented.</p>
  location: LT412 and Online
  material:
  - tag: Link
    address: https://youtu.be/04K0vkcqXvU
    linkDescription: Video
- tag: Talk
  date: '2025-03-10T15:00:00Z'
  speaker: Zanzi Mihejevs
  speakerurl: ''
  institute: GlAiVe Research
  insturl: https://glaive-research.org/
  title: A canonical bidirectional typing discipline through polarised System L
  abstract: What is the relationship between polarity and bidirectional typing? It
    has long been observed that there is a connection between the two, but the precise
    relationship has remained unclear. Moreover, it has been argued that the link
    itself is a red herring, and that bidirectional typing is better explained not
    by polarity but by chirality - the duality between producers and consumers. <p>In
    this talk we will look at Polarised System L, a type theory that combines both
    dualities - the positive fragment is driven by a cut between a primitive producer
    and a pattern, and the negative fragment is driven by a cut between a primitive
    consumer and a co-pattern.</p> <p>Remarkably, linear System L admits a canonical
    bidirectional typing discipline based on a combination of ideas from both standard
    and co-contextual typing, giving us a <q>bi-contextual</q> typing algorithm.</p>
    <p>We will see how this lets us equip a type system based on full classical linear
    logic - containing all four connectives and derivable implication and co-implication
    - with a bidirectional discipline where all typing annotations are exclusively
    limited to shifts between sythesisable and checkable expressions.</p>
  location: LT412 and Online
  material:
  - tag: Link
    address: https://youtu.be/0Qg_RnSHyhU
    linkDescription: Video
- tag: Talk
  date: '2025-03-03T15:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Representing type theory in type theory
  abstract: It is often claimed that type theory can act as a foundation of mathematics.
    If that is so, then type theory should in particular be able to reason about type
    theory itself. Of course, Dr Gödel points out that this cannot work, in general,
    but we would expect that type theory could still reason about a slightly weaker
    version of itself. This turns out to be true, but messy, because type theory is
    quite complicated as a theory. After heroic attempts by Danielsson (2006) and
    Chapman (2009) to represent type theory internally in type theory, Altenkirch
    and Kaposi (2016) made a breakthrough in using so-called quotient inductive-inductive
    types to represent the well typed terms of type theory, where quotient constructors
    are used to encode beta and eta laws as equalities in the type. Being able to
    treat such laws as actual equalities is a major improvement, but quickly leads
    into so-called <q>transport hell</q>, where explicit transports along equalities
    show up in terms and needs to be reasoned about. I will report on some recent
    work together with Liang-Ting Chen and Tzu-Chun Tsai on how one can use experimental
    (and hopefully future) features of Agda to improve on the quotient inductive-inductive
    representation and remove most uses of transport.
  location: LT412 and Online
  material: []
- tag: Talk
  date: '2025-02-24T15:00:00Z'
  speaker: Robert Atkey
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Semantic proofs of Cut-elimination for Deep Infererence
  abstract: 'Deep Inference systems are a kind of proof calculus that allow inference
    rules to be applied anywhere in a formula. Cut-elimination for these systems is
    similar to that for Sequent calculi: rules that introduce intermediate formulas
    can be removed from proofs. Prior proofs of cut-elimination relied on intricate
    syntactic method. I''ll talk about a semantic approach that builds a model of
    the whole calculus from cut-free proofs, such that every proof constructed in
    this model can be read back as a cut-free proof. This is a similar technique to
    the one used in Normalisation by Evaluation (NbE). The technique is very flexible
    and extends to many extensions of Multiplicative Linear Logic, including BV''s
    self-dual non-commutative <q>before</q> connective, additives, and exponentials.
    <p>This is joint work with Wen Kokke and was published at MFPS last year: https://bentnib.org/sem-cut-elim-mfps.html</p>'
  location: LT412 and Online
  material:
  - tag: Link
    address: https://youtube.com/live/urIEmeRuxTU
    linkDescription: Video
- tag: Talk
  date: '2025-02-17T15:00:00Z'
  speaker: Clovis Eberhart
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Weakest Precondition of Open Coalgebras
  abstract: Coalgebras are a categorical framework that have proved useful to describe
    and reason about different types of systems. We define open coalgebras, a compositional
    framework where coalgebras can be composed as string diagrams. We give them a
    semantics in terms of weakest precondition predicate transformers computed as
    a fixed point and link it to previous work on weakest precondition predicate transformers
    by Aguirre, Katsumara, and Kura. We give several examples of verification problems
    this semantics can compute, showing its practical usefulness. We give conditions
    under which this semantics is compositional for the string diagram structure of
    open coalgebras. Finally, we give a syntactic precomputation of open coalgebras
    that removes their internal states while preserving their semantics.
  location: LT1414a and Online
  material: []
- tag: Talk
  date: '2025-02-10T15:00:00Z'
  speaker: Ezra Schoen
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Coequations via proof systems
  abstract: "<p><b>What even is a coequation?</b> While Universal Algebra enjoys a
    set-in-stone consensus on both the correct syntax of equations, as well as what
    an equation even is, Universal Coalgebra is in no such position. There are many
    attempts at definitions and syntaxes of coequations, but it is hard to say which
    one is 'the correct one'.</p> <p>Rather than sorting out this mess, why not add
    yet another proposal? If we squint, we can see proof systems for modal logic as
    coequations. This then leads to some fun, natural questions. Which coequations
    can be captured by what kind of proof systems? If we restrict our attention to
    a class of 'simple' systems, can we specify <q>every</q> coequation?</p> <p>As
    this is work in progress, I have a fewer answers than questions. The aim of this
    talk is to introduce coequations in all their colours, and to get the audience
    to a point where the questions may be appreciated.</p>"
  location: LT209 and Online
  material:
  - tag: Link
    address: https://youtu.be/VCfCkAwK2pg
    linkDescription: Video
- tag: Talk
  date: '2025-02-03T15:00:00Z'
  speaker: Jules Hedges
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: We solved dependent optics!
  abstract: "<p>There are two major generalisations of lenses. First there are optics,
    which require almost nothing of their base category and give you something in
    return. And then there are dependent lenses (aka container morphisms, aka natural
    transformations of polynomials), which require a lot of their base category but
    give you even more in return. One day several years ago I innocently twote the
    question of how to unify these two constructions, which is motivated for mathematical,
    computational and sociological reasons. The problem ended up occupying us (joint
    work with Dylan Braithwaite, Matteo Capucci, Bruno Gavranović, Eigil Rischel and
    André Videla) for several years, and its difficulty became a meme.</p> <p>I will
    explain the answer that finally satisfied us. This involves first constructing
    a category of <q>dependent adaptors</q> and then freely adjoining a particular
    family of monoidal costates using a technique we call <q>weighted coparametrisation</q>
    that we reinvented. The definition began life as a prototype in Idris using QTT
    features, and was then translated back into category theory using what might or
    might not be a novel semantics of polymorphic dependent type theory.</p>"
  location: LT209 and Online
  material:
  - tag: Link
    address: https://youtu.be/yhxwUnWKK2I
    linkDescription: Video
- tag: Talk
  date: '2025-01-27T15:00:00Z'
  speaker: André Videla
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Pipelining and dependent types
  abstract: Pipelining is a crude CPU optimisation to speed up execution of sequential
    programs. By allowing the manipulation of types as values, dependent types enable
    new abstractions to manipulate large-scale of software based on sequential computation
    inspired by CPU pipelining. I will show how to define pipelines, sequential programs
    that cannot easily be parallelised using a list of types as a specification. Given
    this list of type, the implementation of a pipeline is given by the functions
    between each type. This pipeline abstraction can be generalised to categories
    such that the pipeline is made up of objects and its implementation is given by
    the morphisms between them. This enable the use of kleisli morphisms for effectful
    programs. The pipeline can be further abstracted over graded categories enabling
    automatic composition of errors. Finally, I will show how to use dependent pipelines
    to allow composition of programs with type-dependency. An architecture particularly
    useful for single-pass compilers with well-scoped and well-typed implementations.
  location: LT412 and Online
  material:
  - tag: Link
    address: https://youtu.be/dQU4IA1hDa4
    linkDescription: Video
  - tag: Link
    address: https://gitlab.com/avidela/types-laboratory/-/blob/main/src/MSP101Cheat.idr?ref_type=heads
    linkDescription: Code of the talk
  - tag: Link
    address: https://gitlab.com/glaive-research/pipelines
    linkDescription: Library code
- tag: Talk
  date: '2025-01-20T15:00:00Z'
  speaker: Conor McBride
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: My Favourite Double Category
  abstract: I'll (re)introduce the <q>codeBruijn</q> representation of syntax with
    binding, in which terms are intrinsically indexed over their support (the variables
    they are involved with) rather than their scope. These supports form the objects
    of a category of order-preserving injections (<q>thinnings</q> to MSP locals and
    <q>my triangle</q> to Blaise Pascal), whose dual (<q>selections</q>) plays a crucial
    role in managing the restrictions of the variable support in specific substructures.
    Meanwhile, the notion of <q>simultaneous substitution</q> tightens to a relevant
    structure where every variable in the source support has an image, and every variable
    in the target support is used by at least one of those images. The action of substitution
    (which includes substitution composition) respects support precisely. It is reliant
    on the way a selection from a substitution's source support variables retains
    only some of their images and is itself relevant only once we have identified
    the corresponding selection from the target support of only those variables used
    in the retained images. We acquire squares with selections for vertical edges
    and relevant substitutions for horizontal edges which compose in both dimensions,
    forming a double category. (For anyone who saw, or for that matter, gave Phil
    Wadler's talk at the last SPLS, codeBruijn shifting happens at the root of a term,
    obviating the complex relationship between renaming and substitution which happens
    only because de Bruijn shifting happens at the leaves.) (For dependently typed
    programmers, more generally, there may be transferable lessons in managing coherence.)
  location: LT412 and Online
  material:
  - tag: Link
    address: https://youtu.be/aAgqu1y4Xto
    linkDescription: Video
- tag: SpecialEvent
  date: '2025-01-17T13:30:00Z'
  endDate: '2025-01-17T14:30:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: LT1414a and Online
  locationurl: ''
  description: ''
- tag: Talk
  date: '2025-01-17T13:00:00Z'
  speaker: April Gonçalves
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Type-Sensitive Algebraic Macros
  abstract: Despite recent advances made by Idris and Lean teams, metaprogramming
    in a typed language is still hard, frustrating and error-prone. In this short
    paper, we investigate a new view on macros via a type-sensitive algebraic theory
    for typechecker scripting for a more principled approach to type-directed macros.
    We show that our theory encodes typechecking and elaboration for STλC, and from
    there, we build two other variations, Bidirectional STλC and Search-based Type
    Inference, to showcase the versatility of our framework. Our results are implemented
    in Agda.
  location: LT1414a and Online
  material: []
- tag: CancelledTalk
  date: '2024-12-13T13:00:00Z'
  speaker: Neil Ghani
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Scientific anarchy
  abstract: TBD
  location: LT412 and Online
  material: []
- tag: CancelledTalk
  date: '2024-12-13T13:00:00Z'
  speaker: Clemens Kupke
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Parity Formulas
  abstract: In this talk, I will discuss how modal mu-formulas can be succinctly represented
    as graphs, thus avoiding some of the variable naming issues that Sean sketched
    in his recent 101. A key technical problem when switching to graphs is that the
    natural dependency order between fixpoint operators is obfuscated. Therefore our
    graphs need to be equipped with a parity function that encodes this order. We
    call the resulting graphs with parity functions <q>parity formulas</q>. This is
    based on joint work with Johannes Marti and Yde Venema.
  location: LT511 and Online
  material: []
- tag: Talk
  date: '2024-11-29T13:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: 'Data type science: how to reason about classes of data types in type theory'
  abstract: Different proof assistants and programming languages have different notions
    of data types. Sometimes this means that we can prove more theorem in one system
    compared to another, and sometimes it only means that one system is more convenient
    to use. How can we tell the difference? I'll give an introduction to how we can
    represent and reason about classes of data types in type theory, and I'll show
    some examples from the zoo of classes that have been considered.
  location: LT210 and Online
  material: []
- tag: CancelledTalk
  date: '2024-11-22T13:00:00Z'
  speaker: Danielle Marshall
  speakerurl: ''
  institute: University of Glasgow
  insturl: ''
  title: TBC
  abstract: TBC
  location: LT412 and Online
  material: []
- tag: Talk
  date: '2024-11-15T13:00:00Z'
  speaker: Jade Master
  speakerurl: https://sites.google.com/view/jadeedenstarmaster
  institute: GLAIVE
  insturl: ''
  title: Representation Matters (Taking Categories Seriously)
  abstract: When we endeavor to build software based on category theory, we often
    have two categorically equivalent structures that represent the same underlying
    data and the correct choice of structure subtly depends on what you would like
    to do. The first generation of categorical programming languages heavily used
    the monad to represent algebraic effects. However, what if we made a different
    choice? Categorically equivalent to Monads are Lawvere theories, whose presentation
    as categories allows for many useful constructions which are more awkward in the
    Monad representation. In this talk, I will imagine what a system for algebraic
    effects based on Lawvere theories might look like. This talk will include a lightning
    introduction to Lawvere theories as well as a tour through an idris2 implementation
    of these ideas which still contains too many holes to float.
  location: LT310 and Online
  material:
  - tag: Link
    address: https://youtu.be/FlOWErswJzw
    linkDescription: Video
  - tag: Link
    address: https://gitlab.com/glaive-research/lawvereeffects
    linkDescription: Code
- tag: Talk
  date: '2024-11-08T13:00:00Z'
  speaker: Bob Atkey
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: How to Make Good Choices
  abstract: What to do? One way to find out is to explore all the consequences of
    our choices and pick the best one. Or we could assume we have a magic device that
    tells us what the outcome of our choice will be, and to pick the best one straight
    off. In terms of programming, the former can be modelled using a monad for non-deterministic
    choices and the latter using the Selection monad of Escardo and Oliva. I'll relate
    these two monads via a logical relation, showing that if we are careful to respect
    abstraction boundaries, the two are equivalent for closed programs. I'll then
    extend this correspondence to account for different kinds of choice-making program
    and see how we can reconstruct concepts like Nash equilibrium. This talk may involve
    some live coding in Agda.
  location: LT210 and Online
  material:
  - tag: Link
    address: https://youtu.be/8ueFihu8Ja8
    linkDescription: Video
  - tag: Link
    address: https://gist.github.com/bobatkey/b9ba09a9934bed48ae3551493173f952
    linkDescription: Agda code
- tag: Talk
  date: '2024-11-01T13:00:00Z'
  speaker: Guillaume Allais
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Partial evaluation
  abstract: Partial evaluation shows up all across PL in compilation (optimization),
    meta-theory (normalization), and code-generation (staging). I will give a gentle
    introduction to partial evaluation using semantic methods, showing how we can
    strategically build different models to decide different equational theories.
    This will be an Agda-mediated live coding show.
  location: LT309 and Online
  material:
  - tag: Link
    address: https://youtu.be/O-bHGWL7PNY
    linkDescription: Video
- tag: Talk
  date: '2024-10-28T14:00:00Z'
  speaker: Sean Watters
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: The Madness of the Modal &mu;-Calculus
  abstract: In this talk, I'll give you the <q>what</q>, <q>why</q>, and <q>how</q>
    of the &mu;-calculus - what it is, why I find it interesting (and hopefully why
    you should too!), and how to tame it in Agda. </p>I'll start by introducing and
    motivating the field of model checking, before quickly diverting to the modal
    &mu;-calulus, a fixpoint modal logic of foundational importance in that field.
    I'll talk about its semantics first, because that's only sensible, then the rest
    of the talk will be devoted to the weird and wonderful (but mostly weird) syntactic
    issues that arise from this formalism. In particular, I'll focus on an important
    syntactic construction called <q>the closure</q> of a &mu;-calculus formula, which
    is not stable under alpha-equivalence, and whose inductive structure is somewhat
    non-obvious. </p>In the second half, we'll code up an implementation of the &mu;-calculus
    in Agda, which will also serve as an introduction to well-scoped De Bruijn syntax.
    I'll work towards defining parallel substitution and weakening, and finish with
    the definition of the closure, and a (very) brief sketch of its correctness proof.
    The data type of thinnings between natural numbers will feature.</p>If there's
    time (which there probably won't be), I'll discuss an extension of well-scoped
    De Bruijn syntax that I've been calling <q>sublimely-scoped</q> syntax, which
    is still very WIP.
  location: LT310 and Online
  material:
  - tag: Link
    address: https://youtu.be/opJpkKgP288
    linkDescription: Video
- tag: Talk
  date: '2024-10-18T13:00:00Z'
  speaker: Clovis Eberhart
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: A Compositional Approach to Verification Models
  abstract: We will present a compositional approach to graph-like verification models
    (e.g., parity games, Markov decision processes, or Petri nets) based on <q>open</q>
    structures. Such open structures are graphs with potentially dangling edges called
    <q>open ends</q>, and which form interfaces along which open structures can be
    composed. We thus define a syntactic category of interfaces and open structures
    between them. We then define a semantic category representing relevant information
    about the structure (e.g., a category of probabilistic rewards). Finding an interpretation
    functor from the syntactic category to the semantic one shows that these structures'
    semantics can be computed compositionally. (This is joint work with Kazuki Watanabe,
    Kazuyuki Asada, Ichiro Hasuo, and Serge Lechenne.)
  location: LT714 and Online
  material:
  - tag: Link
    address: https://youtu.be/FRBpabpuBGE
    linkDescription: Video
- tag: Talk
  date: '2024-10-11T13:00:00Z'
  speaker: Jan de Muijnck-Huges
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Bidirectional Typing & Session Types, A Beautiful Friendship?
  abstract: Session Types are a neat typing discipline to reason both statically and
    dynamically about program interaction. An interesting question is how best we
    should check communicating programs against a given global type.</p>Bidirectional
    typing is an important technique for programming language design and implementation,
    enabling us to transform the theory of how we should check the type of a term
    and incorporate the practice of inferring the term's type.</p>This talk serves
    as a gentle introduction to bidirectional type system design and session types,
    and how combining the two can help make type checking session typed programs that
    little bit easier.
  location: LT714 and Online
  material: []
- tag: Talk
  date: '2024-10-04T13:00:00Z'
  speaker: André Videla
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Cooking with Proofs
  abstract: The Curry-Howard correspondence says that types are propositions and programs
    are proofs. But what proof is Super Mario World on the SNES? In this introductory
    presentation we'll explore how the Curry-Howard correspondence manifests in different
    programming environments and how to employ it for software development.
  location: LT210 and Online
  material: []
- tag: Talk
  date: '2024-09-27T13:00:00Z'
  speaker: Conor McBride
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Effing W
  abstract: I shall revisit the Hindley-Milner type system for the traditional Core
    ML (old sense) language of variables, application, monomorphic abstraction and
    polymorphic definition, to give a new twist on its implementation. In particular,
    I shall consider the role that the context plays in the type inference process,
    and then make it disappear, replacing context-as-data-structure with context-as-control-structure,
    demonstrating the power of effects and handlers. The extra ingredient which gives
    this new recipe its spice is to index with respect to a suitably compositional
    notion of "progress". I shall make that disappear, too!
  location: LT210 and Online
  material: []
- tag: SpecialEvent
  date: '2024-09-20T13:00:00Z'
  endDate: '2024-09-20T14:00:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: LT1310 and Online
  locationurl: ''
  description: ''
- tag: Talk
  date: '2024-04-17T13:00:00Z'
  speaker: Dov M. Gabbay
  speakerurl: https://en.wikipedia.org/wiki/Dov_Gabbay
  institute: Augustus De Morgan Professor Emeritus of Logic, King's College London
  insturl: ''
  title: Intro to argumentation
  abstract: This is a blackboard talk introducing the audience to argumentation.
  location: LT11, boardroom
  material: []
- tag: Talk
  date: '2024-02-13T12:00:00Z'
  speaker: Nobuko Yoshida
  speakerurl: https://mrg.cs.ox.ac.uk/people/nobuko-yoshida/
  institute: Strachey Chair at University of Oxford
  insturl: ''
  title: Session types, Linear Logic and Expressiveness
  abstract: |-
    I will first talk about the origin of session types and its relationship with expressiveness.

    The first technical part of this talk will present an expressiveness result between Linear Logic-based Session Types and System F. The second part gives a summary of recent results on session types, highlighting the expressiveness correspondence between various session-based process calculi.
  location: LT412
  material: []
- tag: SpecialEvent
  date: '2024-05-03T15:00:00Z'
  endDate: '2024-05-03T16:00:00Z'
  title: Academic Promotion Information Meeting
  url: ''
  location: LT209 (TBC)
  locationurl: ''
  description: ''
- tag: SpecialEvent
  date: '2024-03-29T15:00:00Z'
  endDate: '2024-03-29T16:00:00Z'
  title: No talk this week (Easter Bank Holiday)
  url: ''
  location: ''
  locationurl: ''
  description: ''
- tag: Talk
  date: '2024-03-15T15:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Can ordinal exponentiation be defined constructively in homotopy type theory?
  abstract: |-
    A cornerstone of the classical theory of ordinals is its rich theory of arithmetic, extending the arithmetic of natural numbers. While addition and multiplication are easily seen to be realized by disjoint union and Cartesian product of wellorders respectively, exponentiation is more mysterious. Using classical logic, it can be defined using a case distinction on the exponent, but constructively, this can not serve as a definitional principle, but rather as a specification of what exponentiation should satisfy. Sierpiński [1958] gives an explicit construction for a base with a least element as the set of functions with finite support. This construction again relies on classical logic in several places, but working in homotopy type theory, we have managed to to refine the idea in a more intensional manner to define a^b for ordinals a of the form a = 1 + a' for some ordinal a'. In a sense, this is the best we can hope for: we can prove that an operation a^b satisfying the specification of ordinal exponentiation for all inputs a and b is definable if and only if the law of excluded middle holds.

    This is joint work with Tom de Jong, Nicolai Kraus, and Chuangjie Xu.
  location: LT209 and Online
  material:
  - tag: Link
    address: https://github.com/fredrikNordvallForsberg/TypeTopology/blob/exponentiation/source/Ordinals/Exponentiation.lagda
    linkDescription: Agda formalisation (messy, WIP)
  - tag: Link
    address: https://www.youtube.com/watch?v=o9llIj0nlz4
    linkDescription: Video
- tag: Talk
  date: '2024-05-24T15:00:00Z'
  speaker: Jan de Muijnck-Hughes
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Propagating Rose Trees with Dependent Types to Grow Shaped ASTs Generically
  abstract: Dependently typed languages support the construction of intrinsically-typed
    (well-scoped) terms, ensuring that our core language representations are correct-by-construction.
    The datatypes we use to represent Abstract Syntax Trees (AST) are not well-typed
    nor well-scoped, nor should they be. Nonetheless, ASTs are often represented as
    a collection of bespoke datatypes that capture what it means for an AST to be
    ‘well-structured’. Such artisan crafting of our ASTs comes at the price of generality.
    We must define the same traversals and operations time and time again over each
    AST.<br/>Taking inspiration from intrinsically-typed datatypes and compact encoding
    of primitives, we show how rose trees can have their shape dictated by a description
    contained within a dependent type. We can thus, describe (type) the structure
    of our ASTs similar to how we describe the concrete syntax using eBNF and embed
    the description inside a pre-existing datatype. Through this novel combination,
    we now have a single generic datatype for ASTs and single operations that act
    on them.
  location: LT209 and Online
  material: []
- tag: SpecialEvent
  date: '2024-05-31T15:00:00Z'
  endDate: '2024-03-29T16:00:00Z'
  title: No talk this week
  url: ''
  location: ''
  locationurl: ''
  description: ''
- tag: Talk
  date: '2024-06-07T15:00:00Z'
  speaker: Guillaume Allais
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: From Separation Logic to Dependent Parallel Skeletons
  abstract: I will give a high level motivation for separation logic and then show
    how we can (WIP) use these ideas in Quantitative Type Theory as implemented in
    Idris 2 to give a correct-by-construction treatment of effectful parallel programming
    over buffers.
  location: LT209 and Online
  material: []
- tag: Talk
  date: '2024-05-17T15:00:00Z'
  speaker: Ross Horne
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: What is deep inference?
  abstract: Deep inference is a branch of proof theory where inference rules can be
    applied in any context, much like in categorical logic. What I find fun in this
    area is that it has been used to define new logics for which there exists no sequent
    calculus nor even a semantics (yet). I'll introduce some simple deep inference
    systems first. Next, I'll point to recent work where we generalise logic beyond
    formulas to graphs.
  location: LT209 and Online
  material: []
- tag: Talk
  date: '2024-05-10T15:00:00Z'
  speaker: Clemens Kupke
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: A Coalgebraic Interpretation of the Lee/Yannakakis Minimisation Algorithm
  abstract: Minimisation of transition systems wrt bisimulation is important for the
    verification of properties of such systems. In my talk I will discuss a minimisation
    algorithm by Lee and Yannakakis, that intertwines minimisation with reachability
    checking. The algorithm caught our eye due to clear similarities with our own
    variant of Angluin's algorithm that allows to learn a minimal, reachable quotient
    of a given transition system. In the talk I aim to compare Lee/Yannakakis and
    Angluin and will sketch a possible coalgebraic generalisation of the Lee/Yannakakis
    algorithm. This is based on ongoing joint work with Simone Barlocco.
  location: LT209 and Online
  material: []
- tag: Talk
  date: '2024-04-26T15:00:00Z'
  speaker: Zanzi
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Free Relative Monads and Kan Algebras for Type and Scope Safe DSLs
  abstract: 'What are relative monads and why are they interesting? Functional programmers
    are familiar with using fixpoints of endofunctors and free monads to model datatype-generic
    evaluators. In this applied talk we will see how free relative monads allow us
    to extend these techniques to the realm of well-scoped and well-typed languages
    with binders.  A crucial role will be played by kan extensions: in a slogan, "Left
    Kan Extensions for Syntax, Right Kan Extensions for Semantics".'
  location: LT209 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=1UEN7AY0Xeg
    linkDescription: Video
- tag: CancelledTalk
  date: '2024-04-19T14:00:00Z'
  speaker: Ezra Schoen
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Modal Fixpoint Logics, Categorically
  abstract: Fixpoint logics are fun and exciting - they're second-order, which makes
    them quite expressive, but they still enjoy neat algorithmic properties. They're
    also difficult to work with; proofs are often intricate beasts, with swarms of
    technical lemmas and taylor-made tools. While this can be rewarding to work your
    way through, it's not necessarily efficient, and commonalities and similarities
    are often not exploited. <br/> This makes modal fixpoint logics an excellent target
    for us category theorists - finding and formalizing commonalities is our bread
    and butter. There's an exceedingly elegant framework for defining and working
    with one-step modal logics, based on dual adjunctions. In this talk, I'll sketch
    how (certain) modal fixpoint logics may be treated in the same way. I'll assume
    familiarity with category theory and basic (Kripke) modal logic, but not much
    else. <br/> This is joint work with Clemens Kupke, Jurriaan Rot and Ruben Turkenburg.
  location: LT209 and Online
  material: []
- tag: Talk
  date: '2024-04-12T15:00:00Z'
  speaker: Dylan Braithwaite
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Foundational Structures for Communicating Processes
  abstract: In 2009 Cockett and Pastro introduced a model for a typed process calculus
    in terms of a ‘linear actegory’. They note that the sequent rules of their calculus
    can be naturally viewed as living in a ‘poly-actegory’, a polycategory whose terms
    are additionally indexed by a list of objects of a multicategory, of ‘message
    types’. Although poly-actegories are mainly used as a tool to study the soundness
    of their language, they could arguably be taken as the foundational concept. <br/>
    Indeed recently Shulman has proposed a nearly identical structure under the name
    ‘LNL-polycategories’. Shulman shows that by asking that different collections
    of universal properties be present, LNL-polycategories may be used as a model
    for the LNL calculus, CBPV, and other models of effectful calculi. Inspired by
    this I will survey the universal properties required for implementing the basic
    communication primitives in a process calculus. With this framework, we can compare
    process models with the structures present in linear logic models, or effectful
    models, offering an additional perspective into the existing connections between
    the pi-calculus and linear logic or algebraic effects.
  location: LT209 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=I50O7cCCnFk
    linkDescription: Video
- tag: Talk
  date: '2024-04-05T15:00:00Z'
  speaker: Jade Master
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: I Think Indexed Enriched Categories are Nice.
  abstract: First proposed by Lawvere in 1973, indexed enriched categories are a very
    complicated mathematical structure studied in only the most privileged ivory towers.
    In this talk I intend to bring them down to earth by exploring their viability
    as a data structure. I will cheat by only considering enrichments where the axioms
    are satisfied trivially. I will explain how these 'trivial' enriched categories
    are nice data structures for holding solutions to algebraic path problems. Then
    I will explain how making them indexed allows us to work with distributed, concurrent,
    and compositional algebraic path problems. This talk will be in line with the
    research programme I started to develop before I quit and left for industry. Namely,
    that indexed categories and Grothendieck constructions may be used to develop
    a general theory of compositional computation. This talk will feature Idris2 code
    and categorical terminology side-by-side so that those familiar with either language
    will be able to follow along.
  location: LT209 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=coOArj1VyTw
    linkDescription: Video
- tag: Talk
  date: '2024-03-22T15:00:00Z'
  speaker: Matteo Capucci
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Softmax is Argmax, and the Logic of the Reals
  abstract: I will report some work in progress on the semiotics of softmax. This
    is an operator used in machine learning (but familiar to physicists way before
    that) to normalize a log-distribution, turning a vector of (thus, a function valued
    in) logits (i.e. additive reals) into a probability distribution. Its name is
    due to the fact it acts as a 'probabilistic argmax', since the modes of a softmax
    distribution reflects the minima (by an accident of duality) of the function.
    I will show an attempt to make this statement precise, by exhibiting the semantics
    of a 'very linear logic' on the *-autonomous quantale of extended multiplicative
    reals. In this logic, additive connectives are also linear, but are still in the
    same algebraic relation with the multiplicative ones. I will show how to define
    quantifiers, and thus softmax. If time permits, I'll show a construction of an
    enriched equipment of relations in which softmax should be characterizable as
    a Kan lift, in the same way argmax is characterized as a Kan lift in relations.
  location: LT209 and Online
  material:
  - tag: Link
    address: https://msp.cis.strath.ac.uk/101/slides/2024-03-22_capucci.pdf
    linkDescription: Slides
  - tag: Link
    address: https://www.youtube.com/watch?v=y1rpNTHOsf4
    linkDescription: Video
- tag: Talk
  date: '2024-03-08T15:00:00Z'
  speaker: Paulo Torrens
  speakerurl: ''
  institute: University of Kent
  insturl: ''
  title: TBD
  abstract: The continuation-passing style (CPS) translation employed within compilers
    gives rise to a class of target calculi where direct style functions don't exist
    anymore. While those may be studied using the lambda calculus, this might not
    be desired if the language should not be closed under beta-reduction, such as
    in the intermediate representation (IR) of Appel's compiler. The purpose of this
    talk is to introduce ongoing work on the metatheory of Thielecke's CPS-calculus,
    a small theory of continuations based on production IRs, how it relates to actual
    implementations, and how this allows us to have a strong theoretical background
    on the study of name-passing IRs in a similar way that the lambda calculus works
    as a theoretical foundation for functional programming.
  location: LT209 and Online
  material: []
- tag: Talk
  date: '2024-03-01T15:00:00Z'
  speaker: Wen Kokke
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Type-Logical Grammar, Controlled Substructure, and Display Calculus
  abstract: ''
  location: LT209 and Online
  material: []
- tag: Talk
  date: '2024-02-23T15:00:00Z'
  speaker: Andre Videla
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Containers for compiler architecture
  abstract: Compiler architecture sucks. It's been left behind by years of software
    engineering development that have been very successful in developing software
    past the command-line age. Today, applications are meant to be responsive, accessible
    from a web browser, enable collaboration, be multi-platform, include some generative
    AI. Some of those ideas are good, some are bad, but most compilers do not include
    any of them. In this presentation, I aim to showcase how we can revisit the classical
    "compiler as a function" architecture using containers to bring the idea of compiler
    architecture to the XXI century.
  location: LT209 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=BnzAxT-O0Y8
    linkDescription: Video
  - tag: PDF
    slideName: 2024-02-23_videla.pdf
- tag: Talk
  date: '2024-02-16T15:00:00Z'
  speaker: Jules Hedges
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Making lenses less pointless
  abstract: This talk contains two ideas. The first is a small trick for programming
    with lenses in a not-pointfree way, without using macros or other brittle hacks.
    The key is something I call a "dialectic", which is a value that carries around
    a delimited continuation with it. The second idea is realising that the central
    construction of Matteo's "Diegetic Open Games" paper amounts to a monad on the
    category of lenses that arises as the Kleisli dual of the linear ! comonad in
    a Dialectica category. By putting these two ideas together we get a shallow DSL
    for open games, differentiable programming, and other applications of categorical
    cybernetics. This will be a live coding talk using Haskell, although I think the
    same ideas should work in any language with first class functions.
  location: LT209 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=_572EOJPP6M
    linkDescription: Video
- tag: Talk
  date: '2024-02-09T15:00:00Z'
  speaker: Bob Atkey
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Stable domain theory, Program slicing, and Automatic Differentiation
  abstract: I'll talk about a connection I think I've discovered between stable domain
    theory and program slicing by Galois Connections. Stable domain theory considers
    a refinement of continuous functions between domains that captures the intuitive
    idea that a "nice" computable functions that produce values must do so by only
    looking at part of their input, and that part must be uniquely determined. The
    same idea turns up in Perera et al.'s formulation of program slicing as Galois
    connections. I'll try to connect the two via ideas from Automatic Differentiation.
  location: LT209 and Online
  material: []
- tag: Talk
  date: '2024-02-02T11:00:00Z'
  speaker: Conor McBride
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Presheaves on Purpose
  abstract: 'Dependently typed programming languages allow us to define indexed families
    of datatypes, e.g. <code>Term (n : Nat) : Set</code> as the type of lambda-terms
    with <code>n</code> variables free. As declared, <code>Term</code> is functorial
    only on the discrete structure of <code>Nat</code>, which is to say that it respects
    equality and nobody will faint with amazement. But by an outrageous coincidence
    (which I learned from Altenkirch, Hofmann and Streicher), such terms can be acted
    on by <em>thinnings</em> from <code>n</code> to some larger scope <code>m</code>,
    allowing us to carry terms under binders. That is, we can demonstrate by honest
    toil that <code>Term</code> is a functor from <code>Thin</code> to <code>Set</code>.
    I dislike honest toil, and will show you how to design it away in this and similar
    situations. To that end, I present a universe construction for descriptions of
    datatypes indexed over the objects of some category <code>C</code> which, by construction,
    extend to a functors from <code>C</code> to <code>Set</code>, a.k.a. presheaves
    on <code>Cop</code>.'
  location: LT401 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=3gef0_NFz8Q
    linkDescription: Video
- tag: Talk
  date: '2024-01-26T15:00:00Z'
  speaker: Malin Altenmüller
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Plane Graphs, (Co-)Operads, and Pattern Matching
  abstract: |-
    I will present work on open surface-embedded graphs as representations of string diagrams. The key feature of these graphs' definition are distinguished boundary vertices which represent their (outer and inner) boundaries. These special vertices make it possible to define surface-embeddings of graphs using a rotation system which specifies an ordering of incident edges at each vertex. We can then also express graph rewrite rules by their action on boundary vertices. Additionally, boundary vertices are a convenient structure to define planar graphs as operads, similar to Spivak's Operad of Wiring Diagrams [1]. I will explain this construction, as well as a dual "co-operad" version of it, and finally the operad-cooperad interaction which yields a notion of graph pattern matching.

    [1] https://arxiv.org/abs/1305.0297
  location: LT209 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=XG65L3PVexc
    linkDescription: Video
- tag: SpecialEvent
  date: '2023-12-04T10:30:00Z'
  endDate: '2023-12-04T17:00:00Z'
  title: CATNIP
  url: https://sites.google.com/view/catniporg/home?authuser=0
  location: University of Strathclyde (MC301)
  locationurl: ''
  description: The second Categories Network Project (CATNIP) meeting.
- tag: Talk
  date: '2023-11-23T15:00:00Z'
  speaker: Danel Ahman
  speakerurl: https://danel.ahman.ee/
  institute: University of Ljubljana
  insturl: https://www.fmf.uni-lj.si/en/
  title: What do bidirected containers (co-)interpret into?
  abstract: |-
    Directed containers are a neat specialisation of containers that fully faithfully interpret into comonad structures on the polynomial functor interpretation of the underlying containers. In terms of shapes and positions, a directed container requires the family of positions to form a certain kind of dependently typed monoid acting on the shapes. In terms of data types, directed containers capture structures where every position in a shape determines a subshape rooted at that position, e.g., positions in a non-empty list determine sublists rooted at those positions.

    In this talk I will discuss bidirected containers and what they interpret into. Bidirected containers specialise directed containers further by asking the positions to form a certain kind of dependently typed group acting on the positions. In terms of data types, this corresponds to every sub data structure having a position in it that takes one back to the parent data structure, i.e., data types that behave like zippers. I will also discuss what we need to seem to ask from comonads to get a similarly tight correspondence as we have for directed containers. I will end by wondering whether an analogous story also applies to the cointerpretation of directed containers as update monads.
  location: LT210 and Online
  material: []
- tag: Talk
  date: '2023-09-29T14:00:00Z'
  speaker: Conor McBride
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: An Introduction to Bricks
  abstract: ''
  location: LT711 and Online
  material: []
- tag: CancelledTalk
  date: '2023-12-15T14:00:00Z'
  speaker: Neil Ghani
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: TBD
  abstract: ''
  location: LT210 and Online
  material: []
- tag: Talk
  date: '2023-12-07T11:00:00Z'
  speaker: Georgi Nakov
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: LabMate --- your faithful and type-safe Matlab assistant
  abstract: |-
    Can you write type-safe Matlab code? And what can we do to help you write type-safe Matlab?

    This talk is a report on our progress on LabMate --- an interactive system designed to improve on current best practices of writing Matlab code. Our key proposition can be eloquently described as "add types, all the types".

    I will give a brief tour of the various features in LabMate and the rationale behind including them. We will also recall the basics of bidirectional type checking, what to do to incorporate dimension and unit checking, and how to represent matrices with high degree of generality in our type system. Some of the non-trivial challenges with Matlab's permissive syntax and elaborating operator overloading will become apparent in the process.

    This is joint work with Fred and Conor.
  location: LT210 and Online
  material: []
- tag: BasicTalk
  date: '2023-12-01T14:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Non-standard analysis
  abstract: I will give a basic 101-style introduction to the first-order logic concept
    of non-standard models. Intuitively, a non-standard model of say Peano Arithmetic
    PA is a model which contains infinitely large numbers. Yet, by virtue of being
    a model of PA, such a model still validates all the axioms of PA, including the
    induction axiom schema! It is an interesting and beautiful feature/bug of first-order
    classical logic that such models exist.
  location: LT711 and Online
  material: []
- tag: CancelledTalk
  date: '2023-11-24T14:00:00Z'
  speaker: Jade Master
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: TBD
  abstract: ''
  location: LT210 and Online
  material: []
- tag: SpecialEvent
  date: '2023-11-22T12:00:00Z'
  endDate: '2023-11-22T17:00:00Z'
  title: SPLS
  url: https://scottish-pl-institute.github.io/spls/meetings/2023/november/
  location: University of Strathclyde / Online
  locationurl: ''
  description: ''
- tag: Talk
  date: '2023-11-17T14:00:00Z'
  speaker: Riu Rodríguez Sakamoto
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Categorical cybernetics for Markov decision processes
  abstract: |-
    I will introduce two ingredients to MSPs 'categorical cybernetics':
    - "open game"-like categories for backward-filtering problems
    - semiring valuations to formalize softmax as a *preference* relation (generalizing selection relations)

    This will allow us to fit Markov decission processes and certain estimation problems to the existing framework, clearing our path towards connecting control and estimation problems.
  location: LT210 and Online
  material: []
- tag: CancelledTalk
  date: '2023-11-10T14:00:00Z'
  speaker: Georgi Nakov
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: TBD
  abstract: ''
  location: MC303 and Online
  material: []
- tag: Talk
  date: '2023-11-03T14:00:00Z'
  speaker: Joe Collins
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Hopf-Frobenius Algebras
  abstract: |-
    Hopf algebras and Frobenius algebras are two fairly common algebraic structures. They even look pretty similar if you squint your eyes - both consist of a monoid/ comonoid pair, and some algebraic rule that tells you how they interact. There are a few instances where a single object in a category has the properties of both a Hopf algebra and a Frobenius algebra, called a Hopf-Frobenius algebra. In particular, ZX calculus, a way of modelling quantum circuits using symmetric monoidal categories, has this property. Why? And where else does this occur?

    In this talk, I will be talking about what a Hopf-Frobenius algebra is and where it comes from.
  location: LT210 and Online
  material: []
- tag: Talk
  date: '2023-10-27T14:00:00Z'
  speaker: Bruno Gavranović
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: 'Category Theory ∩ Deep Learning : Where are we, and where can we go?'
  abstract: |-
    Four years ago I embarked on my PhD with the goal of exploring the landscape of category theory, and its application to artificial neural networks. Specifically, I aimed to understand at which level of generality can we express components of artificial neural networks, and still meaningfully capture learning.

    In this talk I will give a progress report on this goal, and outline future directions for improvement.
  location: LT210 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=I1DlBnK1tks
    linkDescription: Video
- tag: Talk
  date: '2023-10-20T14:00:00Z'
  speaker: Ezra Schoen
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: The double category of adjunctions
  abstract: There's a particular double category which I've noticed floating around
    for a while. The purpose of this talk is to explicitly describe this double category,
    play around in it and see if we can leverage it to get some `theorems for free'.
    I'll only be assuming prior familiarity with 1-categories, so it should be of
    general interest. In fact, part of the purpose behind this talk is demonstrating
    that even for staunch 1-category theorists, having some higher categories `in
    the back pocket' may help in getting a clear picture of what's `really going on'.
  location: LT210 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=4XG8MgQDbtA
    linkDescription: Video
- tag: Talk
  date: '2023-10-13T14:00:00Z'
  speaker: Sean Watters
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: "(Reflexive) Partial Monoids 101"
  abstract: Partial monoids came up in my work recently, and I found them quite interesting.
    The main goal of this talk is to introduce the notion into our local sphere of
    consciousness. After going over the basics I'll focus mostly on reflexive partial
    monoids, the suprisingly tricky problem of defining exponentiation for them, and
    the free reflexive partial monoid. I'll finish by outlining some remaining questions
    that I'm still wondering about.
  location: LT711 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=p44LyR-iDtw
    linkDescription: Video
- tag: Talk
  date: '2023-10-06T14:00:00Z'
  speaker: Andre Videla
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Writing interactive programs using containers
  abstract: Containers and their morphisms provide a bidirectional structure that
    matches a lot of programs that are interactive in nature (databases, servers,
    compilers). In this presentation I will show how to build such programs using
    containers, container morphisms and their algebra.
  location: Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=ft8LYjB22fc
    linkDescription: Video
- tag: Talk
  date: '2023-09-22T14:00:00Z'
  speaker: Guillaume Allais
  speakerurl: ''
  institute: MSP
  insturl: ''
  title: Staging by Evaluation
  abstract: I will present an Agda implementation of a simply typed version of András
    Kovács' Staged compilation with two-level type theory. Starting from an intrinsically
    typed language mixing static and dynamic parts using quotes and splices, we perform
    a model construction à la normalisation by evaluation and obtain a staging by
    evaluation algorithm.
  location: LT210 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=6meBs-M5PQc
    linkDescription: Video
- tag: Talk
  date: '2023-07-05T11:00:00Z'
  speaker: Anton Chernev
  speakerurl: ''
  institute: University of Groningen
  insturl: ''
  title: A dual adjunction between Ω-automata and Wilke algebras
  abstract: The notion of ω-regular language captures the idea of a regular language
    that consists of infinite words. The most standard type of automata for ω-regular
    languages are called Büchi automata. Ω-automata are another type of automata for
    ω-regular languages that, instead of infinite words, read pairs of finite words,
    called lassos, that represent ultimately periodic words. We study the categorical
    relationship between Ω-automata and Wilke algebras – the latter are algebraic
    structures recognising ω-regular languages. We present a chain of adjunctions
    starting from the category of Ω-automata without initial states and ending with
    the dual of the category of quotients of the free Wilke algebra. This is joint
    work with Helle Hvid Hansen (University of Groningen) and Clemens Kupke (University
    of Strathclyde).
  location: GH 513 and Online
  material:
  - tag: Link
    address: https://msp.cis.strath.ac.uk/101/slides/2023-07-05_anton.pdf
    linkDescription: Slides
- tag: Talk
  date: '2023-06-27T16:00:00Z'
  speaker: Meven Lennon-Bertrand
  institute: University of Cambridge
  speakerurl: https://www.meven.ac/
  insturl: https://www.cl.cam.ac.uk/research/clash/
  title: A Shiny Hammer and Many Nails to Hit – Bidirectional typing is not only an
    implementation technique
  abstract: |-
    In 2000, Pierce and Turner introduced a new technique to perform type inference for ML-like languages, whose main idea was to carefully understand the local flow of information in the algorithm. This technique, which came to be referred to as bidirectional typing, did not come out of a void: similar ideas had appeared independently in many other contexts. In particular, bidirectional typing has been a part of the folklore of dependently typed languages implementers since the dawn of time.

     But even in that context where it has a long history, bidirectional typing was for a long time mostly confined to implementations. Yet, its type-theoretic structure turns out to be a very versatile and powerful tool when studying (dependent) type systems and their meta-theory.

     In this talk, I will try and give some of my understanding of bidirectional typing, how it is rooted in type-checker implementations but is more than just this, and how it can be used to make many facets of the infamously painful meta-theory of dependent type systems a bit less painful.
  location: GH 513 and Online
  material:
  - tag: Link
    address: https://msp.cis.strath.ac.uk/101/slides/2023-06-27_meven.pdf
    linkDescription: Slides
- tag: Talk
  date: '2023-06-30T15:00:00Z'
  speaker: Joey Eremondi
  institute: University of Edinburgh
  speakerurl: https://eremondi.com/
  insturl: https://web.inf.ed.ac.uk/lfcs
  title: On The Design of a Gradual Dependently Typed Language for Programming
  abstract: I describe a design for gradual dependent types, a system by which dependently
    typed programs can be run when missing parts of types, proofs, or programs. This
    serves a dual purpose. First, it reduces the barrier to entry for dependent types,
    making it easier to migrate code to use dependently typed languages, and allowing
    indexed types to be safely used even when type or proof information is missing.
    Second, it gives dynamic semantics to the typed holes that are already found in
    modern languages, so programs can be safely run when holes are missing, providing
    the programmer with useful information of what terms should fill the holes. In
    the talk, I present a vision for what programming with gradual dependent types
    could look like, along with technical challenges that arise with it and solutions
    to some of these challenges.
  location: GH 513 and Online
  material: []
- tag: Talk
  date: '2023-06-16T15:00:00Z'
  speaker: Jan de Muijnck-Hughes
  institute: MSP
  speakerurl: http://jfdm.github.io/
  insturl: ''
  title: Session Types & Imperative Languages & Observations, Oh My!
  abstract: |-
    Session Types are a neat typing discipline to reason both statically and dynamically about program behaviour. An interesting question is how best we can incorporate session types into our programming languages and reach the fabled Emerald City of Type-Driven Validation of Communicating Systems!

     Earlier this year, I gave a talk at PLUG that discussed the dependently-typed mechanics that pushed me along the yellow brick road to create Capable, a featherweight imperative language that supports Multi-Party Session-Types (MPSTs). Capable has been mechanised within Idris2 to ensure that including MPSTs is done honestly as the Good Witch Glinda would appreciate.

     In this talk I intend to step away from the keyboard and take a detour along a yellow-ish cobbled street to look at some of the theoretical observations that arise from mechanisation. Specifically, I will discuss the design decisions that the Wicked Dependent-Type Checker of the East has requested I do to ensure unification and execution, but more importantly the trade-offs that come with those decisions.

     This work is, slowly, getting ready for publication (we do in fact run our session-typed programs) and I am certain that I don't need to return that brain, yet....
  location: LT310 and Online
  material: []
- tag: CancelledTalk
  date: '2023-06-19T15:00:00Z'
  speaker: John Power
  institute: University of Bath
  speakerurl: ''
  insturl: ''
  title: A Category Theoretic Analysis of Binders
  abstract: In the late 1990's, Fiore, Plotkin and Turi proposed a category theoretic
    model for binders. Instead of having a set of terms, they proposed a presheaf
    of terms over F, the category of finite sets, which provided cartesian contexts.
    They used a substitution monoidal structure on the category [F,Set] and characterised
    the notion of term in this setting by combining the notion of monoid in the substitution
    monoidal structure with the usual free generation of terms. Their modelling of
    binder was derived from that of substitution. A little later, Tanaka, following
    their lead, modelled linear binders, replacing F by P, the category of finite
    sets and permutations. These are instances of an axiomatic situation, where one
    has a 2-monad S on Cat, with a pseudo-distributive law, subject to a caveat about
    size, of S over what, except for size, would be a pseudo-monad [-^op,Set]. Tanaka
    and I developed the axiomatics in a series of papers that I propose to explain.
    The same mathematics was also used by Martin Hyland and several other authors
    in modelling general notions of algebra.
  location: LT310 and Online
  material: []
- tag: Talk
  date: '2023-06-21T14:00:00Z'
  speaker: John Power
  institute: University of Bath
  speakerurl: ''
  insturl: ''
  title: Computational Effects in Mathematical Perspective
  abstract: In the late 1980's, Eugenio Moggi introduced the idea of "monads as notions
    of computation", the latter more recently called computational effects, supported
    by several impressive examples. He used the definition of monad but did not make
    substantial use of mathematics that gives rise to monads. In category theory,
    monads systematically arise from universal algebra. But universal algebra can
    also be understood, from a category theoretic perspective, in terms of Lawvere
    theories, this fact shedding considerable light on computational effects, in particular
    the operations that give rise to effects. That observation has been fundamental
    to a deep, further development, giving rise to the notion of algebraic effect.
    I shall try to explain the conceptual line of thought that gives rise to algebraic
    effects, modelled by Lawvere theories and thence my monads. It was joint work
    primarily with Gordon Plotkin but also with others, notably Martin Hyland.
  location: MC319 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=7D5o-ZM_P90
    linkDescription: Video
- tag: Talk
  date: '2023-05-12T15:00:00Z'
  speaker: Ethel Morgan
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Just when I thought I was out, they pull me back in.
  abstract: Experiences from industrial academia & academic industry.
  location: LT711 and Online
  material: []
- tag: Talk
  date: '2023-05-05T15:00:00Z'
  speaker: Johannes Marti
  institute: Oxford
  speakerurl: http://johannesmarti.com/
  insturl: https://www.cs.ox.ac.uk/
  title: Modal unification and graph homomorphisms
  abstract: The problem of unifiability in a modal logic L asks, whether for a given
    formula phi there exists a substitution such that applying the substitution to
    phi turns it into a theorem of L. For the many non-transitive modal logics, most
    notably the modal logic K, it is not known whether this problem is decidable.
    I present joint work with Sam van Gool, where we reformulate unifiability relative
    to some modal logics L as a problem about the existence of a graph homomorphism
    for some generalised notion of graph that depends on a coalgebra functor T.
  location: LT711 and Online
  material: []
- tag: Talk
  date: '2023-04-28T15:00:00Z'
  speaker: Vikraman Choudhury
  institute: University of Glasgow
  speakerurl: https://vikraman.org/
  insturl: https://www.gla.ac.uk/schools/computing/research/researchsections/fata-section/
  title: Continuations and co-exponentials
  abstract: |-
    Growing up in Indiana, I learned about corn-mazes and continuations, but I found them very confusing, often getting lost and struggling to get back on track. Now that I’m living far away in Scotland, I find myself reminiscing about my midwestern roots.

     In this talk, I will present a different perspective on continuations: just as higher-order functions give you exponentials, higher-order continuations give you co-exponentials. On this motif, I will develop the theory of co-exponentials and some applications. I will show how to: (1) combine exponentials and co-exponentials in the same language without degeneracy, (2) give a computational interpretation for bi-intuitionistic logic, (3) recover classical control operators and the computational interpretation of classical logic using Faustian sums, (4) use co-exponential combinators to do speculative execution, backtracking, and encode effect handlers, (5) add co-exponentials to a first-order programming language, with a computational interpretation. I will develop these ideas both in syntax and semantics.

     The main idea occurred to me while studying linear logic and star-autonomous categories, from Mellies’ micrological study of negation. The rest of the work builds upon old ideas of Hofmann, Streicher, Reus on models of lambda-mu calculus, Moggi’s computational lambda calculus, Thielecke’s ⊗¬ categories, Freyd categories of Power, Thielecke, Führmann and others, and Hasegawa’s contextual calculus. This work is situated as part of a bigger research programme on trying to understand the foundations of quantum programming languages, starting from first-order reversibility, instead of linearity.
  location: LT711 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=rsEJaLVVNIc
    linkDescription: Video
- tag: Talk
  date: '2023-04-14T15:00:00Z'
  speaker: Thorsten Altenkirch
  institute: University of Nottingham
  speakerurl: http://www.cs.nott.ac.uk/~txa/
  insturl: http://www.cs.nott.ac.uk/
  title: What are higher categories and groupoids?
  abstract: |-
    Categories are like drugs: once you get addicted to one, your dealer comes up with something stronger and you aquire a new addiction. This is the games with higher categories.

     I want to look at the definition of higher cats, actually w,1-cats in HoTT  using semi-simplicial types and the directed replacement of simplicial types. Also I may discuss the globular approach (which works for higher groupoids but could also made to work for higher cats) I am wondering how these are related. This may help to address some open problems.
  location: LT711 and Online
  material: []
- tag: Talk
  date: '2023-03-14T15:00:00Z'
  speaker: Nathaniel Virgo
  institute: Earth-Life Science Institute (Tokyo)
  speakerurl: ''
  insturl: https://www.elsi.jp/en/
  title: Systems that model their environments, and systems that plan.
  abstract: |2-
     Consider a system interacting with its environment, perhaps in pursuit of some goal. We might want to ask whether the system has a model of its environment, especially in POMDP-like cases where the environment is partially observable and the system must make inferences about the environment's state in order to pursue its goal.

     But where does the model live in relation to the system? A simple answer is that the system's state parametrises a probability distribtion over environment states. This distribution isn't part of the system but is imposed upon it by an external observer. I will talk about how to model this observer-dependence via notion of 'interpretation' of a sytem, in which a system's internal states are interpreted as being 'about' a hidden environment state and as being updated using Bayes' theorem. A given system may have many interpretations, so that interpretations form a fibration over systems.

     A more interesting case is where a system uses a model not just to keep track of its environment but to reason about how to influence it. This is a lot harder to model, and I will talk about various pieces of work in progress towards understanding the relationships between systems, models and goals, with an emphasis on a category-theoretic perspective.
  location: LT310 and Online
  material:
  - tag: PDF
    slideName: 2023-03-14_nathaniel.pdf
- tag: Talk
  date: '2023-05-19T15:00:00Z'
  speaker: Andre Videla
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: How to be a real™ (C) programmer for beginner type theorists
  abstract: Feeling impostor syndrome from writing proof trees yet never executing
    any programs? Tired of being marginalized from online communities because you've
    never dereferenced raw memory? Finally, you can become a C-programmer neckbeard
    with this one crazy trick without leaving the comfort of your pen&paper. By extending
    QTT with pointer operations one can finally achieve their dream of submitting
    a patch to the linux kernel and have it be rejected for naming conventions. At
    least the program would be correct by construction since you can inherit all your
    inductive proofs inside your imperative program.
  location: LT711 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=dwutzLQ4ClA
    linkDescription: Video
- tag: Talk
  date: '2023-06-09T15:00:00Z'
  speaker: Malin Altenmüller
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Control Flow as a Contour of Data Flow
  abstract: |-
    I will be talking about some ongoing work on a compositional graph data structure for encoding control flow information of a program. At the centre of this definition is the notion of contour for a given tree-like structure. The notion of contour category was introduced by Melliès and Zeilberger [1], who use it in the context of representing derivations in context-free grammars as functors. I will give an overview over their constructions, and present how we generalise the notion of contour, moving to a non-linear, non-deterministic version. We use these generalised contours to express control flow information of a program on top of its abstract syntax tree. I will discuss how normal flow as well as exceptional program behaviour is represented in this framework. This is joint work with Dan Ghica.

     [1] <a href='https://arxiv.org/abs/2212.09060'>https://arxiv.org/abs/2212.09060</a>
  location: LT711 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=pnNy16sfnUk
    linkDescription: Video
- tag: Talk
  date: '2023-05-26T15:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org/
  insturl: ''
  title: From Lenses to Composable Continuations, and what lies between
  abstract: Continuation-Passing Style (CPS) is a programming discipline that parametrises
    programs by "the thing that happens next" - the continuation. Programs in CPS
    gain superpowers by being able to directly manipulate the continuation and use
    it as many times as they want. In this talk, I'll try to convince you that lenses
    are a restricted form of CPS where the continuation must be used exactly once.
    In fact, lenses and CPS form a category with lenses as the initial object and
    CPS as the terminal object. But what lies between them?
  location: LT711 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=YpklMn5yNA0
    linkDescription: Video
- tag: Talk
  date: '2023-03-31T15:00:00Z'
  speaker: Clemens Kupke
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/clemens.kupke/
  insturl: ''
  title: Towards a categorical representation of thin trees
  abstract: Deterministic Automata on infinite trees lack expressivity. The situation
    is different when restricting one’s attention to so-called thin trees where every
    regular language can be seen as the language of a so-called unambiguous automaton.  In
    my talk I will explain our motivation for why we are interested in unambiguous
    tree automata and I will present work in progress that aims to understand thin
    trees more abstractly. This is based on ongoing joint work with Corina Cirstea,
    Jade Master and Alexandre Goy.
  location: LT711 and Online
  material: []
- tag: Talk
  date: '2023-03-24T15:00:00Z'
  speaker: Riu Rodríguez Sakamoto
  institute: ''
  speakerurl: ''
  insturl: ''
  title: From discounted value to discounted state
  abstract: The discounted value is a concept in Reinforcement Learning methods such
    as Value Iteration that allows to aggregate expected future rewards. It can be
    formalized as lens precomposition with a value function (which is a counit). We
    give some progress towards another class of RL methods that are based on parametrized
    policies, where this composition happens without the need of a counit, leading
    to a "discounted state" of a dynamical system. This has some resemblance to a
    List algebra, taken over a bicategory of linear relations of a vector space instead
    of over Set. The discounted state is used in the literature to prove the Policy
    Gradient Theorem, which we interpret as an Euler integration for noncommutative
    operators.
  location: LT711 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=yOze3Vmj9jQ
    linkDescription: Video
- tag: Talk
  date: '2023-03-10T15:00:00Z'
  speaker: Dylan Braithwaite
  institute: MSP
  speakerurl: https://dylanbraithwaite.github.io/
  insturl: ''
  title: String Diagrams for Actegories
  abstract: |-
    Actions of monoidal categories are structures useful for modelling interacting systems. They are central to the definition of optics, but have also found use elsewhere, for example in the semantics of message-passing. When working in categorical cybernetics we often depict monoidal actions using string diagrams with multiple categories juxtaposed, but this steps away from the formally specified semantics of string diagrams for monoidal categories which have coherence and completeness results making their manipulation valid for proving equalities. I will discuss how diagrams for actegories can be modelled more formally by considering them as certain bicategories using the construction of the collage of a bimodule.

     By depicting actegories as bicategories we obtain satisfying visual representations for actegory structures. We will see that the lax compositional structure of the collage gives rise to useful visualisations for the emergent behaviour between categories interacting via the action of a common monoidal category. This gets represented as coloured string diagrams glued together along certain shared boundaries. As a special case we can depict optics as diagrams with several regions which neatly frame the “forward”, “backward”, and “residual passing” stages of their morphisms.
  location: LT711 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=R19L6Z4x7ZU
    linkDescription: Video
- tag: Talk
  date: '2023-03-03T15:00:00Z'
  speaker: Carlos Zapata-Carratalá
  institute: Society for Multidisciplinary and Fundamental Research
  speakerurl: https://czapatacarratala.wixsite.com/home
  insturl: https://semf.org.es/index.html
  title: 'Chemoids: a rewrite approach to general compositionality'
  abstract: In this talk I will motivate and introduce the notion of 'chemoid', a
    compositional structure generalizing many diagram-based formal systems such as
    algebras, categories, operads, tensor networks, etc. I will then present some
    newly found, somewhat exotic, compositional structures that relate to chemical
    and biological computing (hence the name 'chemoid'). I will be using some of the
    functionality that I am currently developing with other colleagues at the Wolfram
    Institute.
  location: LT711 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=6WmuVW8YUqw
    linkDescription: Video
- tag: Talk
  date: '2023-02-24T15:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: 'Type theory vs set theory: whose ordinals are better?'
  abstract: |-
    In constructive set theory, an ordinal is a hereditarily transitive set. In homotopy type theory, an ordinal is a type with a transitive, wellfounded, and extensional binary relation. Which notion is more expressive? We can tackle this question if we first interpret set theory into type theory, using Peter Aczel's sets as trees interpretation (recast in homotopy type theory using higher inductive types), and then compare the notions directly in type theory. With more work, it is possible to generalise the comparison to capture all sets in Aczel's interpretation rather than only the ordinals. This leads to a natural class of ordered structures which contains the type-theoretic ordinals and realises the higher inductive interpretation of set theory.

     This is joint work with Tom de Jong, Nicolai Kraus, and Chuangjie Xu.
  location: LT711 and Online
  material:
  - tag: Link
    address: 'https://arxiv.org/abs/2301.10696 '
    linkDescription: 'Preprint: "Set-Theoretic and Type-Theoretic Ordinals Coincide"'
- tag: Talk
  date: '2023-02-17T15:00:00Z'
  speaker: Neil Ghani
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/neil.ghani/
  insturl: ''
  title: Why Fibrations are your Friend
  abstract: I'll tell you why fibrations should be your friends.
  location: LT711 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=c4xnDZLSEKE
    linkDescription: Video
- tag: CancelledTalk
  date: '2023-02-10T15:00:00Z'
  speaker: Jade Master
  institute: MSP
  speakerurl: https://sites.google.com/view/jadeedenstarmaster/home/
  insturl: ''
  title: TBD
  abstract: TBD
  location: LT711 and Online
  material: []
- tag: Talk
  date: '2023-02-03T15:00:00Z'
  speaker: Jules Hedges
  institute: MSP
  speakerurl: https://julesh.com/
  insturl: ''
  title: Contexts and emergent effects in categorical systems theory
  abstract: One of the most exciting ideas in categorical systems theory is being
    able to give a clean definition to “emergent effects”, namely failure of a lax
    functor to be a functor. But there is a lack of theoretical tools to do useful
    things after identifying this common situation. I will present work in progress
    towards a “theory of contexts”, talking formally about the idea that an open system’s
    behaviour can depend on what other systems are nearby, by isolating 1 of the 3
    key theoretical ingredients of open games. This hopefully allows situations with
    emergent effects to be seen as an ordinary functor, although working out examples
    is irritatingly difficult.
  location: LT711 and Online
  material:
  - tag: PDF
    slideName: 2023-02-03_jules.pdf
- tag: Talk
  date: '2023-01-27T15:00:00Z'
  speaker: Sean Watters
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Sorted Lists and Free Idempotent Commutative Monoids (over strict total orders)
  abstract: |-
    Free monoids are very well-understood and widely used, both on paper and in code. However, their commutative cousins are slightly trickier to pin down a neat data type for. There is a well-established mathematical story involving finite multisets, but they are notoriously tricky to implement sensibly in code.

     Instead, I want to focus on a datatype for sorted lists which turns out to be nearly the same thing if you squint the right way. I'll first demonstrate how we can construct and work with these things, and then the squinting shall begin! We can easily show it to be a commutative monoid, but thinking of it as the free one will require adopting the correct perspective. Specifically, we'll need to work in the land of total orders rather than sets.

     I'm actually interested in finite subsets rather than finite multisets, and that pleasingly only requires adding idempotency to the monoid multiplication, and strictness to the total order. Although, this actually leads to some interesting wrinkles when we try to prove freeness.
  location: LT1310 and Online
  material: []
- tag: Talk
  date: '2023-01-20T15:00:00Z'
  speaker: Matteo Capucci
  institute: MSP
  speakerurl: https://matteocapucci.wordpress.com/
  insturl: ''
  title: On a fibrational construction for optics, lenses, and Dialectica categories
  abstract: Categories of lenses/optics and Dialectica categories are both comprised
    of bidirectional morphisms of basically the same form. In this talk I’m going
    to introduce both and show how they can be considered a special case of an overarching
    fibrational construction, generalizing Hofstra’s construction of Dialectica fibrations.
    At its highest level of generality, it’s a construction that turns a tower of
    fibrations into another tower of fibrations by twisting each of the components
    using the opposite fibration construction.
  location: LT1310 and Online
  material: []
- tag: SpecialEvent
  date: '2023-01-11T15:00:00Z'
  endDate: '2023-01-11T16:00:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: LT1310 and Online
  locationurl: ''
  description: ''
- tag: CancelledTalk
  date: '2022-12-14T11:00:00Z'
  speaker: Neil Ghani
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Why Fibrations are your Friend
  abstract: I'll tell you why fibrations should be your friends.
  location: LT1310 and Online
  material: []
- tag: CancelledTalk
  date: '2022-12-08T14:00:00Z'
  speaker: Sean Watters
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Sorted Lists and Free Commutative Monoids (over total orders)
  abstract: |-
    Free monoids are very well-understood and widely used, both on paper and in code. However, their commutative cousins are slightly trickier to pin down a neat data type for. There is a well-established mathematical story involving finite multisets, but they are notoriously tricky to implement sensibly in code.

     Instead, I want to focus on a datatype for sorted lists which turns out to be nearly the same thing if you squint the right way. I'll first demonstrate how we can construct and work with these things, and then the squinting shall begin! We can easily show it to be a commutative monoid, but thinking of it as the free one will require adopting the correct perspective. Specifically, we'll need to work in the land of total orders rather than sets. In the end, we'll hopefully have a mostly sensible idea of when and how sorted lists can be thought of as the free commutative monoid.
  location: LT1310 and Online
  material: []
- tag: Talk
  date: '2022-11-30T11:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: 'Brouwerian counterexamples: being a know-it-all 101'
  abstract: 'Some statements are not provable, in the sense that they imply falsity
    (for example: "every inhabited subset of real numbers has a least upper bound").  Other
    statements are not provable constructively, even though they are true when using
    classical logic (for example: "every bounded inhabited subset of real numbers
    has a least upper bound"). How can we convince ourselves of this fact, so that
    we do not waste time and effort looking for a constructive proof? We can construct
    a so-called Brouwerian counterexample by showing that the claimed statement implies
    a known non-constructive principle. Brouwer called such principles omniscience
    principles, because only an all-knowing being can hope to for example decide if
    P or not P holds for every proposition P. I will give an introduction to some
    of the more common omniscience principles such as LPO, LLPO and Markov''s Principle,
    and try to give some intuition for when one should expect a statement to not have
    a constructive proof; an important skill in order to avoid heartbreak when working
    in a constructive setting such as type theory or the internal logic of a category. '
  location: LT1310 and Online
  material: []
- tag: Talk
  date: '2022-11-23T11:00:00Z'
  speaker: Matteo Capucci
  institute: MSP
  speakerurl: https://matteocapucci.wordpress.com/
  insturl: ''
  title: " How I stopped worrying and learned to love triple categories (of cybernetic
    systems)"
  abstract: A good chunk of MSP is busy trying to come up with convincing applications
    of category theory in 'cybernetics', which is an umbrella term for game theory,
    learning theory, control theory, and more. I'm busy trying to understand what
    all these people (including me) are doing. What do the systems we are interested
    in have in common? What does it mean to say game theory and gradient-based learning
    look alike? How do we study the behaviour of cybernetic systems? Inspired by Myers'
    categorical system theory I formulated some tentative answers to these questions.
    Alas, they require the full breadth of spatial dimensions this universe provides.
    In this talk I will quickly introduce the ideas behind my version of 'categorical
    cybernetic system theory', including recent developments regarding the definition
    of a theory of cybernetic systems. The hope is that conceptual motivation will
    defuse some fear in the higher structures involved.
  location: LT1310 and Online
  material: []
- tag: SpecialEvent
  date: '2022-11-16T09:30:00Z'
  endDate: '2022-11-16T16:00:00Z'
  title: Agda Implementors' Meeting XXXI
  url: https://wiki.portal.chalmers.se/agda/Main/AIMXXXI
  location: University of Edinburgh
  locationurl: ''
  description: ''
- tag: Talk
  date: '2022-11-09T11:00:00Z'
  speaker: Ezra Schoen
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Hylomorphism complexity
  abstract: Algebra and coalgebra morphisms are well-known and widely applied. They
    have a more niche cousin in coalgebra-to-algebra morphisms, also known as hylomorphisms.
    These are occasionally used to formalize divide-and-conquer algorithms. They can
    also be used in defining semantics for coalgebraic logics, as well as solving
    certain sets of recursive equations. Taking the perspective of 'solving recursive
    equations', it is natural to ask for the computational complexity of deciding
    the existence of solutions. This turns out to depend essentially on the type functor
    for the (co)algebras. In this talk, I will give a simple classification of (polynomial)
    functors by the complexity of their corresponding decision problem. On the way,
    we will take in a few different intuitions towards (co)algebras and hylomorphisms.
  location: LT1310 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=LiClSD0k-7A
    linkDescription: Video
- tag: Talk
  date: '2022-11-02T11:00:00Z'
  speaker: Radu Mardare
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/r.mardare/
  insturl: ''
  title: Fixed points and recursion in quantitative reasoning
  abstract: This talk summarizes a series of results regarding the extension of quantitative
    algebraic reasoning with fixed points and recursion. The work extends the quantitative
    algebras (which are universal algebras on metric spaces) with syntactic constructs
    that allow us to encode Banach fixed points on complete metric spaces. In effect,
    one gets (a generalization of) a Conway and an iteration theory. I will demonstrate
    that most of the results known about classic iteration theories on ordered structures
    remain true in the metric context. And, in fact, that the metric settings generalize
    the results for ordered structures.
  location: LT1310 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=V8T4HGG1NrE
    linkDescription: Video
- tag: SpecialEvent
  date: '2022-10-26T12:00:00Z'
  endDate: '2022-10-26T17:00:00Z'
  title: SPLS
  url: https://spls-series.github.io/meetings/2022/october/
  location: University of Stirling / Online
  locationurl: ''
  description: ''
- tag: Talk
  date: '2022-10-19T11:00:00Z'
  speaker: Guillaume Allais
  institute: University of St Andrews
  speakerurl: ''
  insturl: ''
  title: Tools of the Dependently Typed Compiler Trade
  abstract: Vélo is a tiny language to explore the implementation of compilers for
    functional languages in a dependently typed host. I will highlight some of the
    design choices striking a balance between enforcing invariants, getting work done,
    and compiling to relatively efficient code. Features include support for well-scoped
    typed holes, constant folding, and common sub-expression elimination.
  location: LT1310 and Online
  material: []
- tag: CancelledTalk
  date: '2022-10-12T11:00:00Z'
  speaker: Ezra Schoen
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Hylomorphism complexity
  abstract: Algebra and coalgebra morphisms are well-known and widely applied. They
    have a more niche cousin in coalgebra-to-algebra morphisms, also known as hylomorphisms.
    These are occasionally used to formalize divide-and-conquer algorithms. They can
    also be used in defining semantics for coalgebraic logics, as well as solving
    certain sets of recursive equations. Taking the perspective of 'solving recursive
    equations', it is natural to ask for the computational complexity of deciding
    the existence of solutions. This turns out to depend essentially on the type functor
    for the (co)algebras. In this talk, I will give a simple classification of (polynomial)
    functors by the complexity of their corresponding decision problem. On the way,
    we will take in a few different intuitions towards (co)algebras and hylomorphisms.
  location: LT1310 and Online
  material: []
- tag: Talk
  date: '2022-10-05T11:00:00Z'
  speaker: Jacques Carette
  institute: McMaster University
  speakerurl: https://www.cas.mcmaster.ca/~carette/
  insturl: ''
  title: A guided tour through my work
  abstract: |-
    I will attempt to do something that's generally ill-advised: give a shallow talk with many components without diving in to any part too deeply. Why? The wrong reason to give such a talk is to impress people with all you're doing. A potentially viable reason is to cover that work which might be of interest to the audience, cause discussion and, hopefully, collaboration.

     I was tempted to call this a "meander through my work", but that really would be ill-advised. There are patterns to the madness, and indeed the tour will be organized around those patterns.
  location: LT1310 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=-m2PKhW4_bs
    linkDescription: Video
- tag: Talk
  date: '2022-09-28T11:00:00Z'
  speaker: Jérémy Ledent
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/jeremy.ledent/
  insturl: ''
  title: 'The Topology of Knowledge: Simplicial Models for Epistemic Logic'
  abstract: Multi-agent Epistemic Logic is a modal logic of knowledge. It allows to
    reason about a finite set of agents who may know facts about the world, and about
    each other. In this talk, I will present a new semantics for epistemic logic,
    based on simplicial complexes. In this approach, the knowledge of the agents is
    modeled by a higher-dimensional space called a simplicial model; and the truth
    of an epistemic logic formula can be evaluated by inspecting the various possible
    paths in this space. I will illustrate these ideas using examples from the theory
    of distributed computing, where the agents correspond to individual processes
    who can exchange information in order to solve a task. Both topological invariants
    and logical invariants can be leveraged to prove that some distributed computing
    tasks are impossible to solve.
  location: LT1310 and Online
  material: []
- tag: Talk
  date: '2022-09-21T11:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Citizens and Subjects
  abstract: I'll explore a distinction which emerges from my reimagining of type systems
    in terms of client-server interaction. A typing rule is a server for its conclusion
    and a client for its premises. Every signal in a typing interaction has a sender,
    transmitting the signal as a syntactic object, but also a guarantor, promising
    that the signal is in some way meaningful. We are thus in a position to distinguish
    "citizens" (signals whose guarantor is their sender) from "subjects" (signals
    whose guarantor is their receiver). The two can and should be treated rather differently.
    Citizens should be free from the relitigation of their status and judged according
    to their semantics. Subjects should be investigated syntactically in order to
    establish their status. Like caterpillars and butterflies, every subject should
    aspire to citizenship, but when they achieve it, they will not be who they were.
  location: LT1310 and Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=EezkKDY1DEU
    linkDescription: Video
- tag: Talk
  date: '2022-06-30T14:00:00Z'
  speaker: Bruno Gavranović
  institute: MSP
  speakerurl: https://www.brunogavranovic.com/
  insturl: ''
  title: Can we compose Dependent Lenses as Optics?
  abstract: In this talk, I'll use Idris 2 to live code work in progress thoughts
    related to lenses and optics. I'll focus on the relatively unknown fact that,
    even though lenses and optics are denotationally equivalent, operationally they
    have a different composition rule, with a different space-time complexity. In
    the case of optics this composition uses up more space, but less time. While in
    the non-dependent case it is well understood how to take a bidirectional gadget
    and switch between a lens-like and an optic-like composition, in the dependent
    case it not. In this talk, I won't answer the question in the title, but am instead
    hoping to frame it in proper context. I'll do type-directed programming, and at
    points invoke linear types, hoping to be guided by the compiler in search of an
    answer.
  location: Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=hIKCPJfU3Xo
    linkDescription: Video
- tag: Talk
  date: '2022-06-16T14:00:00Z'
  speaker: Jules Hedges
  institute: MSP
  speakerurl: https://julesh.com/
  insturl: ''
  title: A unified visual language for games
  abstract: |-
    The starting point of this talk is the observation that string diagrams for open games have more in common with extensive form trees than first appears. I will introduce a 3-dimensional syntax that has usual string diagrams and extensive form as 2 orthogonal projections. But first, we need to talk about parallel universes…

     This talk summarises a paper I’ve had brewing for a couple of years and want to actually write soon, that clarifies and expands on a tweet I wrote in October 2019. It is the secret thread connecting a couple of bits of my research in that time: dependent optics (joint work with half of MSP) and sheet diagrams (joint work with Antonin Delpeuch and Cole Comfort). In short: We define a bimonoidal category of dependent open games with tensor product and external choice, and then equip it with the natural 3d syntax for bimonoidal categories.
  location: Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=FojQsyDR5no
    linkDescription: Video
- tag: Talk
  date: '2022-06-09T14:00:00Z'
  speaker: Ezra Schoen
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Filtrations in modal logic
  abstract: |-
    Filtration is a common technique in modal logic. The central idea is to consider a (large or even infinite) model M satisfying a property P of interest. By identifying states in a controlled way, one may (greatly) reduce the size of the M — in fact, one has an upper bound depending only on P. Filtration for basic modal logic is quite straightforward, but may be more difficult for extensions, particularly those involving fixpoint operators. PDL (propositional dynamic logic) is a much-studied such extension of modal logic, used for reasoning about properties of programs.

     I will introduce filtration for basic modal logic, and prove preservation of the desired properties. I will do the same for PDL, highlighting the difficulty introduced by the fixpoint operator.

     If there is enough time and interest, I will also discuss filtrations for monotone PDL, which is PDL interpreted on a more general class of models (namely monotone neighborhood models).
  location: Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=a5yQMd1IrDc
    linkDescription: Video
- tag: Talk
  date: '2022-05-26T14:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: Constructive Ordinal Theory in Homotopy Type Theory
  abstract: |-
    Many constructions proceed in stages: we give a base case, a step case showing how to go from stage n to stage n+1, and then the desired result is achieved in the limit. In more complicated situations, we have to go beyond stages indexed by natural numbers to stages indexed by larger structures — ordinals, a cornerstone of modern mathematics. These are well understood classically, but less so in a constructive setting, where different equivalent classical notions split apart, with different advantages and disadvantages for each. I will show how a theory of different ordinals can be developed constructively in the setting of homotopy type theory, and how modern type-theoretic features such as higher inductive types and inductive-inductive definitions can be used to construct ordinal notation systems that truly behave like ordinals, with extensional and wellfounded order relations.

     Joint work with Nicolai Kraus and Chuangjie Xu.
  location: Online
  material: []
- tag: Talk
  date: '2022-05-19T13:00:00Z'
  speaker: Jade Master
  institute: MSP
  speakerurl: https://sites.google.com/view/jadeedenstarmaster/home/
  insturl: ''
  title: How to Compose Shortest Paths
  abstract: The magic of the min-plus semiring allows one to express the shortest
    path problem as an exponential. A weighted graph is represented by a matrix M
    whose shortest paths are found as F(M) = Sum_{n >=0} M^n. Weighted graphs may
    be joined along a common boundary via pushout and the composition problem for
    F asks how the values of F on a pushout may be obtained from the values of F on
    its components. In this talk I will show how this abstract nonsense may be turned
    into an actual algorithm which computes shortest paths compositionally. Optimistically,
    this algorithm and the relevant results may be adapted to the more general setting
    of the algebraic path problem.
  location: Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=nR3k-C25bjk
    linkDescription: Video
- tag: Talk
  date: '2022-05-12T13:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Everybody Used To Be Somewhere
  abstract: |-
    I will report work in progress on my marking-disrupted incomplete formalisation of the action of relevant substitutions on relevant terms, indexed over their variable support. A relevant term uses every variable in its support at least once; a relevant substitution uses every variable in its target support in the image of at least one variable in its source support; relevant substitutions thus map terms relevant in their source support to terms relevant in their target support.

     The "codeBruijn" machinery that makes my treatment of relevant terms work is based on the semisimplicial category: its objects are variable supports and its hom-sets are binomial coefficients seen as types of bit vectors representing selections. There are deep connections between the structure exhibited by this category and the Good Old Boolean Logic of the bits in the vectors. Meanwhile, relevant substitutions themselves constitute the morphisms of a category whose objects are also variable supports. What keeps the roof up is the double category whose squares tell you what happens to the target scope of a relevant substitution when you select some particular variables from its source.
  location: Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=_CGOpwXhe3w
    linkDescription: Video
- tag: Talk
  date: '2022-05-05T14:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org/
  insturl: ''
  title: Some more constructions on containers
  abstract: The category of containers (~ polynomials) contains a wealth of structure
    for building structures representing question / answer type patterns. I'll discuss
    these and a few more that I think are novel. I'll try to relate them to ideas
    about data accessors like prisms and traversals.
  location: Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=19GlxEjoi70
    linkDescription: Video
- tag: Talk
  date: '2022-04-28T14:00:00Z'
  speaker: Matteo Capucci
  institute: MSP
  speakerurl: https://matteocapucci.wordpress.com/
  insturl: ''
  title: Strategic games as cybernetic systems
  abstract: This talk I will show how to correct a conceptual shortcoming in open
    games by showing how Nash equilibria can be described locally, internally and
    dynamically instead of relying on external devices. Doing so homogenizes compositional
    game theory with the general yoga of categorical cybernetics. In order to do so,
    we show how feedback in cybernetic systems is handled in a more structured way
    than previously considered, which abstracts the formal properties of backpropagation
    of gradients and gradient descent.
  location: Online
  material:
  - tag: PDF
    slideName: 2022-04-28_matteo.pdf
  - tag: Link
    address: https://www.youtube.com/watch?v=mPd0ZfoczK8
    linkDescription: Video
- tag: Talk
  date: '2022-04-21T14:00:00Z'
  speaker: Dylan McDermott
  institute: ICE-TCS, Reykjavik University
  speakerurl: https://dylanm.org/
  insturl: http://icetcs.ru.is/
  title: Flexible presentations of graded monads
  abstract: |-
    Graded monads are a generalization of monads that are used, for example, to track quantitative information in models of effects. There is an existing notion of presentation (by operations and equations) for graded monads, which has the problem that many examples of interest fail to admit natural presentations. I will talk about a more general notion of presentation for graded monads, which resolves this problem by permitting more flexible forms of operation and equation. Every such presentation induces a canonical graded monad equipped with interpretations of these operations. As part of this work, we reformulate graded monads and related concepts in terms of locally graded categories, which provide a useful setting for working with grading.

     This is joint work with Shin-ya Katsumata, Tarmo Uustalu and Nicolas Wu.
  location: Online
  material:
  - tag: PDF
    slideName: 2022-04-21_dylan.pdf
  - tag: Link
    address: https://www.youtube.com/watch?v=SzjG9OPUvnM
    linkDescription: Video
- tag: SpecialEvent
  date: '2022-04-14T14:00:00Z'
  endDate: '2022-04-14T15:00:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: Online
  locationurl: ''
  description: ''
- tag: Talk
  date: '2022-04-07T14:00:00Z'
  speaker: William Waites
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/william.waites/
  insturl: ''
  title: Beyond Epidemics (ACT version)
  abstract: I’ll speak about some of the material from a short talk I recently gave
    at the “Insights from the RAMP project” and will point out where I see some connections
    to category theory (mainly lens-like objects, but also some graph rewriting) where
    some useful applications might be found. This will be a very informal talk; expect
    digressions and no small amount of hand-waving.
  location: Online
  material: []
- tag: Talk
  date: '2022-03-31T14:00:00Z'
  speaker: Yehuda "John" Levy
  institute: University of Glasgow, Adam Smith Business School
  speakerurl: http://www.levygametheory.com
  insturl: https://www.gla.ac.uk/schools/business/
  title: 'Game Theory & Semi-Algebraic Geometry: A Symbiotic Relationship'
  abstract: This talk will present some of the main results from the long and symbiotic
    history between game theory and semi-algebraic (s.a.) geometry. On the one hand,
    tools from s.a. geometry have been used to characterize sets of Nash equilibria,
    study stability properties of equilibria, and have had applications to equilibrium
    selection and stochastic games, among others. On the other hand, a series of results
    developed in particular in the past decade have shown that Nash equilibria are,
    in certain senses, universal for s.a. sets, and that the Nash equilibrium correspondence
    contains, in a certain sense, all s.a. functions as well as some classes of correspondences.
    Relations to some problems concerning complexity of finding Nash equilibria will
    be mentioned. No prior knowledge of semi-algebraic geometry is assumed.
  location: Online
  material:
  - tag: PDF
    slideName: 2022-03-31_yehuda.pdf
  - tag: Link
    address: https://www.youtube.com/watch?v=dLYITjU9QBQ
    linkDescription: Video
- tag: CancelledTalk
  date: '2022-03-24T14:00:00Z'
  speaker: William Waites
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/william.waites/
  insturl: ''
  title: Composite Models and the Need to go Beyond just Modelling Epidemics to Understand
    Epidemics
  abstract: TBA
  location: Online
  material: []
- tag: Talk
  date: '2022-03-17T14:00:00Z'
  speaker: Andre Videla
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Practical dependent lenses for backend architecture
  abstract: |2-
     Backend architecture is hard, requirements change, databases migrate, authentication systems evolve, but our strategy to tackle those problems have remained the same: Employ humans to perform all the necessary changes in the code, until the next product needs to ship.

     To help with this, I will show how we can leverage dependent lenses and different lens composition operators in order to represent common operations on servers, including managing server resources, updating endpoints and their routing, and even swapping in and out middleware as necessary, without affecting the operation of the server, and preserving its typing.
  location: Online
  material:
  - tag: PDF
    slideName: 2022-03-18_andre.png
- tag: SpecialEvent
  date: '2022-03-09T11:00:00Z'
  endDate: '2022-03-09T17:00:00Z'
  title: SPLS
  url: https://spls-series.github.io/meetings/2022/march/
  location: University of Edinburgh / Online
  locationurl: ''
  description: ''
- tag: Talk
  date: '2022-03-03T14:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: On the differential structure of containers
  abstract: 'About twenty years ago, Conor noticed a curious connection between rules
    for computing the type of `one-hole contexts'' for algebraic data types, and Leibniz''s
    calculus differentiation rules: they are exactly the same! Together with Neil
    and Conor, I''ve had some fun recently trying to put this result in Blute, Cockett
    and Seely''s categorical framework of differentiation, by constructing a so-called
    Cartesian differential category of containers. Of course, I will explain what
    these are during the talk.'
  location: Online
  material: []
- tag: Talk
  date: '2022-02-24T14:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org/
  insturl: ''
  title: An introduction to Non-idempotent Intersection Types
  abstract: |-
    Are types for telling us what to program, or for telling us what we have programed? MSP dogma leans to the former, but it is worth looking at the latter too.

     If we take types to be explanations of programs' behaviour, then it is only natural that they can have multiple types, since programs may have multiple behaviours. Intersection types are the basic tool that allows the assignment of multiple behavioural descriptions to a single program.

     Traditional intersection types are idempotent: if we know that a term has some behaviour, then it is of no interest to know this twice. Inspired by linear logic, however, we can start to wonder what happens if we record how many times we will need a program to have some behaviour -- non-idempotent intersection types.

     When we start counting behaviours, something remarkable happens. In a result due to Daniel de Carvalho, it turns out that the size of the typing derivation is equal to the number of steps taken to evaluate the program in the Krivine Abstract Machine.

     I'll describe the non-idempotent intersection type system for a CBN untyped lambda-calculus, and how to prove de Carvalho's result. If here is time, I'll also discuss how non-idempotent intersection types relate to the relational semantics of Linear Logic.

     An Agda formalisation of de Carvalho's result is written up here: <a href='https://bentnib.org/posts/2020-08-13-non-idempotent-intersection-types.html'>https://bentnib.org/posts/2020-08-13-non-idempotent-intersection-types.html</a>
  location: Online
  material:
  - tag: PDF
    slideName: 2022-02-24_bob.pdf
  - tag: Link
    address: https://www.youtube.com/watch?v=ks5AIMNwNAE
    linkDescription: Video
- tag: Talk
  date: '2022-02-17T14:00:00Z'
  speaker: Bruno Gavranović
  institute: MSP
  speakerurl: https://www.brunogavranovic.com/
  insturl: ''
  title: Operational view on Optics
  abstract: " Optics, lenses, prisms, and similar abstract gadgets are our best friends
    when it comes to modelling bidirectional processes. While optics are more general
    than lenses, it's understood that they're equivalent in the special setting of
    a cartesian monoidal category. Fixing the setting of a cartesian monoidal category,
    in this talk I'll explore how this equivalence is denotational in nature, and
    the result of erasure of important operational data. I'll advocate that the operational
    aspect is not optional, but rather crucial in understanding what these systems
    are doing."
  location: Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=BNHVySBzR3M
    linkDescription: Video
  - tag: Link
    address: https://www.brunogavranovic.com/posts/2022-02-10-optics-vs-lenses-operationally.html
    linkDescription: Blog Post
- tag: Talk
  date: '2022-02-10T14:00:00Z'
  speaker: Jérémy Ledent
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/jeremy.ledent/
  insturl: ''
  title: An informal introduction to Game Semantics
  abstract: |-
    Denotational semantics specifies the meaning of a computer program by associating it with an abstract mathematical object (its <em>denotation</em>), which represents its behaviour. In the case of game semantics, a program is interpreted as a two-player game, played between the program and its environment. More precisely, types are modelled by arenas (on which the game is played), while the programs themselves are modelled by strategies played on those arenas. Game semantics originated in the 1990's to solve the full abstraction problem for PCF (i.e., λ-calculus with a fixpoint operator); but the framework is very flexible, and many variants have been proposed to describe control, state, probability, concurrency, and many other program constructs.

     In this talk, I will start with a (very) brief introduction to denotational semantics in general, and define the concept of full abstraction. Then, I will present the game semantics model for PCF (à la Hyland-Ong), and if time allows, show how to extend it to model mutable references. I aim to keep the presentation intuitive and informal, relying mostly on examples and pictures.
  location: Online
  material:
  - tag: PDF
    slideName: 2022-02-10_jeremy.pdf
- tag: Talk
  date: '2022-02-03T14:00:00Z'
  speaker: Daniele Palombi
  institute: Sapienza University of Rome
  speakerurl: https://dpl0a.github.io/
  insturl: ''
  title: An introduction to Synthetic Guarded Domain Theory
  abstract: Synthetic Guarded Domain Theory (SGDT) arose as a generalization of step-indexing
    and guarded recursion in ultrametric spaces. While clearly taking inspiration
    from Synthetic Domain Theory, a geometric account of the field is still missing.
    This talk will serve as an introduction to SGDT sprinkled with remarks about the
    very geometric flavor of relevant properties of its known topos-theoretic models.
  location: Online
  material:
  - tag: PDF
    slideName: 2022-02-03_daniele.pdf
- tag: Talk
  date: '2022-01-27T14:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Ways of Staring at Free Monoidal Categories
  abstract: 'What''s a free monoidal category? Imagine planar circuits connecting
    a sequence of inputs to a sequence of outputs, built from components similarly
    taking a sequence of inputs to a sequence of outputs. They are categorical: you
    can wire the outputs of one circuit to the inputs of another if they match. They
    are monoidal: you can place them in parallel, concatenating input and output sequences.
    They have an equational theory which amounts to allowing arbitrary jiggling around
    in the plane, just as long as you keep everything connected in the same way and
    treat wires and components as deformable but impassable boundaries. Can we decide
    this equational theory? Yes, in principle, but how might we do it in practice?
    What would it take to give unique normal forms for such circuits as inductively
    defined data? Fred, Jules and I were staring at this puzzle one evening, looking
    over a notebook for a clue to plant upon the page, in a pub not so many minutes
    away known for the central stairway up to its mezzanine. We were staring at circuits
    and staring at the stairway, until we began to see the stairways in the circuits.
    And it made us wonder!'
  location: Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=QkMkVg41WeE
    linkDescription: Video
- tag: SpecialEvent
  date: '2022-01-12T16:00:00Z'
  endDate: '2022-01-12T17:00:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: Online
  locationurl: ''
  description: ''
- tag: SpecialEvent
  date: '2021-10-20T11:00:00Z'
  endDate: '2021-10-20T17:00:00Z'
  title: SPLS
  url: https://spls-series.github.io/meetings/2021/october/
  location: Online
  locationurl: ''
  description: ''
- tag: Talk
  date: '2021-12-15T15:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org/
  insturl: ''
  title: Data types with negative information
  abstract: |-
    Inductive data types are a foundational tool for representing data and knowledge in dependently typed programming languages. The user provides a collection of rules that determine positive evidence for membership in the type. Elimination of an inductive type corresponds to structural induction on its members.

     But what if our data modelling requires negative information as well as positive? For example, representing the result of a backtracking parser requires evidence that a certain parsing attempt *didn't* work. Standard formulations of inductive types do not allow negative information mixed with positive.

     Mixing positive and negative information has been studied in logic programming, resulting in concepts like Negation as Failure, stable models, and answer set programming. Incorporating negative information into systems of rules leads us into the realm of non-monotonic logics, where simply adding knowledge does not necessarily preserve existing conclusions.

     In this talk, I'll describe a way to understand data types with negative information in type theory by combining ideas from 3-valued stable models in logic programming and constructive negation (or refutation) from linear logic. The hope is that by adding negation to data types we will be able to represent some reasoning tasks more easily in dependent types.
  location: Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=QvWuZzfbleE
    linkDescription: Video
- tag: Talk
  date: '2021-12-08T15:00:00Z'
  speaker: Clemens Kupke
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/clemens.kupke/
  insturl: ''
  title: Constructing disjunctive formulas in the modal mu-calculus
  abstract: |-
    The modal mu-calculus is a general modal fixpoint logic that allows to reason about the ongoing, possibly infinite behaviour of a transition system. For example, the temporal logics from Sean's 101 talk a few weeks ago can be seen as fragments of the mu-calculus.

     In this talk I am planning to give a brief introduction to the mu-calculus and then focus on a key result about the logic: every formula is equivalent to a so-called disjunctive formula. Constructing a disjunctive formula of "small" size is important e.g. for satisfiability checking. I am going to sketch a construction that yields a disjunctive formula that is single-exponential in the closure size of the input formula. The construction will highlight a few subtleties that arise when thinking about the size of a mu-calculus formula.

     Based on joint work with Johannes Marti and Yde Venema.
  location: Online
  material: []
- tag: Talk
  date: '2021-12-01T15:00:00Z'
  speaker: Georgi Nakov
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: 'When completeness is not enough: introduction to algebraisable logics'
  abstract: |-
    The relation between logic and algebra is often expressed by existence of equational completeness theorems stating that a certain logic L is complete with respect to a certain class of algebras K. Perhaps the most famous example is given by the class of Boolean algebras and classical propositional logic. However, CPC is also complete with respect to the class of Heyting algebras by a negative translation. In order to recover a univocal connection, we need to dig deeper into the theory of algebraisability [1] - an algebraisable logic admits a unique algebraic semantics.

     In this talk we will introduce some notions and basic results from the theory of algebraisable logics. We will further propose an extension to the theory to accommodate for logics with weaker forms of substitutions (e.g. logics of dependence and independence, various epistemic logics).

     This is joint work with Davide Quadrellaro.

     [1] W. J. Blok and D. Pigozzi. Algebraizable logics, <a href='https://bookstore.ams.org/memo-77-396/'>https://bookstore.ams.org/memo-77-396/</a>
  location: Online
  material:
  - tag: PDF
    slideName: 2021-12-01_georgi.pdf
- tag: Talk
  date: '2021-11-24T15:00:00Z'
  speaker: Jonathan Gorard
  institute: University of Cambridge
  speakerurl: https://www.wolframphysics.org/people/jonathan-gorard/
  insturl: https://www.lsc.phy.cam.ac.uk/
  title: Homotopic and Compositional Aspects of (Hyper)graph Rewriting and Fundamental
    Physics
  abstract: |-
    Graph grammars and double-pushout rewriting are pretty old news at this point. But the abstract rewriting systems produced by (hyper)graph grammars actually carry an extremely rich compositional and algebraic structure, many aspects of which have remained woefully under-investigated. We will show how causality relations in non-deterministic hypergraph rewriting systems can effectively be captured by means of a strict monoidal 2-category (a “multiway system”), and how higher homotopy types may consequently be constructed by adjoining appropriate sets of additional rewriting rules, with the n → ∞ limit of the resulting n-fold category yielding an ∞-groupoid (the classifying space of which forms an (∞,1)-topos). We will discuss how this general framework has been applied pragmatically in the design of efficient automated theorem-proving and diagrammatic reasoning software, before concluding with a more speculative discussion of the potential applicability of the overall formalism to the foundations of physics (especially categorical quantum mechanics and discrete quantum gravity).

     This is joint with Xerxes Arsiwalla.
  location: Online
  material:
  - tag: PDF
    slideName: 2021-11-24_jonathan.pdf
  - tag: Link
    address: https://www.youtube.com/watch?v=5SenXV-fQK0
    linkDescription: Video
- tag: Talk
  date: '2021-11-17T15:00:00Z'
  speaker: Matteo Capucci
  institute: MSP
  speakerurl: https://matteocapucci.wordpress.com/
  insturl: ''
  title: Optics in three acts
  abstract: 'Optics can be constructed in at least three different ways: from Tambara
    theory (profunctor encoding), as open diagrams (existential optics) and as free
    ''categories with a counit'' (free teleological categories). Each of these three
    constructions highlights a different point of view on optics, and their interplay
    is an elegant mathematical story and a(n arguably) successful story for abstract
    nonsense. In this <del>play</del> talk, we look at all three constructions and
    contemplate their equivalence.'
  location: Online
  material:
  - tag: PDF
    slideName: 2021-11-17_matteo.pdf
  - tag: Link
    address: https://www.youtube.com/watch?v=KrneXa9gU7o
    linkDescription: Video
- tag: Talk
  date: '2021-11-10T15:00:00Z'
  speaker: Sean Watters
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: A Tour of Temporal Logic
  abstract: "Modal logic can be applied to a diverse range of use-cases by fixing
    different notions of model and modality. Our motivation today will be the formal
    verification technique of model checking, and with this in mind, I will focus
    on temporal logic. In temporal logics, the models represent systems which change
    over time, and the modalities allow us to reason about exactly how they proceed
    in time.\n\n I will first introduce basic relational modal logic, and show its
    limitations in this domain. We will then go on a tour of LTL, CTL, CTL*, and the
    modal \U0001D707-calculus. Key destinations on the tour will include the respective
    expressive power and model-checking complexity of each, particularly in comparison
    to the \U0001D707-calculus. <del>I will end the tour with a closer look at the
    model-checking problem of the \U0001D707-calculus, and its relationship to parity
    games.</del>"
  location: Online
  material:
  - tag: File
    path: 2021-11-10_sean/scribbles.png
    fileDescription: Scribbles
  - tag: PDF
    slideName: 2021-11-10_sean.pdf
  - tag: Link
    address: https://www.youtube.com/watch?v=74tM1l7sAuA
    linkDescription: Video
- tag: Talk
  date: '2021-11-03T15:00:00Z'
  speaker: Dylan Braithwaite
  institute: MSP
  speakerurl: https://dylanbraithwaite.github.io/
  insturl: ''
  title: An Introduction to Finite Model Theory
  abstract: Model theory in classical logic provides a number of tools useful for
    classifying structures described by sets of axioms. In computer science we are
    often interested in cases where these structures are finite, but many results
    in classical model theory fail to specialise to cases where we require all models
    to be finite. In this talk I will give an introduction to some of the alternative
    techniques used for studying expressibility of finite models and discuss some
    interesting connections with complexity theory.
  location: Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=3FyTV_hYfA4
    linkDescription: Video
- tag: CancelledTalk
  date: '2021-10-27T15:00:00Z'
  speaker: Malin Altenmüller
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: TBA
  abstract: TBA
  location: Online
  material: []
- tag: Talk
  date: '2021-10-27T15:00:00Z'
  speaker: Riu Rodríguez Sakamoto
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Categories for persistent homology
  abstract: 'Data analysis has dealt traditionally with regression, clustering and
    dimensionality reduction. Persistent homology, a tool in Topological Data Analysis,
    can be thought of as the counterpart of clustering: Instead of looking at clusters
    of data, it classifies holes of data. And we mean `holes'' in the most visual
    way: given some point cloud in a metric space, it addresses how do we characterize
    regions of the space where there''s no data. This talk will introduce persistence
    modules, which are a central concept of the theory. We will overview their construction
    from data, how we can compare between, and stability properties.'
  location: Online
  material:
  - tag: PDF
    slideName: 2021-10-27_riu.pdf
  - tag: Link
    address: https://www.youtube.com/watch?v=KtYiZW9DQf8
    linkDescription: Video
- tag: Talk
  date: '2021-10-13T15:00:00Z'
  speaker: Toby Smithe
  institute: Topos Institute and University of Oxford
  speakerurl: https://tsmithe.net/
  insturl: https://topos.institute/
  title: The changing shapes of cybercats
  abstract: 'The ménagerie of categorical models of dynamical systems is becoming
    a veritable zoo, but what makes all these animals tick? In this talk, I will introduce
    a new specimen: a symmetric monoidal category of continuous-time open Markov processes
    with general state spaces. I will explain how this category is obtained from a
    category of ``continuous-time coalgebras'''' opindexed by polynomials, and describe
    how this recipe also gives categories of nondeterministic systems in arbitrary
    (continuous) time. These new specimens are motivated by the cybernetic question
    of how to model systems that are continuously performing approximate Bayesian
    inference. I will therefore sketch why their better-known cousins weren''t quite
    up to the job, and show that our new SMC admits Bayesian inversion. Finally, I
    will attempt to make contact with the MSP branch of categorical cybernetics, asking
    what makes the shapes of our structures seem so similar-but-different, and how
    we might begin to understand systems nested within systems.'
  location: Online
  material:
  - tag: PDF
    slideName: 2021-10-13_toby.pdf
  - tag: Link
    address: https://www.youtube.com/watch?v=RQEtz1i29Dg
    linkDescription: Video
- tag: Talk
  date: '2021-10-06T15:00:00Z'
  speaker: Jules Hedges
  institute: MSP
  speakerurl: https://julesh.com/
  insturl: ''
  title: A very abridged introduction to open games
  abstract: Open games allow you to talk about some amount of game theory (and thus,
    some amount of economics) in terms of a lot of familiar ideas from category theory
    and compositionality. It isn’t possible to introduce open games adequately to
    anyone in this amount of time, but this talk will be the best I can manage in
    the circumstances. I’ll explain approximately how open games work, and how they
    relate to some other interests of MSP.  I’ll also do a quick demo of the open
    game engine, a Haskell implementation that’s robust enough to do some Real Economics
    ™.
  location: Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=4F8wJD8yU_s
    linkDescription: Video
- tag: Talk
  date: '2021-09-29T15:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: 'Dependently typed programming: do you know what you are doing?'
  abstract: |-
    Wouldn't it be nice if you could tell the computer what you mean, so that it could help you catch not only syntax errors, but also semantics errors? Even better, so it could help you and guide you towards the program that you want to write? So that knowing what you are doing could become a responsibility shared between human and machine, instead of being only your problem? Using dependent types, and some care, we can achieve this by encoding the precise meaning of the program in its type -- any implementation will consequently be correct *by construction*. I will give a demonstration of such dependently typed programming, based in part on a nice recent draft functional pearl by Wouter Swierstra: "A correct-by-construction conversion to combinators" [1]. I will not assume that you know much about correct-by-construction programming, or combinatory logic.

     [1] <a href='https://webspace.science.uu.nl/~swier004/publications/2021-jfp-submission-2.pdf'>https://webspace.science.uu.nl/~swier004/publications/2021-jfp-submission-2.pdf</a>
  location: Online
  material:
  - tag: File
    path: 2021-09-29_fred/SK.agda
    fileDescription: Agda file
  - tag: Link
    address: https://www.youtube.com/watch?v=L-RIYtKJNiU
    linkDescription: Video
- tag: Talk
  date: '2021-09-23T15:00:00Z'
  speaker: Jade Master
  institute: MSP
  speakerurl: https://sites.google.com/view/jadeedenstarmaster/home/
  insturl: ''
  title: Building the behavior of graphs compositionally
  abstract: The free category on a graph may be understood as an operational semantics.
    The objects of this free category represent states and the morphisms represent
    possible sequences of events which may occur. How can this operational semantics
    be built from smaller components? We will see how gluing graphs together is the
    composition of category and how the operational semantics of graphs extends to
    a functor on this category. Blackboxing is a process which takes a system and
    focuses only the relationship it induces between its inputs and outputs.  In this
    talk we will explain how blackboxing is almost a functor, and how the categorical
    framework developed so far gives insight into computation.
  location: Online
  material:
  - tag: PDF
    slideName: 2021-09-23_jade.pdf
  - tag: Link
    address: https://www.youtube.com/watch?v=ec6IuXMEU5E
    linkDescription: Video
- tag: Talk
  date: '2021-09-16T15:00:00Z'
  speaker: Ezra Schoen
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Introduction to universal coalgebra
  abstract: The aim of this presentation is to give an overview of various concepts
    within universal coalgebra. We will explore such topics as corecursion, bisimulation
    and coalgebraic (modal) logic. No prior knowledge is required, save for some elementary
    category theory.
  location: Online
  material:
  - tag: PDF
    slideName: 2021-09-16_ezra.pdf
  - tag: Link
    address: https://www.youtube.com/watch?v=2tXgrS-ufPM
    linkDescription: Video
- tag: Talk
  date: '2021-09-09T15:00:00Z'
  speaker: Andre Videla
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: All kinds of types
  abstract: What are types? What types of types exist? Why do we do bother and what
    does this buy us? This introduction to type theory aims to motivate the study
    of type systems and demonstrate their power. No knowledge is required except for
    basic programming concepts, like functions and data structures. Our journey will
    take us from the Set theory slums, through the curry-howard plains, into the type-theory
    ivory tower and end looking at the stars where modal logic and QTT live.
  location: Online
  material: []
- tag: SpecialEvent
  date: '2021-09-02T15:00:00Z'
  endDate: '2021-09-02T16:00:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: Online
  locationurl: ''
  description: ''
- tag: Talk
  date: '2021-07-08T15:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Bite me! (Rational Fixpoints of Containers)
  abstract: |-
    Least fixpoints, often written mu X. Blah(X), give us inductive types (for strictly positive Blah), e.g. finite lists of A given as mu X. 1 + A*X: all the lists of finite length. Greatest fixpoints, often written nu X. Blah(X), give us possibly infinite type (for strictly positive Blah), e.g. finite lists, but also wild infinite lists like [0,1,2,3,...] which never repeat.

     There is no Greek letter between mu and nu. But there is at least one interesting fixpoint between the least and the greatest: things which can loop back on themselves, but not diverge into the wide blue yonder. That is the rational fixpoint.

     What are we to do with it? I don't know but I intend to find out.

     I shall give a deeply unsatisfactory talk on this topic which leaves more questions than answers, for the purpose of infecting people with this problem. There will be at least one solid clue.
  location: Online
  material:
  - tag: File
    path: 2021-07-08_conor/Rat101.hs
    fileDescription: Haskell file
- tag: Talk
  date: '2021-07-01T15:00:00Z'
  speaker: Matteo Capucci
  institute: MSP
  speakerurl: https://matteocapucci.wordpress.com/
  insturl: ''
  title: Translating Extensive Form Games to Open Games with Agency
  abstract: |-
    We show open games cover extensive form games with both perfect and imperfect information. Doing so forces us to address two current weaknesses in open games: the lack of a notion of player and their agency within open games, and the lack of choice operators. Using the former we construct the latter, and these choice operators subsume previous proposed operators for open games, thereby making progress towards a core, canonical and ergonomic calculus of game operators. Collectively these innovations increase the level of compositionality of open games, and demonstrate their expressiveness.

     This is a practice talk for ACT'21.
  location: Online
  material:
  - tag: Link
    address: https://github.com/mattecapu/act21-open-games-with-agency/blob/master/main.pdf
    linkDescription: Slides
- tag: Talk
  date: '2021-07-15T15:00:00Z'
  speaker: Samuel Arsac
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Expressivity of BCI algebras
  abstract: |-
    I will have a look into the expressivity of BCI-algebras, by implementing them in Coq and by looking at them from a categorical point of view. The first step will be to implement the λ* operator as shown in [1], which will allow for the use of linear lambda-calculus. From this point it will be much easier to define useful terms with BCI combinators, and I will use the encoding of booleans in linear lambda-calculus defined in [2] to create a type of duplicable and discardable booleans. In parallel, I will talk about the categorical aspects with the notion of realisability and category of assemblies [1], with the aim of showing that we can obtain a linear-non-linear model.

     [1] <a href='https://www.kurims.kyoto-u.ac.jp/~naophiko/paper/realizability.pdf'>https://www.kurims.kyoto-u.ac.jp/~naophiko/paper/realizability.pdf</a>
     [2] <a href = 'https://www.cs.brandeis.edu/~mairson/Papers/jfp02.pdf'>https://www.cs.brandeis.edu/~mairson/Papers/jfp02.pdf</a>
  location: Online
  material: []
- tag: SpecialEvent
  date: '2021-06-30T11:00:00Z'
  endDate: '2021-06-30T17:00:00Z'
  title: SPLS
  url: https://www.eventbrite.com/e/spls-2021-june-30th-tickets-154107512719
  location: Online
  locationurl: ''
  description: ''
- tag: Talk
  date: '2021-06-24T14:00:00Z'
  speaker: Andre Videla
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Optics for generic declarative server APIs
  abstract: |-
    Martin-Löf type theory has provided us with a new programming paradigm: One where types and terms have shed their differences in order to live harmoniously in the same universe. Despite this successful reunion we have yet to communicate this story to the people building today’s software, for whom it is still a fairy-tale, rather than reality.

     For this, I will demonstrate how to use dependent types for a purpose that is extremely common in commercial software: Web servers. Web servers are a great example because of how ubiquitous they are. Every service, company or product probably has a web server running behind it in some way (if only to serve web pages). Dependent types help the implementation of servers in small and big ways and the experience can be further enhanced by combining it with lenses in order to reach powerful new levels of abstraction.
  location: Online
  material:
  - tag: PDF
    slideName: 2021-06-24_andre.pdf
- tag: Talk
  date: '2021-06-10T14:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org/
  insturl: ''
  title: Real Numbers in Agda
  abstract: |-
    In a constructive logic real numbers are even more interesting than they are in the classical world. To demonstrate the differences, I'll talk about how we can construct a type of real numbers in Agda in terms of the Cauchy completion of the metric space of rational numbers. This yields an implementation of real numbers that is reasonably efficient and that we can do proofs about. The basic construction closely follows Russell O'Connor's "A monadic, functional implementation of real numbers" [1]. I'll also talk about using the completion of a metric space to implement quantitative equational theories over complete separable metric spaces in Agda. I'll try to work from the assumption that the audience knows nothing about metric spaces, completion, or construction of real numbers.

     [1] <a href='https://arxiv.org/abs/cs/0605058'>https://arxiv.org/abs/cs/0605058</a>
  location: Online
  material:
  - tag: PDF
    slideName: 2021-06-10_bob.pdf
- tag: SpecialEvent
  date: '2021-05-27T15:00:00Z'
  endDate: '2021-05-27T16:00:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: Online
  locationurl: ''
  description: ''
- tag: Talk
  date: '2021-06-17T15:00:00Z'
  speaker: William Waites
  institute: LSHTM Centre for the Mathematical Modelling of Infectious Diseases
  speakerurl: https://www.tardis.ed.ac.uk/~wwaites/
  insturl: https://www.lshtm.ac.uk/research/centres/centre-mathematical-modelling-infectious-diseases
  title: Executable Storytelling with Rule-Based Models
  abstract: I will tell a (very simplified) story about how the adaptive immune system
    works through the medium of rules. Rules are compositional creatures that can
    be looked at from the perspective of structured cospans, algebras or double pushout
    graph rewriting systems. I won't belabour the abstract interpretation, rather
    I will concentrate on how they can be used to good effect to both explain (normal
    mode) immune response to a pathogen like SARS-CoV-2 and generate a model that
    can be simulated and reproduces some interesting heterogeneity that is observed
    in the world. Furthermore, compositionality means that this set of rules can be
    freely combined with sets of rules for transmission and diagnostic testing and
    will show this in action. Finally, I’ll speculate about some other kinds of models
    that it might be interesting to incorporate.
  location: Online
  material:
  - tag: PDF
    slideName: 2021-06-17_william.pdf
- tag: Talk
  date: '2021-06-03T15:00:00Z'
  speaker: Georgi Nakov
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: A relationally parametric model of Quantitative Type Theory
  abstract: Polymorphism allows a single function to be instantiated with multiple
    types. It is parametric if all of the instances behave uniformly. Reynolds managed
    to give rigorous formalization of this notion in his abstraction theorem for polymorphic
    lambda calculus. The key insight is that types may also be interpreted as relations.
    In this talk, I will give an overview of relational parametricity and some of
    its consequences, focus on an approach of extending parametricity to dependent
    type theories using reflexive graphs (due to Atkey, Ghani and Johann) and finish
    by presenting a relationally parametric model of Quantitative Type Theory.
  location: Online
  material: []
- tag: Talk
  date: '2021-05-20T15:00:00Z'
  speaker: Chuangjie Xu
  institute: fortiss GmbH
  speakerurl: https://cj-xu.github.io/
  insturl: https://www.fortiss.org/en/
  title: A Generic Framework for Analyzing (Featherweight) Java Programs
  abstract: As a notion to represent disjoint sets of memory locations, regions serve
    as the basis of various techniques for e.g. memory management and pointer analysis.
    They are closely interrelated with effects, and have been illustrated to be useful
    for improving the precision of analysis. We generalize the notion of region to
    represent properties of values, introduce a region type system for Featherweight
    Java (FJ) that is parametrized with a monad-like structure, and prove a uniform
    soundness theorem. Its instances include some type systems studied by Martin Hofmann
    et al. as well as a new one that performs more precise analysis of trace-based
    program properties. Our region type system is separate from the FJ type system,
    making it simpler and also easier to move to larger fragments of Java. The uniform
    framework helps to avoid redundant work on the meta-theory when extending the
    system to cover other language features such as exception handling. This is joint
    work with Ulrich Schöpp.
  location: Online
  material:
  - tag: PDF
    slideName: 2021-05-20_chuangjie.pdf
- tag: Talk
  date: '2021-05-13T15:00:00Z'
  speaker: Jan de Muijnck-Hughes
  institute: Glasgow
  speakerurl: http://jfdm.github.io/
  insturl: https://www.gla.ac.uk/schools/computing/
  title: Formalising the (Sub-)Structural Aspects of SystemVerilog, Again...
  abstract: |-
    Hardware design is commoditised and it might be the case that several components of your design use encrypted bitstreams bought from third-parties. We must have faith that the encrypted bitstreams do what they are supposed to. In the Border Patrol Project  we are interested in being able to reason about the structure & behaviour of designs as a whole, regardless of if we can inspect each module down to the individual gates.

     Following on from my SPLS Nov '20 I want to update everyone on my journey in capturing the physical structure of hardware design using lambda-calculi. Specifically, I will re-introduce System-V, a typed lambda calculus that is based upon the well-known hardware description and verification language SystemVerilog. I will show how a System-V design can capture physical hardware design in the Verilog style, and its type-system enforce correct wiring. I will then show how we can formally look beyond System-V itself (and hardware design by extension) by leveraging known-things from programming-language theory, and posit on where to go from here.
  location: Online
  material: []
- tag: Talk
  date: '2021-05-06T15:00:00Z'
  speaker: Andre Videla
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Categorical semantics of the Simply typed lambda calculus
  abstract: The Simply typed lambda calculus is a tried and true tool for experimentation
    and teaching, today we're going to use it as our guide through an introduction
    to category theory. Category theory without proper motivation or context can be
    a bit puzzling to get into. But using the simply typed lambda calculus as our
    framework we will see what it takes in order to interpret it as a Cartesian Closed
    Category. This walkthough should provide you with the tools to understand Cartesian
    Closed Category as well as some hands-on experience with proving your first results
    in Category theory!
  location: Online
  material:
  - tag: Link
    address: https://youtu.be/1V4_gfy-dsQ
    linkDescription: Video
  - tag: Link
    address: https://gitlab.com/avidelaeko/-/blob/main/src/Section4Correction.idr/
    linkDescription: Source code
  - tag: Link
    address: https://gitlab.com/avidelaeko/-/raw/main/Notes/Category%20theory%20stlc%20reference.jpg/
    linkDescription: Notes
- tag: Talk
  date: '2021-04-29T15:00:00Z'
  speaker: Matteo Capucci
  institute: MSP
  speakerurl: https://matteocapucci.wordpress.com/
  insturl: ''
  title: Games with players
  abstract: The algebra of open games is a compelling language for modelling large
    and medium scale games, with many interacting players. Its most striking features
    are compositionality and an intuitive and expressive graphical calculus. In this
    talk I'll go through some recent developments in this area to sketch a general
    way to build open games, starting from an informal specification, a classical
    game, or a bunch of given other games. The most important novelty is the presence
    of a well-defined and correct notion of player, which was missing until now. The
    guiding principle will be that ‘games and players live in orthogonal planes’,
    as suggested by the graphical language of the para construction.
  location: Online
  material:
  - tag: PDF
    slideName: 2021-04-29_matteo.pdf
- tag: CancelledTalk
  date: '2021-04-22T15:00:00Z'
  speaker: Georgi Nakov
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: A relationally parametric model of Quantitative Type Theory
  abstract: Polymorphism allows a single function to be instantiated with multiple
    types. It is parametric if all of the instances behave uniformly. Reynolds managed
    to give rigorous formalization of this notion in his abstraction theorem for polymorphic
    lambda calculus. The key insight is that types may also be interpreted as relations.
    In this talk, I will give an overview of relational parametricity and some of
    its consequences, focus on an approach of extending parametricity to dependent
    type theories using reflexive graphs (due to Atkey, Ghani and Johann) and finish
    by presenting a relationally parametric model of Quantitative Type Theory.
  location: Online
  material: []
- tag: Talk
  date: '2021-04-01T15:00:00Z'
  speaker: Jules Hedges
  institute: MSP
  speakerurl: https://julesh.com/
  insturl: ''
  title: All about convex sets
  abstract: |-
    This talk is about the algebras of the finite support probability monad on Set. They consist of a set equipped with a “mixture” operator satisfying some axioms, and are variously known as (abstract) convex sets, convex algebras, barycentric algebras, etc. Every actually-convex subset of a real vector space is a convex set, but there are less expected examples too: every join-semilattice can be seen as a convex set, and there are examples that combine aspects of both vector spaces and semilattices.

     I will spend a lot of time on the basic theory and examples, which is mostly due to Marshall Stone. I’ll then transition into talking about work in progress with Paolo Perrone and Sharwin Rezagholi, in which we aim to prove a version of Brouwer’s fixpoint theorem for convex sets. Specifically, we aim to construct a “topological realisation” functor F: Conv -> Top and find sufficient convex properties on X such that F(X) satisfies the fixpoint property for continuous maps. Along the way we prove a classification theorem: every convex set can be decomposed as a family of convex subsets of vector spaces “fibred over” a semilattice (slightly improving a similar unpublished result by Tobias Fritz).
  location: Online
  material: []
- tag: Talk
  date: '2021-03-25T15:00:00Z'
  speaker: Donovan Crichton
  institute: Australian National University
  speakerurl: ''
  insturl: https://cecs.anu.edu.au/research/theory/logic
  title: Type Preserving Crossover Operations for Genetic Programs
  abstract: This talk serves as my formal introduction to the MSP101 Group, and covers
    work from my Bachelor thesis. We will look at how dependent types can be used
    to enable a type-safe crossover operation to allow the generation of program examples
    that are guaranteed to be well typed. We'll also cover alternate approaches I
    could've taken, as well as further work in the area.
  location: Online
  material: []
- tag: Talk
  date: '2021-03-18T15:00:00Z'
  speaker: Clemens Kupke
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/clemens.kupke/
  insturl: ''
  title: Propositional Dynamic Logic(s)
  abstract: I will provide an introduction to dynamic modal logics such as Propositional
    Dynamic Logic (PDL) and Game Logic (GL) and will then describe a (co)algebraic
    framework for these logics. This framework relates program/game constructs of
    these logics to monad structure. The axioms of these logics express compatibility
    requirements between the modal operators and the monad structure.
  location: Online
  material:
  - tag: PDF
    slideName: 2021-03-18_clemens.pdf
- tag: Talk
  date: '2021-03-11T15:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: Quantitative containers
  abstract: |-
    Quantitative Type Theory combines linear types (where we keep track of how many times a variable is used) and dependent types (where terms can appear in types). This gives a logical system which is both expressive and precise with respect to the resource usage of programs and proofs, with a rich model theory. I will talk about work in progress investigating data types in this setting, in the form of "resource-aware" quantitative containers, and their initial algebra semantics.

     This is joint work with Georgi Nakov.
  location: Online
  material:
  - tag: PDF
    slideName: 2021-03-11_fred.pdf
- tag: Talk
  date: '2021-03-04T15:00:00Z'
  speaker: Radu Mardare
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/r.mardare/
  insturl: ''
  title: Quantitative Iteration Theories
  abstract: |-
    We develop a fixed-point extension of quantitative equational logic and give semantics in one-bounded complete quantitative algebras.  Unlike previous related work about fixed-points in metric spaces, we are working with the notion of approximate equality rather than exact equality.  The result is a novel theory of fixed points which can not only provide solutions to the traditional fixed-point equations but we can also define the rate of convergence to the fixed point.  We show that such a theory is the quantitative analogue of a Conway theory and also of an iteration theory; and it reflects the metric coinduction principle.  We study the Bellman equation for a Markov decision process as an illustrative example.

     This is a recent joint work with Gordon Plotkin and Prakash Panangaden.
  location: Online
  material: []
- tag: Talk
  date: '2021-02-25T15:00:00Z'
  speaker: Malin Altenmüller
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Some Thoughts on a Datatype for Higher Genus Graphs
  abstract: Circuit diagrams are commonly modelled by graphs embedded into some oriented
    surface (maps). When the circuit's topology is non-trivial (e.g. for quantum circuits),
    the maps live on higher genus surfaces. I will give an introduction to the relevant
    graph theory and discuss some ideas on how we might be able to program with these
    higher genus structures. Starting from the plane case, a multi-stack approach
    seems promising for approaching these more complex maps. Strategies for modelling
    structures with multiple stacks exist in various different contexts and any of
    your experiences are most welcome in the discussion!
  location: Online
  material:
  - tag: PDF
    slideName: 2021-02-25_malin.pdf
- tag: Talk
  date: '2021-02-18T16:00:00Z'
  speaker: Nicolai Kraus
  institute: University of Nottingham
  speakerurl: https://nicolaikraus.github.io/
  insturl: https://www.nottingham.ac.uk/research/groups/fp-lab/index.aspx
  title: Internal ∞-Categories with Families
  abstract: It is natural to formalise the notion of a model of type theory (especially
    the syntax = intended initial model) inside type theory itself. This is often
    done by writing the definition of a category with families (CwF) as a generalised
    algebraic theory. What could the success criterion from a HoTT point of view be?
    The typical first goal is that the initial model is an h-set or even has decidable
    equality. Our second goal is to make the "standard model" work, i.e. the universe
    U should be a CwF in a straightforward way (cf. Mike Shulman's 2014 question whether
    the n-th universe in HoTT models HoTT with n-1 universes). Unfortunately, it is
    hard to combine these two goals. If we include set-truncatedness explicitly in
    the definition of a CwF, then the "standard model" is not a CwF. If we don't,
    then the initial model is not an h-set. The root of the problem is that 1-categories
    are not well-behaved concepts in an untruncated setting. The natural approach
    are higher categories, which corresponds to "equipping the syntax with all coherences"
    instead of truncating. In this talk, I will explain one approach to this based
    on a type-theoretic formulation of Segal spaces, expressed in HTS/2LTT. I will
    discuss what works and what is still open. The talk will be based on <a href='https://arxiv.org/abs/2009.01883'>arXiv:2009.01883</a>.
  location: Online
  material:
  - tag: PDF
    slideName: 2021-02-18_nicolai.pdf
- tag: Talk
  date: '2021-02-11T15:00:00Z'
  speaker: Bruno Gavranović
  institute: MSP
  speakerurl: https://www.brunogavranovic.com/
  insturl: ''
  title: Categorical Foundation of Gradient-Based Learning
  abstract: I will give an introduction to the categorical foundation of gradient-based
    learning algorithms. I'll define three abstract constructions and show how they
    can be put together to form general neural networks. The Para construction is
    used to compose neural networks while keeping track of their weights. Lenses/Optics
    which are used to take care of the forward-backward data flow and lastly, reverse
    derivative categories are used to functorially construct the backward wires from
    the forward ones. In addition, we'll see that gradient descent, Momentum, and
    a number of optimizers are lenses too, and that this framework includes learning
    on boolean circuits, in addition to standard Euclidean spaces.
  location: Online
  material:
  - tag: Link
    address: https://www.youtube.com/watch?v=ji8MHKlQZ9w
    linkDescription: Video
- tag: Talk
  date: '2021-02-04T15:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org/
  insturl: ''
  title: Reviewing
  abstract: I'll talk about how I go about writing, reading, and responding to reviews.
    Reviews are an essential part of academic publishing, but why do we do them (for
    free!), and why do we care what they say? I discuss how reviews are used by programme
    committees and chairs to decide what papers are selected for conferences (and
    journals), how I think you should go about doing reviews, and why you should write
    reviews. I'll also talk about reading reviews written about your own work, and
    how to go about the author response period effectively.
  location: Online
  material:
  - tag: PDF
    slideName: 2021-02-04_bob.pdf
- tag: Talk
  date: '2021-01-28T15:00:00Z'
  speaker: Jérémy Ledent
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/jeremy.ledent/
  insturl: ''
  title: 'Combinatorics, Topology and Game theory: a proof of Nash''s theorem'
  abstract: 'The aim of this talk is to state and prove Nash''s theorem, which says
    that every finite game with mixed strategies has a Nash equilibrium. The proof
    makes use of two other famous results: Sperner''s lemma, a combinatorial result
    about coloring the vertices of a triangulation, and Brouwer''s fixed-point theorem.
    Thus, my talk will be organised into three largely independent parts: first I
    will sketch the proof of Sperner''s lemma; then I will use Sperner''s lemma to
    prove Brouwer''s theorem; and finally I will use Brouwer''s theorem to prove the
    existence of Nash equilibria.'
  location: Online
  material: []
- tag: Talk
  date: '2021-01-07T13:00:00Z'
  speaker: James Wood
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/james.wood.100/
  insturl: ''
  title: Generic metatheory of linear programming languages
  abstract: I will give an introduction to generic metatheory in the style of Allais,
    Atkey, Chapman, McBride, and McKinna, leading into new work from me and Bob. Generic
    metatheory is about deriving proofs and operations for a whole class of programming
    languages, rather than the usual 1 language. The class we consider combines variable
    binding with usage-sensitivity, and contains many variants of linear natural deduction
    calculi (and, as a special case, intuitionistic and classical calculi). We build
    on <a href='https://arxiv.org/abs/2001.11001'>the framework of Allais et al.</a>
    and our recent use of <a href='https://arxiv.org/abs/2005.02247'>linear algebra
    in linear metatheory</a>.
  location: Online
  material: []
- tag: Talk
  date: '2020-12-17T13:00:00Z'
  speaker: Sam Lindley
  institute: University of Edinburgh
  speakerurl: http://homepages.inf.ed.ac.uk/slindley/
  insturl: http://www.ed.ac.uk/informatics/
  title: Algebraic effects and effect handlers
  abstract: I'll give an introduction to algebraic effects and effect handlers as
    a general approach to programming and reasoning about effectful computation. I'll
    present the notion of a computation over an algebraic effect as a command-response
    tree over an effect signature quotiented by some equational theory. I'll consider
    how to interpret command-response trees and motivate effect handlers as the reification
    of such interpretations as an object language feature that provides a generic
    implementation strategy for algebraic effects. I'll give examples to show that
    it can be useful to interpret the same command-response tree using different interpretations
    which may not respect the same equational theory. Thus effect handlers can provide
    an expressive programming feature independently of any non-trivial algebraic theory.
  location: Online
  material:
  - tag: PDF
    slideName: 2020-12-17_sam.pdf
- tag: Talk
  date: '2020-12-10T13:00:00Z'
  speaker: Uma Zalakain
  institute: University of Glasgow
  speakerurl: https://umazalakain.info/
  insturl: http://www.dcs.gla.ac.uk/research/formalmethods/
  title: Session Types
  abstract: This talk is a brief introduction to session types, a type formalism for
    structured communication between concurrent programs. Instead of typing programs,
    we will session type channel endpoints, to then ensure that the programs that
    make use of these endpoints do so in a principled manner, according to their session
    types. I will go over some of the key ideas that enable session-typed programming,
    and comment on the properties that session-typed programs exhibit. As an example,
    I will introduce (and comment on the oddities of) a type system that uses session
    types to type the pi calculus. I will close mentioning some of the extensions
    to session types and more advanced type systems.
  location: Online
  material: []
- tag: Talk
  date: '2020-12-03T13:00:00Z'
  speaker: Radu Mardare
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/r.mardare/
  insturl: ''
  title: Metrics in probabilistic context
  abstract: |-
    This talk will (probably) be a tutorial on how metrics meet probability theory and how this provides us with the context for innovative paradigms in computer science. The novel challenges that machine learning, cyber-physical systems and statistical computational methods rise to computer science require a fundamental change of the semantics of computation. While in the past we were happy to know whether two programs/algorithms/machines behave the same or not, today it is obvious that this is not enough for our purposes. We need, more and more, to be able to reason about and measure the similarity of non-identical computational behaviours. Moreover, we need to speak about randomness in computational phenomena, especially when we formalize learning or behaviours in unknown contexts. Last but not least, we need to eventually replace the classic metatheory of computation with a probabilistically-based one, where questions can be answered probabilistically within controlled confidence boundaries.

     I will not have the time to approach all these during the talk, but I will try to give an overview of the mathematical instruments one needs to approach such a complex challenge.
  location: Online
  material:
  - tag: PDF
    slideName: 2020-12-03_radu.pdf
- tag: Talk
  date: '2020-11-26T13:00:00Z'
  speaker: Glynn Winskel
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Event Structures and Games
  abstract: 'I’ll introduce event structures, a model of computation in which behaviour
    is captured through partial orders of causal dependency between events.  As an
    application I''ll show their role in a theory of concurrent/distributed games
    and strategies, which has been useful in the semantics of computation, also for
    probabilistic and quantum programs.  Though originally motivated by the limitations
    of traditional semantics, through determinacy and value theorems, and the preservation
    of winning/optimal strategies under composition, a form of structural game theory
    is emerging.  In this talk I''ll concentrate on what I see as connection points
    with work here at Strathclyde: as a lead in, relations with the stable domain
    theory of Berry and Girard; then, the view of strategies as profunctors, whence
    how they connect to the traditional domain theory of Scott; concluding with how
    distributed strategies support certain dialectica categories and lenses, and through
    them open games.  My hope is that these connections will be fruitful.  On the
    one side, distributed games can offer a rich metalanguage which extends to probabilistic
    and quantum computation.'
  location: Online
  material:
  - tag: PDF
    slideName: 2020-11-26_glynn.pdf
- tag: Talk
  date: '2020-11-19T13:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: Containers
  abstract: |-
    How do we represent and reason about data types, in general? The theory of containers is one answer, which is locally quite popular in the MSP group (and beyond). A container is given by a collection of shapes, and for each shape, a collection of positions, where one is meant to plug in data. Containers can be used to analyse generic constructions on data types, without resorting to a messy induction over syntax.

     Each container induces a functor from Set to Set, which maps an "element type" X to the set of containers with data drawn from X. Furthermore, there is a natural notion of morphism of containers, with the remarkable property that it completely captures the natural transformations between the functors the containers represent: the interpretation functor from containers to the functor category from Set to Set is full and faithful. In general, the category of containers is extremely nice, eg containers are closed under almost all operations you can imagine (composition, products, coproducts, exponentials, initial algebras, final coalgebras, ...). I hope to give an introductory talk that will make the above more precise.
  location: Online
  material:
  - tag: PDF
    slideName: 2020-11-19_fred.pdf
- tag: Talk
  date: '2020-11-12T13:00:00Z'
  speaker: Jules Hedges
  institute: MSP
  speakerurl: https://julesh.com/
  insturl: ''
  title: Lenses 101
  abstract: I’ll talk about the zoo of closely-related structures (with a lot of clashing
    terminology) known as “lenses” and “optics”. Lenses and optics are a way of managing
    inherently state-heavy applications (for example videogames) in purely functional
    languages, which turn out to have a lot of surprisingly deep category theory behind
    them. I will also talk about some of the places where lenses have recently appeared
    far outside their original domain, for example in game theory, machine learning
    and systems theory.
  location: Online
  material: []
- tag: Talk
  date: '2020-11-05T13:00:00Z'
  speaker: Eigil Rischel
  institute: MSP
  speakerurl: https://erischel.com/
  insturl: ''
  title: Probability theory with string diagrams
  abstract: |-
    Going back to Lawvere, people have tried to study probability theory in terms of monads - the idea being that for each "space" of some type, X, there should be a space PX of probability distributions on X, with point-distributions and integration of distributions giving the monad structure. The Kleisli category of this monad is of particular interest: it corresponds to "stochastic maps" between spaces.

     It turns out that one can actually often do without the monad - the Kleisli category itself carries enough structure that one can do probability theory "internally", rederiving the notions of determinism, independence of measures, and many others. I will present this picture of probability, and give some examples of results that can be proven in this framework.
  location: Online
  material: []
- tag: Talk
  date: '2020-10-29T13:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org/
  insturl: ''
  title: Realisability
  abstract: Sometimes, we think of the category of sets and functions as a simple
    model of programs in a functional programming language. But sets and functions
    are much too expressive -- there are plenty of set theoretic functions that aren't
    expressible in any implementable programming language. Realisability is a way
    to bring functions down to earth by requiring that they are computable in some
    model of computation. I'll cover the construction of categories of realizable
    functions, usually called the category of Assemblies, and its interesting sub-category,
    the category of Modest Sets or PERs. I'll also sketch how to interpret type theory
    in the category of assemblies. If there is time, I'll also cover linear realisability.
  location: Online
  material: []
- tag: Talk
  date: '2020-10-22T13:00:00Z'
  speaker: Matteo Capucci
  institute: MSP
  speakerurl: https://matteocapucci.wordpress.com/
  insturl: ''
  title: Fantastic sheaves and where to find them
  abstract: 'Sheaves are among the oddest creatures roaming the world of mathematics.
    They come from the far land of algebraic geometry, they speak a tricky language,
    and they organize in unfathomably big herds (''topoi''). There''s no reason to
    be afraid, though: sheaves can be the tamest beasts and provide many useful services
    to the mathematician who''s willing to learn their ways. In this talk, I''ll try
    to demystify sheaves by giving an elementary exposition of their basic features,
    trying to convey useful intuition about their behaviour. I will also try to give
    a taste some of their most astounding tricks, such as sheaf cohomology and topos-theoretic
    forcing.'
  location: Online
  material:
  - tag: Link
    address: https://github.com/mattecapu/fantastic-sheaves/blob/main/main.pdf
    linkDescription: Slides
- tag: Talk
  date: '2020-10-15T13:00:00Z'
  speaker: Andre Videla
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Quantitative Type Theory and its application
  abstract: To build upon last week's talk on Dependent types, we will develop the
    intuition around Quantitative types and their usage in modern programming languages.
    What does it mean to program when the type system is responsible for tracking
    resources rather than leave this task to the programmer? What new patterns do
    we see? And what are the limitations we encounter and how do we fix them? This
    talk aims to answers those questions in an approachable and interactive way.
  location: Online
  material: []
- tag: Talk
  date: '2020-10-08T13:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Dependent Types
  abstract: I'll give an introduction to the setup for dependent type theories, in
    the bidirectional style, again sketching why fundamental metatheoretic properties
    hold by not asking the wrong questions. In particular I'll develop the theory
    of dependent function types, then add lists. Let's conspire to make append associative,
    and if time permits, map a functorial action.
  location: Online
  material: []
- tag: Talk
  date: '2020-10-01T13:00:00Z'
  speaker: Joe Collins
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Introduction to Monoidal Categories
  abstract: A nice, chill introduction to the basic definitions and theorems on monoidal
    categories. We will be defining monoidal categories and symmetric monoidal categories,
    and talking about the coherence theorem and string diagrams.
  location: Online
  material: []
- tag: Talk
  date: '2020-09-24T13:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Bidirectional STLC
  abstract: 'By way of kicking off this semester of MSP101, I''ll give an introduction
    to our local dialect of bidirectional type systems, defined as mutually inductive
    systems of moded judgments. That is, we not only assign a syntactic category to
    each place in a judgment form, but also designate its mode as being "input", "subject",
    or "output". The syntactic categories of introduction and elimination forms are
    distinguished: the former have types as inputs, the latter types as outputs. I''ll
    illustrate this using the Simply Typed Lambda-Calculus, and I''ll rattle through
    as much metatheory thereof as I can before you bottle me off.'
  location: Online
  material: []
- tag: SpecialEvent
  date: '2020-09-10T13:00:00Z'
  endDate: '2020-09-10T14:00:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: https://meet.jit.si/MSP101/
  locationurl: https://meet.jit.si/MSP101/
  description: ''
- tag: Talk
  date: '2020-07-03T14:00:00Z'
  speaker: Jérémy Ledent
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/jeremy.ledent/
  insturl: ''
  title: Compositional Game Theory, compositionally
  abstract: |-
    The recent notion of Open Games allows to study game theory in a compositional way: complex games can be obtained from smaller ones using various operators such as sequential and parallel composition. Thus, Open Games form a symmetric monoidal category. There are many flavors of open games, ranging from small variations on how equilibria are treated, to more radical changes such as introducing probabilistic behavior. Proving from scratch that each variant still forms a monoidal category is tedious.

     I will present a compositional construction of the category of Open Games, which consists of three main steps. In each step, one can swap a component for a similarly-behaved one, without disturbing the rest of the structure. Thus, one can define many variants of Open Games with minimal effort. This compositional approach is based on the notion of Arrows, a concept first introduced in functional programming.

     This is a practise talk for ACT20 next week, and joint work with Bob, Bruno, Neil, Clemens and Fred.
  location: Online
  material: []
- tag: CancelledTalk
  date: '2020-06-26T14:00:00Z'
  speaker: Georgi Nakov
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: TBA
  abstract: TBA
  location: Online
  material: []
- tag: Talk
  date: '2020-06-19T14:00:00Z'
  speaker: Jan de Muijnck-Hughes
  institute: Glasgow
  speakerurl: http://jfdm.github.io/
  insturl: https://www.gla.ac.uk/schools/computing/
  title: Building Resource-Dependent EDSLs in a Dependently-Typed Language
  abstract: |-
    While many people use dependent types for theorem proving some of us like to use dependent types for building, and running, safer programs.

     Idris' <i>Effects</i> library demonstrates how to embed resource dependent algebraic effect handlers into a dependently typed host language, providing run-time and compile-time based reasoning on type-level resources. Building upon this work, <i>Resources</i> is a framework for realising EDSLs with type systems that contain domain specific substructural properties. Differing from <i>Effects</i>, <i>Resources</i> allows a language's substructural properties to be encoded within type-level resources that are associated with language variables. Such an association allows for multiple effect instances to be reasoned about autonomically and without explicit type-level declaration. We use type-level predicates as proof that a language's substructural properties hold.

     Using <i>Resources</i> we have shown how to provide correctness-by-construction guarantees that substructural properties of written programs hold when working with =Files=, specifying Domain Specific =BiGraphs=, and Global Session Descriptions---=Sessions=. With this talk I want to discuss the how and why of <i>Resources</i>, and show how we can use the framework to build EDSLs with interesting type-systems.

     This talk is part practise talk for ECOOP 2020, part tutorial on an important idiom for practical dependently-typed programming, and part chance to highlight more how dependent-types are useful when programming in the real world.
  location: Online
  material: []
- tag: Talk
  date: '2020-06-12T14:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org/
  insturl: ''
  title: Interpreting Dependent Type Theory in Containers
  abstract: In her PhD thesis, Tamara von Glehn showed that the Category of Containers
    (a.k.a. Category of Polynomials, Category of Dependent Lenses, Dialectica Category)
    supports an interpretation of dependent types. I'll present the basic constructions
    used, and, if I get to it, show that the model refutes the principle of functional
    extensionality.
  location: Online
  material: []
- tag: SpecialEvent
  date: '2020-06-05T09:00:00Z'
  endDate: '2020-06-05T14:30:00Z'
  title: Verification of Session Types Workshop (VEST)
  url: http://groups.inf.ed.ac.uk/abcd/VEST/
  location: Online
  locationurl: ''
  description: ''
- tag: Talk
  date: '2020-05-29T11:00:00Z'
  speaker: Dominic Orchard
  institute: University of Kent
  speakerurl: http://dorchard.co.uk
  insturl: https://www.cs.kent.ac.uk/
  title: 'The ''graded types'' paradigm: past, present, and a possible future'
  abstract: 'In the 1970s, the notion of ''grading'' appeared in analytic philosophy
    and logic as a way of making reasoning more fine-grained, capturing ''degrees''
    of necessity or possibility. Somewhat independently, grading has become a topic
    of interest in type theory and programming language semantics, with graded structures
    again providing a means of more fine-grained reasoning. In this talk, I will give
    an overview of this idea (both its past and present) and explore two uses: (1)
    using graded modal types for program reasoning in the context of an experimental
    functional language with linear and indexed types, called Granule; (2) specialising
    program semantics to give correct-by-construction arguments about program analyses
    and transformations.  I will also give a mathematical characterisation of grading
    which suggests a broad paradigm, and will briefly mention various ongoing works.'
  location: Online
  material: []
- tag: Talk
  date: '2020-05-22T14:00:00Z'
  speaker: Jérémy Ledent
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/jeremy.ledent/
  insturl: ''
  title: A quantitative model for λ-calculus
  abstract: 'Resource monoids and length spaces are a semantic framework inspired
    from realizability, which was introduced by Dal Lago and Hofmann in the context
    of implicit complexity. It has been used to define quantitative models for various
    programming languages (such as Elementary Affine Logic, LFPL), and deduce soundness
    properties of the form: "Every definable function lies in a given complexity class".
    In this talk, I will show how this framework can be used to measure different
    quantitative properties of a language than time complexity. Namely, I will present
    a model of simply-typed λ-calculus such that the interpretation of a λ-term contains
    an upper bound on the size of its normal form.'
  location: Online
  material: []
- tag: Talk
  date: '2020-05-15T14:00:00Z'
  speaker: James Wood
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/james.wood.100/
  insturl: ''
  title: A Linear Algebra Approach to Linear Metatheory
  abstract: |-
    Since its introduction, linear logic has been the cause of and solution to many problems in theoretical computer science. There are many examples in the literature of calculi which restrict usage of variables, allowing them to capture linearity, monotonicity, sensitivity analysis, privacy constraints, and other coeffects. However, the syntactic metatheory of these calculi is often difficult, and rarely in a form amenable to formalisation in a proof assistant.

     In this talk, I will introduce the notion of kits and environments yielding generic traversals – a method developed by Conor for proving renaming and substitution lemmas. Then, I will discuss recent work by myself and Bob on adapting this method to semiring-graded calculi. The result is a pleasingly and surprisingly minor variation on the original, comprising the introduction of a linear map to mediate usage annotations. This solution gives us confidence that we can tackle all of quantitative metatheory in the familiar intuitionistic style.
  location: Online
  material: []
- tag: Talk
  date: '2020-05-01T14:00:00Z'
  speaker: Radu Mardare
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/r.mardare/
  insturl: ''
  title: Stone duality for Markov processes (second attempt)
  abstract: |-
    The talk will focus on the category of Markov processes, on Markovian logics and Aumann algebras. Markovian logics are modal logics designed to specify (approximated) properties of Markov processes and characterize their bisimilarity. Aumann algebras are the algebraic counterpart of Markovian logics, i.e., they are Boolean algebras with operators that encode probabilistic information. Markovian logics are not compact and for this reason the "classic" Stone duality fails. I will present a different version of Stone duality constructed on top of Rasiowa-Sikorski lemma, which is a result bringing topological results into Model Theory.

     This talk summarizes results obtained in collaboration with Dexter Kozen and Prakash Panangaden.
  location: Online
  material: []
- tag: Talk
  date: '2020-04-24T14:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Something Else About Mary
  abstract: |-
    This is very much work in progress, jointly with Guillaume Allais (now of St Andrews) and Fredrik Nordvall Forsberg, with occasional involvement from others of the usual MSP suspects.

     Mary is our attempt to build a virtual learning environment which offers effective support to our own classes, building from the experience (but thankfully not the codebase) of the tools I built for teaching and assessing my first year hardware class. Last time I talked about Mary, she was just a twinkle in my eye. Now, she is at least a toddler.

     Mary is a variant on pandoc markdown which allows code fragments to be embedded in documents and document fragments to be embedded in code. This talk will focus mainly on the programming language embedded in the system which is currently called "Shonkier", as it is a variant on the "Shonky" language to which Frank compiles. It is untyped, for the time being, but that's an opportunity.

     The key design choice in Shonkier is that the C-style function application notation, f(e1,..,en), is used for all sorts of contextualization, and there are many such sorts. "Functions" (which already generalize to effect handlers) are but one form of context. We have also added first class environments (computed by pattern matching expressions) and guarding contexts (computed by Boolean expressions). One recent tweak which pays dividends is that effect handlers can now reply to requests with effects as well as with values. We are now free to negotiate various forms of contingency in a refreshingly direct style.

     In short, we have abandoned the naive delights of being context-free in favour of being context-negotiable.
  location: Online
  material: []
- tag: SpecialEvent
  date: '2020-04-17T14:00:00Z'
  endDate: '2020-04-17T15:00:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: Online at https://meet.jit.si/MSP101
  locationurl: https://meet.jit.si/MSP101
  description: ''
- tag: Talk
  date: '2020-02-06T14:00:00Z'
  speaker: Alan Jeffrey
  institute: Mozilla
  speakerurl: https://asaj.org/
  insturl: https://www.mozilla.org/
  title: Rust, Servo and Mixed Reality Research at Mozilla
  abstract: Mozilla is a non-profit whose mission is to expand access to, and protect
    privacy on, the Internet. Mozilla Research investigates emerging technologies,
    such as programming languages and new web platforms. This talk is an overview
    of research efforts around the Rust programming language, the Servo web engine,
    and Mixed Reality (VR and AR) on the web.
  location: LT1415
  material: []
- tag: CancelledTalk
  date: '2020-04-03T14:00:00Z'
  speaker: ''
  institute: ''
  insturl: ''
  speakerurl: ''
  title: Agda Implementors' Meeting XXXI
  url: https://wiki.portal.chalmers.se/agda/pmwiki.php?n=Main.AIMXXXI/
  location: University of Edinburgh
  abstract: ''
  locationurl: ''
  description: ''
  material: []
- tag: Talk
  date: '2020-03-27T14:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: Multidimensionally-correct by construction programming
  abstract: |-
    Physical dimensions such as length, mass and time can be used to ensure that equations are physically meaningful -- it makes no sense to add 7 metres to 12 seconds, and in an equation such as PV = nRT, it better be the case that both sides have the same physical dimension (in this case pressure times length^3). Even better, dimensions can not only be used to tell scientists off when making mistakes, but also to deduce non-trivial formulas (the famous example being that of the period of a pendulum as a function of its mass and length, and the acceleration of gravity).

     From an MSP perspective, there is a strong similarity between physical dimensions and types in programming languages, and indeed, this connection was explored in the 1990's by various researchers. A concrete outcome is Andrew Kennedy's implementation of units of measure in Microsoft's F# language, which makes it possible to write F# programs that are dimensionally-correct by construction.

     However, a lot of numerical software is written manipulating not single numbers, but vectors and matrices, using the methods of linear algebra. I will report on work in progress with Conor on extending dimensional analysis to multiple dimensions in this second sense.
  location: https://meet.jit.si/MSP101
  material: []
- tag: Talk
  date: '2020-04-03T14:00:00Z'
  speaker: Clemens Kupke
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/clemens.kupke/
  insturl: ''
  title: Completeness of Modal Logic via Stone Duality
  abstract: 'This talk is intended to be introductory, building on Radu''s earlier
    intro to Stone duality. In my presentation I will show how to use duality for
    proving completeness of basic (propositional) modal logic. To this aim I will
    first recall what completeness means and then discuss two different kinds of semantics
    for modal logic: its algebraic semantics, wrt which completeness of the logic
    is relatively straightforward, and Kripke semantics, which is the semantics one
    usually is interested in. Stone Duality allows to establish a connection between
    the two types of semantics such that completeness of modal logic wrt Kripke semantics
    follows.'
  location: https://meet.jit.si/MSP101
  material: []
- tag: CancelledTalk
  date: '2020-03-13T14:00:00Z'
  speaker: Joe Collins
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: TBA
  abstract: TBA
  location: LT1310
  material: []
- tag: Talk
  date: '2020-03-06T14:00:00Z'
  speaker: James Wood
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/james.wood.100/
  insturl: ''
  title: Classic puns
  abstract: |-
    There are several principles that are taken to be characteristic of non-constructive reasoning. These include the principles of excluded middle, double negation elimination, and choice.

     On the other side, there are several formal systems that are well known to capture only constructive reasoning. These include dependent type theory (à la Martin-Löf) and linear logic.

     However, each of the systems I just listed is able to derive at least one theorem that looks an awful lot like one of the non-constructive principles I listed earlier. What's going on here?
  location: LT1310
  material: []
- tag: Talk
  date: '2020-02-28T14:00:00Z'
  speaker: Georgi Nakov
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: The Dialectica Categories
  abstract: |-
    The Dialectica Categories were introduced in de Paiva's eponymous work as an internalized version of Gödel's functional interpretation. The interpretation translates Heyting Arithmetic (HA) into System T (intended as an axiomatization of primitive recursive functionals of finite type) and was originally developed as a tool to prove the relative consistency of HA. Translating the contraction rule poses certain problems and as a solution, Gödel requires decidability of atomic formulae. Several variants exist that lift this restriction.

     In this talk, I will present the categorical constructions from de Paiva's paper. We will investigate their structure and see how the different versions of the interpretation are accommodated in this setting. Finally, we will conclude that in the process we have obtained a model of Intuitionistic Linear Logic.
  location: LT1310
  material: []
- tag: CancelledTalk
  date: '2020-02-21T14:00:00Z'
  speaker: James Wood
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/james.wood.100/
  insturl: ''
  title: TBA
  abstract: TBA
  location: LT1310
  material: []
- tag: Talk
  date: '2020-02-14T14:00:00Z'
  speaker: Bruno Gavranović
  institute: MSP
  speakerurl: https://www.brunogavranovic.com/
  insturl: ''
  title: Towards Compositional Structures in Neural Networks
  abstract: Neural networks have become an increasingly popular tool for solving many
    real-world problems. They are a general framework for differentiable optimization
    which includes many other machine learning approaches as special cases. However,
    at the moment there is no comprehensive mathematical account of their behavior.
    I'm exploring the hypothesis that the language of category theory could be well
    suited to describe these systems in a precise manner. I will give a short tour
    of recent developments in this area, mostly based around the notion of lenses.
  location: LT1310
  material: []
- tag: Talk
  date: '2020-02-07T14:00:00Z'
  speaker: Radu Mardare
  institute: MSP
  speakerurl: ''
  insturl: https://personal.cis.strath.ac.uk/r.mardare/
  title: Stone Duality in Stochastic Context
  abstract: |-
    We define Aumann algebras, an algebraic analog of probabilistic modal logic.  An Aumann algebra consists of a Boolean algebra with operators modeling probabilistic transitions. We prove that countable Aumann algebras and countably-generated continuous-space Markov processes are dual in the sense of Stone.  Our results subsume existing results on completeness of probabilistic modal logics for Markov processes.

     This summarizes results obtained in collaboration with Dexter Kozen and Prakash Panangaden.
  location: LT1415
  material: []
- tag: Talk
  date: '2020-01-31T14:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org/
  insturl: ''
  title: Resource Constrained Programming with Full Dependent Types
  abstract: I will talk about a system that combines Dependent Types and Linear Types.
    As an application of this system, I will show how to transport Martin Hofmann's
    LFPL and Amortised Resource analysis systems for resource constrained computing
    to full dependent types. This results in a theory where unconstrained computations
    are allowed at the type level, but only polynomial time computations at the term
    level. The combined system now allows one to explore the world of propositions
    whose proofs are not only constructive, but also of restricted complexity.
  location: LT1310
  material: []
- tag: Talk
  date: '2020-01-24T14:00:00Z'
  speaker: Jérémy Ledent
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/jeremy.ledent/
  insturl: ''
  title: Simplicial Models for Multi-Agent Epistemic Logic
  abstract: 'Epistemic Logic is the modal logic of knowledge. It allows one to reason
    about a finite set of agents who can know facts about the world, and about what
    the other agents know. The traditional way to interpret epistemic logic formulas
    is by using Kripke models: that is, graphs whose vertices represent the possible
    worlds, and whose edges indicate the agents that cannot distinguish between two
    worlds. I will present an alternative kind of model for epistemic logic based
    on chromatic simplicial complexes. Simplicial models are equivalent to Kripke
    models; thus, this connection uncovers the higher-dimensional geometric nature
    of knowledge. Finally, I will show how to adapt these geometric models in order
    to interpret other epistemic notions, such as belief, distributed knowledge, and
    more.'
  location: LT1310
  material: []
- tag: Talk
  date: '2020-01-17T14:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Something About Mary
  abstract: |-
    Quite a few colleagues in the MSP group have experienced both the pleasure and the pain of working with my Marx system in the course of delivering our classes. (I never meant to write a virtual learning environment, but somehow, I sort of did.) I propose to re-engineer it from scratch and do a rather better job (suitable for wider deployment) deliberately, and am keen to solicit assistance in this mission, lest it be yet another engineering project distinguished by my madness and dissolution that you are, even so, obliged to put up with. Inevitably, I will struggle and rapidly fail to exclude interesting computer science from the design of the system. There will be fun.

     Mary will be a content management system with pages written in Markdown and stored in git repositories on the department's GitLab server. However, every such page is also a form, supporting interactive content. Pages will therefore need to embed code for processing the data in the form, certainly on the server, but preferably (unlike in Marx) on the client. So Mary will embed a programming language that we might have fun designing and implementing. I propose to base this language on Frank, an effects and handlers language that I cooked up a while back. Access to form fields can be seen as an effect: by remember the resumption for each such access, we can model what to recompute in the client when fields change, after the fashion of spreadsheets, programmed in apparently direct style.

     Mary will also need to maintain a database to achieve cross-session persistence of student work and staff configuration data. The Marx approach to analytics over this database amounted to "grep". In the meantime, however, Fred and I spent quite a while thinking about how to give an account of data models and analytics at a higher level of abstraction using carefully undermarketed ideas from dependent type theory. We should consider how to adapt these ideas to manage our own data.

     Let's get excited and make things!

     (Comrades who are not Strathclyders but who are interested in effects, types, or just having better tools to survive this business we call higher education, should very much feel invited to engage. I will happily export this project.)
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2020-01-16T13:30:00Z'
  endDate: '2020-01-16T14:30:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: LT1310
  locationurl: ''
  description: ''
- tag: SpecialEvent
  date: '2019-10-30T12:00:00Z'
  endDate: '2019-10-30T17:00:00Z'
  title: SPLS
  url: https://spls-series.github.io/meetings/2019/october/
  location: University of Glasgow
  locationurl: ''
  description: ''
- tag: Talk
  date: '2019-12-12T13:30:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Potato Powered Proofs
  abstract: |-
    Stuart and I have been working on interpreters for predicative calculi which are "potato-powered" in that they work by structural recursion on inductive data which may look suspiciously like types, but are not statically checked to be the actual types of the programs in question. This works because the calculi are presented in a bidirectional style which, by design, causes every redex to carry some "potatoes", which hopefully contain enough inductive carbohydrate to keep you going for the whole of the computation to be done.

     Naturally, it would be lovely if we could prove that the interpreter's output is genuinely a reduct of its input, and that well typed input yields normal form output (i.e., that an honest type gives the potatoes required to do the whole computation). How is it done? Potato-powered logical relations, of course! I'll give a crash course on cooking programs and proofs with potatoes.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-12-05T13:30:00Z'
  speaker: Radu Mardare
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/r.mardare/
  insturl: ''
  title: Boolean-valued semantics
  abstract: This talk is based on the paper with the same title that I have presented
    at LICS 2018. It is a joint work with Dana Scott, Dexter Kozen, Prakash Panangaden,
    Robert Furber and Giorgio Bacci. We extend Dana's Boolean-valued set theory (introduced
    in 50's to demonstrate the independence of the continuum hypothesis) to get, initially,
    a denotational model of untyped lambda calculus, and eventually extend it to a
    model of stochastic lambda calculus. The model is constructed over a space of
    random variables, which inherit a natural continuous Boolean algebra structure.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-11-28T13:30:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: Selective Applicative Functors (not a seminar, due to the strike)
  abstract: At this year's ICFP, Mohkov, Lukyanov, Marlow, and Dimino introduced "Selective
    Applicative Functors", a programming interface that is an intermediate stage between
    monads and applicative functors. I'll motivate what they're for, and describe
    what they are, and I'll talk about a more abstract way of thinking about them
    in terms of "right-skew monoidal categories".
  location: off-campus
  material: []
- tag: Talk
  date: '2019-11-21T13:30:00Z'
  speaker: Clemens Kupke
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/clemens.kupke/
  insturl: ''
  title: Expressive Logics for Coinductive Predicates
  abstract: |-
    The classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas of a certain modal logic. I will place this type of result in a general context, moving from transition systems to coalgebras and from bisimilarity to coinductive predicates. Furthermore I will present a sufficient condition for a coalgebraic logic to be expressive, i.e., to fully characterise a coinductive predicate on coalgebras. Our approach will be illustrated with logics characterising similarity, divergence and a behavioural metric on automata.

    This is joint work with Jurriaan Rot to be presented at CSL 2020.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-11-14T13:30:00Z'
  speaker: James Wood
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/james.wood.100/
  insturl: ''
  title: Programs and Proofs in Linear Algebra
  abstract: |-
    I try to understand the ways of linear algebraists from a programming languages perspective. In particular, I investigate the practice of specifying a linear map by giving only its action on basis elements. We can turn this practice into a nice programming language for linear maps. Furthermore, our reasoning about these maps is significantly simplified by only considering the basis elements. Finally, keeping track of basis elements amounts to a typing discipline, and we can expect to get some nice properties just by observation of the types.

    Meanwhile, I will try to elucidate the similarity between, on one side, categories of spaces and linear maps and, on the other, Rel, the category of sets and relations. This forms an important part of our programming languages view.
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2019-11-07T13:30:00Z'
  speaker: Neil Ghani
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/neil.ghani
  insturl: ''
  title: Coends and Kan extensions
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2019-10-31T13:30:00Z'
  speaker: Jérémy Ledent
  institute: MSP
  speakerurl: https://www.lix.polytechnique.fr/Labo/Jeremy.Ledent/
  insturl: ''
  title: Directed algebraic topology for concurrency
  abstract: I will give an introduction to the geometric semantics for concurrent
    programs that have been developed by Goubault, Fajstrup, Raussen et al. since
    the 1990's. A concurrent program can be viewed as a topological space equipped
    with a notion of direction, modeling the passage of time. Thus, in such a space,
    the existence of a path from A to B does not guarantee the existence of a path
    from B to A. A path in a directed space corresponds to an execution of the program;
    and two such executions are equivalent when the corresponding paths are homotopic,
    that is, when they can be deformed continuously into one another. This idea motivated
    the development of directed algebraic topology, the analogue of algebraic topology
    for directed spaces.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-10-24T13:30:00Z'
  speaker: Joe Collins
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Hopf Monads and Formally Adding in Morphisms
  abstract: |-
    It should be noted that this is ongoing work. The talk that you will see is going to be very unpolished; this is stuff that I have been working on for the past while, and the material will not be fully formed yet. The things I say may not end up matching with reality. So with that minor caveat, let us continue.

    A Hopf algebra is a monoid, a comonoid, and an extra endomorphism such that various commutation rules are obeyed, and Hopf monads are a strange generalisation of Hopf algebras in the direction of monads. I have previously talked about when a Hopf algebra is a Hopf-Frobenius algebra, and my goal now is to generalise this to the case of Hopf Monads. However, to keep things interesting, I am doing this in a weird way.

    Let T be a Hopf monad in monoidal category C. T is isomorphic to a Hopf algebra if there exists a natural transformation e: T -> 1 that respects the Hopf monad structure. There are many examples of Hopf monads which are not isomorphic to any Hopf algebras, so this morphism does not exist in C in general. However, what happens if I formally add in this morphism, creating a new category C_e? In this category, T would presumably be isomorphic to a Hopf algebra, and this begs the question: what can T in C_e tell us about T in C? By looking at the natural functor C -> C_e,  can I use this to transfer my theorem about Hopf algebras to Hopf monads? I certainly believe so, but let's find out together!
  location: LT1310
  material: []
- tag: Talk
  date: '2019-10-17T13:30:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: Ordinals below epsilon-zero in cubical Agda
  abstract: Ordinals and ordinal notation systems play an important role in program
    verification, since they can be used to prove termination of programs. We present
    three ordinal notation systems representing ordinals below epsilon_0 in type theory,
    using recent type-theoretical innovations such as mutual inductive-inductive definitions
    and higher inductive types. As case studies, we show how basic ordinal arithmetic
    can be developed for these systems, and how they admit a transfinite induction
    principle. We prove that all three notation systems are equivalent, so that we
    can transport results between them using the univalence principle. All our constructions
    have been implemented in cubical Agda.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-10-10T13:30:00Z'
  speaker: Radu Mardare
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/r.mardare/
  insturl: ''
  title: 'Quantitative algebras: towards a quantitative theory of effects'
  abstract: |-
    We develop a quantitative analogue of equational reasoning meant to provide metric semantics for stochastic/probabilistic/quantitative systems and programming languages. Quantitative algebras are algebras over metric spaces defined by these quantitative equational theories, and they implicitly define monads over the category of (extended) metric spaces. We have a few relevant examples of such algebras, where the induced free algebras  correspond  to  well-known structures; among these are Hausdorff  metrics  from  quantitive  semilattices, p-Wasserstein metrics (hence also the Kantorovich metric) from barycentric algebras, the total variation metrics from a variant of barycentric algebras, and more.

    The talk is based on a series of joint works with Prakash Panangaden and Gordon Plotkin. The main results have been presented at LICS'16, LICS'17 and LICS'18.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-10-03T13:30:00Z'
  speaker: James Wood, Joe Collins, Bob Atkey, Guillaume Allais, Fredrik Nordvall
    Forsberg
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Summer trip reports
  abstract: ''
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2019-09-26T13:00:00Z'
  endDate: '2019-09-26T14:00:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: LT1310
  locationurl: ''
  description: ''
- tag: Talk
  date: '2019-08-30T11:00:00Z'
  speaker: Malin Altenmüller
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: A combinatorial representation of the operad of plane graphs
  abstract: |-
    I will present how we can formalise non-symmetric monoidal categories (i.e. string diagrams) in a combinatorial way. These kind of diagrams will be represented by plane graphs with a distinguished boundary vertex. For encoding plane graphs it is sufficient to store the order of neighbours for each vertex, called a rotation system. I'll show how to define these sorts of graphs, how to compose them and &mdash; together with the right notion of rewriting &mdash; how they form an operad.

    This is practice for a talk I will give at STRINGS in Birmingham next week.
  location: LT1415
  material: []
- tag: Talk
  date: '2019-08-16T16:00:00Z'
  speaker: Rob Myers
  institute: ''
  speakerurl: ''
  insturl: ''
  title: Polynomial certificates for nondeterministic automata
  abstract: Given a deterministic finite automaton accepting <i>L</i>, another accepting
    the reverse language, and an integer <i>n</i>, does there exist a nondeterministic
    acceptor with <i>n</i> or fewer states? We've proved that this problem is in NP
    i.e. polynomial certificates exist. All previous algorithms constructing small
    nondeterministic automata for arbitrary regular languages are at best PSPACE-complete.
    We achieve this by explaining and substantially improving the Kameda-Weiner algorithm
    using coalgebraic methods. At the underlying level we use a categorical equivalence
    between finite join-semilattices and bipartitioned graphs.
  location: LT1415
  material: []
- tag: Talk
  date: '2019-07-05T16:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: 'The Thing with Thinnings: CodeBruijn is (Free;Stuff)'
  abstract: |-
    I've been hacking away on tools to do metatheory using "codebruijn" representation of syntax. The method, as with scoped de Bruijn representation, is to index terms by their <em>scope</em>, but the codebruijn method goes further, by systematically treating the <em>support</em> of terms, i.e., the particular subscope of variables which are actually <em>relevant</em>, paired with the thinning that embeds support into scope. The key codebruijn type constructor is "pair a thing with a thinning from some support", and it turns any old sort of thing into something which uniformly admits further thinning just by postcomposition, without affecting either the thing or its support.

    Stuff-which-uniformly-admits-thinning is stuff with structure, so there is a forgetful functor back to plain old Stuff. The Free functor which adds uniform thinning, is its left adjoint. The codebruijn type constructor is the monad (Free;Stuff). The corresponding comonad, (Stuff;Free), is rather more familiar to semanticists as the abstraction over <em>larger</em> scopes found in Kripke models.

    I've always been a bit shaky on adjunctions, presheaves and what have you, so this talk will not assume categorical confidence, but rather seek to build intuition, guided by a concrete example grounded in the practicalities of manipulating syntax.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-06-27T16:00:00Z'
  speaker: Kevin Dunne
  institute: ''
  speakerurl: ''
  insturl: ''
  title: Isbell Duality, Stone Duality, and Physical Theories
  abstract: |2-
     Isbell duality is an adjunction between a category of "generalised algebras" and a category of "generalised spaces", and is an abstraction of Stone duality. Broadly speaking, a Stone duality is an equivalence between some category of commutative algebras, and some category of spaces, for example: Boolean algebras and Stone spaces; or, commutative C*-algebras and Hausdorff spaces.

    There is a Stone duality which applies in the setting of Newtonian mechanics, between the category of smooth manifolds and a category of commutative algebras, and this equivalence of categories admits an extremely elegant and intuitive interpretation from the perspective of physics.

    I am going to discuss how to build an analogous interpretation for quantum theory using the machinery of Isbell duality, in such a way that directly generalises Newtonian mechanics, with the ultimate aim being to resolve some of the conceptual problems of quantum theory.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-06-07T16:00:00Z'
  speaker: Malin Altenmüller and James Wood
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: TYPES 2019 practice talks
  abstract: Malin and James will practice giving their talks "Containers of Applications
    and Applications of Containers" and "Linear metatheory via linear algebra" respectively.
  location: LT1415
  material:
  - tag: Link
    address: http://www.ii.uib.no/~bezem/abstracts/TYPES_2019_paper_40.pdf
    linkDescription: Containers of Applications and Applications of Containers (abstract)
  - tag: Link
    address: http://www.ii.uib.no/~bezem/abstracts/TYPES_2019_paper_42.pdf
    linkDescription: Linear metatheory via linear algebra (abstract)
- tag: DepartmentalSeminar
  date: '2019-05-29T13:00:00Z'
  speaker: Dan Ghica
  institute: Birmingham
  speakerurl: https://www.cs.bham.ac.uk/~drg/
  insturl: http://www.cs.bham.ac.uk/research/groupings/theory/
  title: The next 700 abstract machines
  abstract: |-
    We propose a new formalism for representing programming languages, based on a universal graph-rewriting abstract machine. The calculus itself only deals with the basic structural aspects of a programming languages, namely variables, names (e.g. memory locations) and thunks (i.e. fragments with delayed execution). Everything else needs to be supplied as extrinsic operations, with associated rewrite rules. This basic calculus allows us to represent all known sequential programming language features in a uniform framework, reason abstractly about their cost, and also reason about challenging equivalences.

    This is joint work with Koko Muroya and Todd Waugh Ambridge.
  location: LT1415
- tag: BasicTalk
  date: '2019-05-03T16:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Fixed points of indexed containers
  abstract: In an attempt to con Agda into allowing alternation of least and greatest
    fixed points, I try to remember how to construct these things for indexed containers.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-05-15T16:00:00Z'
  speaker: Guillaume Allais
  institute: MSP
  speakerurl: http://gallais.github.io
  insturl: ''
  title: Getting the unifier on your side
  abstract: I will explain how to write practical generic n-ary functions and combinators
    for n-ary relations.
  location: LT1310
  material:
  - tag: Link
    address: https://github.com/agda/agda-stdlib/pull/608
    linkDescription: Agda Standard Library pull request
- tag: Talk
  date: '2019-05-10T13:00:00Z'
  speaker: Troels Henriksen
  institute: University of Copenhagen
  speakerurl: http://sigkill.dk/
  insturl: http://diku.dk/
  title: A Purely Functional Array Language and its Optimising GPU Compiler
  abstract: |-
    Futhark is a small programming language designed to be compiled to efficient parallel code. It is a statically typed, data-parallel, and purely functional array language, and comes with a optimising ahead-of-time compiler that generates GPU code via OpenCL and CUDA. Futhark is not designed for graphics programming, but instead uses the compute power of the GPU to accelerate data-parallel array computations ("GPGPU").

    This talk presents the design of the Futhark language, as well as outlines several of the key compiler optimisations that have enabled performance comparable to hand-written GPU code. Through the use of a functional source language, we obtain strong invariants that simplify and empower the application of traditional compiler optimisation techniques. In particular, I will discuss (i) aggressively restructuring transformations such as fusion, (ii) loop interchange and distribution to extract flat parallel kernels from nested parallel source programs, (iii) multi-versioned code generation that exploits as much parallelism as necessary and efficiently sequentialises the rest, and (iv) data layout transformations to ensure coalesced memory access on GPUs.
  location: LT1415
  material: []
- tag: Talk
  date: '2019-04-12T16:00:00Z'
  speaker: Jan de Muijnck-Hughes
  institute: Glasgow
  speakerurl: http://jfdm.github.io/
  insturl: https://www.gla.ac.uk/schools/computing/
  title: A Type-System of Sorts for Bigraphs
  abstract: |-
    Bigraphs are a mathematical model (hypergraph) for representing the spatial and communication structures of networked entities [fn:1]. Bigraph Reactive Systems (BRS) build upon bigraphs by incorporating temporal changes to a model as specified with reaction rules. There is a wealth of theory (category) that supports reasoning about bigraphs, and an emergent tool (BigraphER [fn:2]) for their modelling.

    Bigraphs have an elegant algebraic structure that is general purpose and simply typed. However, it is common to place restrictions on the shape of a bigraph by a <i>system of sorts</i> that are applied as side-conditions. The details, and application, of these sorts are presented as an aside from the bigraph definition itself. This makes transformation of Bigraph models harder to enforce during manipulation as part of a BRS. We must provide runtime checks to provide relevant guarantees over model correctness.

    In this talk, I want to introduce you to the interesting world of Bigraph specification, and my current and ongoing work on developing a dependent type-system to embed a system-of-sorts directly into the algebraic definition of bigraphs. This allows one to provide correct-by-construction guarantees that a given model is correct w.r.t. a provided system-of-sorts.

    [fn:1] Robin Milner. 2009. The Space and Motion of Communicating Agents. Cambridge University Press.
    [fn:2] <a href='http://dcs.gla.ac.uk/~michele/bigrapher.html'>http://dcs.gla.ac.uk/~michele/bigrapher.html</a>
  location: LT1310
  material: []
- tag: Talk
  date: '2019-05-24T16:00:00Z'
  speaker: Michele Sevegnani
  institute: Glasgow
  speakerurl: http://www.dcs.gla.ac.uk/~michele/
  insturl: https://www.gla.ac.uk/schools/computing/
  title: Bigraphs with sharing and their algebra
  abstract: Bigraphical Reactive Systems (BRS) are a universal model of computation
    introduced by Robin Milner for the representation of interacting systems that
    evolve in both time and space. Bigraphs have been shown forming a category called
    symmetric partial monoidal category and their dynamic theory is defined in terms
    of rewriting and transition. A limitation of bigraphs is that the underlying model
    of location is a forest, which means there is no straightforward representation
    of locations that can overlap or intersect. In this talk, I will present bigraphs
    with sharing, an extension of bigraphs which solves this problem by defining the
    model of location as a directed acyclic graph, thus allowing a natural representation
    of overlapping or intersecting locations. I will give a complete presentation
    of the extended theory, including a categorical semantics, algebraic properties,
    a normal form and several essential procedures for computation.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-04-05T16:00:00Z'
  speaker: Bob Atkey and Conor McBride
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Shonan "Programming and Reasoning with Algebraic Effects and Effect Handlers"
    trip report
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2019-04-01T16:00:00Z'
  speaker: Johannes Marti
  institute: Universität Bremen
  speakerurl: http://johannesmarti.com/
  insturl: http://www.informatik.uni-bremen.de/tdki/
  title: Determinacy and the red-green chase
  abstract: |-
    The determinacy problem is to decide for queries v<sub>1</sub>,...,v<sub>n</sub> and q whether for every database D knowing the answers to v<sub>1</sub>,...,v<sub>n</sub> in D suffices to deduce the answer to q in D. It has been shown that this problem is undecidable if v<sub>1</sub>,...,v<sub>n</sub> and q are arbitrary conjunctive queries.

    In this talk I give a gentle introduction to some of the formal tools that are used to study the determinacy problem. Especially, I focus on the red-green chase, which is a neat construction that links the problem of determinacy with query answering relative to ontologies. Lastly, I might present some of our own, very modest, results about classes of conjunctive queries for which the determinacy problem is decidable.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-03-20T16:00:00Z'
  speaker: Alasdair Lambert
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Probabilistic open games
  abstract: We extend the Open Games framework for compositional game theory to encompass
    also mixed strategies, making essential use of the discrete probability distribution
    monad on Set. We show how to compose the resulting probabilistic games in parallel
    and sequentially, and illustrate the framework on the well-known Matching Pennies
    game.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-03-15T16:00:00Z'
  speaker: Joe Collins
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Fropf algebras
  abstract: Last time I talked, you heard about Interacting Frobenius algebras &mdash;
    this time, get ready for "Hopf-Frobenius algebras", as Ross likes to call them,
    or "Fropf algebras", as Ross doesn't like to call them. I am in the process of
    writing about them, so this is going to be quite similar to the last talk except
    we're coming at them from a new angle, and with new results.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-03-08T16:00:00Z'
  speaker: Clemens Kupke
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/clemens.kupke/
  insturl: ''
  title: Coalgebra Learning via Duality
  abstract: |-
    A key result in computational learning theory is Dana Angluin's L* algorithm that describes how to learn a deterministic finite automaton (DFA) using membership and equivalence queries.  I will present a generalisation of this algorithm to the level of coalgebras. The approach relies on the use of logical formulas as tests, based on a dual adjunction between states and logical theories. This allows us to learn, e.g., labelled transition systems, using modal formulas as tests.

    Joint work with Simone Barlocco and Jurriaan Rot.
  location: LT1415
  material: []
- tag: BasicTalk
  date: '2019-02-22T16:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: Proof-irrelevance for Dependent Type Theory
  abstract: 'Proof-irrelevance can mean two similar but different things: on the one
    hand, irrelevant proofs can be discarded when extracting programs to execute (run-time
    erasability), and on the other hand, one might want to treat proofs as irrelevant
    during type checking (type-checking time erasability). I will give an overview
    of the subject, focusing on type-checking time erasability. I suspect that at
    least three people in the audience knows more than me, so my main function will
    be to keep things accessible. I plan to follow the recent paper "Degrees of Relatedness:
    A Unified Framework for Parametricity, Irrelevance, Ad Hoc Polymorphism, Intersections,
    Unions and Algebra in Dependent Type Theory" by Andreas Nuyts and Dominique Devriese
    (LICS 2018).'
  location: LT1310
  material:
  - tag: Link
    address: https://people.cs.kuleuven.be/~andreas.nuyts/paper-reldtt.pdf
    linkDescription: '"Degrees of Relatedness" by  Andreas Nuyts and Dominique Devriese
      (LICS 2018) [PDF]'
- tag: Talk
  date: '2019-02-15T16:00:00Z'
  speaker: Malin Altenmüller
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Finitary indexed containers
  abstract: |-
    I will talk about two different representatives of indexed containers which &mdash; all together in the end &mdash; will construct an application that manages windows on a screen.

    The first instance of containers are rectangular windows. Defining these in terms of finite indexed containers (finite in the number of positions where elements can be stored) lets us interpret indices as outer boundaries. I will show some constructions on these space partitioning structures, e.g. product operations and overlaying of windows (this will hopefully include some pretty pictures!).

    Secondly I will explain how we can encode applications as indexed containers (not necessarily finite, despite the title), being defined in terms of commands and responses. To sum up I present the window managing application where all the above things will occur and get combined.

    I am working on these topics together with Conor and we are currently collocating them in a paper.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-02-08T16:00:00Z'
  speaker: Stuart Gale
  institute: MSP
  speakerurl: http://www.bishboria.com/
  insturl: ''
  title: Evaluators for bidirectional type systems
  abstract: In this talk I'll introduce syntax and semantics of a generic bidirectionally
    type checked lambda calculus. I'll also show that lumps of syntax that act as
    a type annotation are in fact the fuel which powers structural evaluation.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-02-01T16:00:00Z'
  speaker: James Wood
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: 'Linear logic: how hard can it be?'
  abstract: |-
    In the linear world, we are no longer allowed to freely discard or duplicate hypotheses and conclusions. This should mean that there are fewer possible strategies for proving a given proposition, making the task of proving things easier. However, we find that linear logic proof search is a surprisingly powerful model of computation. In this talk, I'll give an introduction to linear logic sequent calculus. I'll then go through a neat construction of [0] embedding quantified boolean formulae into linear logic without bangs, and sketch the proof from the same paper that linear logic with bangs is Turing-complete. Some content from CS106 may come in handy.

    [0]: Lincoln, Mitchell, Scedrov, Shankar, 1992, "Decision problems for propositional linear logic"
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2019-01-25T16:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: Chu spaces
  abstract: I'll talk about Chu Spaces, a general construction of *-autonomous categories
    (a.k.a. models of classical linear logic). Chu spaces are interesting because
    they come with an inbuilt notion of duality, which has been interpreted as a kind
    of player/opponent duality.
  location: LT1310
  material: []
- tag: Talk
  date: '2019-01-18T16:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Metametatheory of Bidirectional Type Systems
  abstract: |-
    In previous talks, I've written down bidirectional versions of particular type systems, with type checking for introduction forms and type synthesis for elimination forms. But what are the metarules for writing down the rules? How do we show that following the metarules ensures good properties of the rules? I'll report some progress towards capturing the syntactic properties of "good" rules which might push us closer to the goal of metatheory by construction.

    NB This talk has nothing to do with bidirectional transformations.
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2019-01-11T16:30:00Z'
  endDate: '2019-01-11T17:30:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: LT1310
  locationurl: ''
  description: ''
- tag: SpecialEvent
  date: '2018-12-17T11:30:00Z'
  endDate: '2018-12-17T12:30:00Z'
  title: SYCO 2
  url: http://events.cs.bham.ac.uk/syco/2/
  location: Strathclyde
  locationurl: ''
  description: ''
- tag: Talk
  date: '2018-12-14T16:15:00Z'
  speaker: Robin Cockett
  institute: 'University of Calgary '
  speakerurl: https://pages.cpsc.ucalgary.ca/~robin/
  insturl: https://www.ucalgary.ca/cpsc/
  title: Abstract differential geometry matters!
  abstract: 'The last few years has seen the development &mdash; largely in Canada
    and Australia &mdash; of an axiomatic approach to differential geometry based
    on tangent categories.  Tangent categories incorporate the previous leading settings
    for differential geometry: finite dimensional manifolds, synthetic differential
    geometry, convenient manifolds, etc.  In addition they widen the scope significantly
    as they also include combinatorial species, Goodwillie Functor calculi, and examples
    from computer science. The talk will give a survey of tangent categories and some
    of the developments so far.'
  location: LT1415
  material: []
- tag: Talk
  date: '2018-11-23T16:15:00Z'
  speaker: Clemens Kupke
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/clemens.kupke/
  insturl: ''
  title: The reachable part of a coalgebra
  abstract: |-
    State-based transition systems are often studied relative to a specified initial state. System behavior then only depends on those states that are "reachable" from the initial state. This has both consequences for the theory (e.g. by allowing to prove non-definability results in modal logic) and practice (by making seemingly large systems more manageable) of such systems.

    Coalgebras provide a general model for transition systems. In this introductory talk I will discuss how to define the reachable part of a coalgebra via the notion of T-base for an endofunctor T from [1]. We will first discuss this notion and then provide a sufficient categorical condition for the existence of the T-base. We will then show how to characterise the reachable part of a coalgebra as least fixpoint of a monotone operator.

    This is based on joint work with Simone Barlocco and Jurriaan Rot.

    ========================
    [1] Alwin Blok. Interaction, observation and denotation. Master's thesis, ILLC Amsterdam, 2012.
  location: LT1310
  material: []
- tag: CancelledTalk
  date: '2018-12-14T16:15:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: Effectful open games
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2018-12-07T16:00:00Z'
  speaker: Joe Collins
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Interacting Frobenius Algebras
  abstract: What is a Frobenius algebra? What is a Hopf algebra? And why are they
    such good friends? In this talk, I will be talking about PROPs, what an interacting
    Frobenius algebra is, and some weird stuff that appears with them, and I shall
    be drawing lots of pretty pictures as well.
  location: LT1310
  material: []
- tag: Talk
  date: '2018-11-30T16:15:00Z'
  speaker: Simone Barlocco
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Dual adjunctions
  abstract: |-
    Coalgebras provide an abstract framework to represent state-based transition systems. Modal logics provide a formal language to specify such systems.  In our recently submitted work (joint work with Clemens Kupke and Jurriaan Rot) we devise a general algorithm to learn coalgebras. Modal formulas are used as tests to probe the behaviour of states.

    In my introductory talk, I will discuss how to set up a general framework that connects coalgebras and their modal logics via a dual adjunction. Moreover, I will show a known result which guarantees that indistinguishable states wrt to modal formulas are behavioural equivalent, a key fact that entails that &mdash; whenever possible &mdash; our algorithm learns a minimal representation of a coalgebra.
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2018-11-16T16:15:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: Polynomial time programming languages
  abstract: Implicit Computational Complexity is the study of programming languages
    or logical systems that capture complexity classes. Roughly, every program that
    can be written in the language is in some complexity class. Many of the languages
    that have been proposed for capturing useful classes like PTIME are not much fun
    to program in. However, the work of the late Martin Hofmann included work on languages
    like LFPL, which only allows polynomial time computation, but is also reasonably
    usable. I'll talk about LFPL, and how the proof of polynomial time bounds works.
  location: LT1310
  material: []
- tag: Talk
  date: '2018-11-09T16:00:00Z'
  speaker: Ben Price
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/benjamin.price
  insturl: ''
  title: The semantics of worldly type systems
  abstract: |-
    I will present a type theory whose judgements are indexed by a preorder of "worlds", representing for example nodes in a distributed computation, or a security level.  This means a term may only typecheck at particular worlds, and will be mobile upwards along the preorder (for instance every low security value is also a high security one). To enable talking about the world structure without compromising mobility, the terms can talk about "shifts", which describe relative worlds.

    I then give a semantic model based on the usual presheaf model for STLC where worlds form the base category, and shifts are endofunctors on the worlds.  This semantics will show our programs are indeed oblivious to data they cannot "see".  Examples will be given to demonstrate this framework in some concrete cases, and to motivate future work.
  location: LT1310
  material: []
- tag: Talk
  date: '2018-11-02T16:00:00Z'
  speaker: Geoff Hamilton
  institute: Dublin City University
  speakerurl: https://www.computing.dcu.ie/~hamilton/
  insturl: https://www.computing.dcu.ie/
  title: The Next 700 Program Transformers
  abstract: In this talk, I will describe a hierarchy of program transformers in which
    the transformer at each level builds on top of the transformers at lower levels.
    The program transformer at the bottom of the hierarchy corresponds to positive
    supercompilation, and that at the next level corresponds to distillation. I will
    then try to characterise the improvements that can be made at each level, and
    show how the transformers can be used for program verification and theorem proving.
  location: LT1310
  material: []
- tag: Talk
  date: '2018-10-26T16:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: 'Syrup: circuits with memory'
  abstract: By way of giving CS106 students better tools to tackle the concept of
    memory in circuits, I implemented a small programming language called (for reasons
    which are unlikely to become clear) Syrup. Syrup is suspiciously like a dialect
    of Haskell, except that the blessed monad allows bits of state. Marking homework
    done in Syrup necessitates checking whether two circuits have the same <i>externally
    observable</i> behaviour, which makes it a matter of <b>bisimulation</b>. I'll
    talk a bit about how much fun it was implementing the decision procedure to find
    either a bisimulation or a countermodel (for purposes of decent feedback).
  location: LT1310
  material: []
- tag: Talk
  date: '2018-10-19T16:00:00Z'
  speaker: Stuart Gale
  institute: MSP
  speakerurl: http://www.bishboria.com/
  insturl: ''
  title: SPLS Post-mortem
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2018-10-12T16:00:00Z'
  speaker: Ross Duncan
  institute: Cambridge Quantum Computing
  speakerurl: http://personal.strath.ac.uk/ross.duncan/
  insturl: https://cambridgequantum.com/
  title: Why quantum computers suck, and what we might do about it
  abstract: Near-term quantum computers have many limitations which make them difficult
    to use for stuff. I will outline some of the difficulties and handwave at some
    new ideas from compositional mathematics that might help us address these problems.
  location: LT1310
  material: []
- tag: Talk
  date: '2018-10-05T16:00:00Z'
  speaker: James Wood
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: ICFP trip report
  abstract: Last week, I attended the ICFP conference and various associated workshops
    in St Louis. In this trip report, I will talk about selected talks and the people
    I met there. If time allows, I may also cover the adventures of Ioan, one of our
    summer interns and current undergraduate.
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2018-10-17T12:00:00Z'
  endDate: '2018-10-17T17:00:00Z'
  title: SPLS
  url: https://msp-strath.github.io/spls-18/
  location: Strathclyde
  locationurl: ''
  description: ''
- tag: SpecialEvent
  date: '2018-09-28T16:00:00Z'
  endDate: '2018-09-28T17:00:00Z'
  title: MSP101 Planning meeting
  url: ''
  location: LT1310
  locationurl: ''
  description: ''
- tag: Talk
  date: '2018-09-21T16:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: First-order unification
  abstract: I'll do a 101 today, filed under "stuff everybody should know" about first-order
    unification (the algorithm underlying Hindley-Milner type inference, Prolog, etc).
    But then I'll throw in the twist of considering syntax with binding. The way I
    cook it, this makes essential use of the structure of the category of thinnings.
  location: LT1310
  material: []
- tag: Talk
  date: '2018-08-31T15:00:00Z'
  speaker: Philippa Cowderoy
  institute: ''
  speakerurl: http://flippac.org
  insturl: ''
  title: 'Telescopic [Constraint] Trees, or: Information-Aware Type Systems In Context'
  abstract: |-
    The minimalist tradition in type systems makes for easy mathematics, but often leaves their mechanisms needlessly obscured.

    I build a structure for Hindley-Milner checking problems in the tradition of Type Inference in Context. This structure is derived from typing rules in the style of my first talk and mirrors data structures used for elaboration problems in dependent type systems &mdash; offering a notation that can be used among designers and implementors of type systems and even in explaining their behaviour to users.
  location: LT1415
  material:
  - tag: PDF
    slideName: 2018-08-31_cowderoy.pdf
    comment: ''
- tag: Talk
  date: '2018-08-29T15:00:00Z'
  speaker: Philippa Cowderoy
  institute: ''
  speakerurl: http://flippac.org
  insturl: ''
  title: Information-Aware Type Systems
  abstract: |-
    The minimalist tradition in type systems makes for easy mathematics, but often leaves their mechanisms needlessly obscured.

    One possible remedy is to track the behaviour of information in a system &mdash; its creation, its destruction and how it flows between constraints and source locations. I illustrate this with the Simply-Typed Lambda Calculus.
  location: LT1415
  material:
  - tag: PDF
    slideName: 2018-08-29_cowderoy.pdf
    comment: ''
- tag: Talk
  date: '2018-07-18T12:00:00Z'
  speaker: Jurriaan Rot
  institute: Radboud University Nijmegen
  speakerurl: http://jurriaan.me/
  insturl: http://www.ru.nl/icis/
  title: Finite and Infinite Traces, Inductively and Coinductively
  abstract: It is a well-known fact (used e.g. in model checking) that, on finitely
    branching transition systems, finite trace equivalence coincides with infinite
    trace equivalence. I will show how to prove this coinductively, which is arguably
    nicer than the standard inductive proof.
  location: LT1310
  material: []
- tag: Talk
  date: '2018-06-13T11:00:00Z'
  speaker: James Chapman
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/james.chapman
  insturl: ''
  title: 'Gillette Fusion: Kits for Hutton''s Razor or Type Unsafe and Scope Unsafe
    Programs and Their Proofs'
  abstract: The paper Type-and-Scope Safe Programs and Their Proofs abstracts the
    common type-and-scope safe structure from computations on lambda-terms that deliver,
    e.g., renaming, substitution, evaluation, CPS-transformation, and printing with
    a name supply. By exposing this structure, we can prove generic simulation and
    fusion lemmas relating operations built this way. In this talk I will present
    this approach but for simpler setting of Hutton's Razor. This reduces the mathematical
    structures involved from relative structures to the ordinary counterparts.
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2018-06-05T12:00:00Z'
  endDate: '2018-06-05T17:00:00Z'
  title: SPLS
  url: http://www.macs.hw.ac.uk/~rs46/spls-june-2018/
  location: Cairn Auditorium, PG G.01, Postgraduate Centre, Heriot-Watt University
  locationurl: ''
  description: ''
- tag: Talk
  date: '2018-05-29T13:00:00Z'
  speaker: Helle Hvid Hansen
  institute: TU Delft
  speakerurl: https://homepage.tudelft.nl/c9d1n/
  insturl: https://www.tudelft.nl/en/tpm/about-the-faculty/departments/engineering-systems-and-services/
  title: A Coinductive Proof of Policy Iteration Correctness
  abstract: This is the second half of Helle's talk on a (co)algebraic treatment of
    Markov Decision Processes. It focuses on a coinductive explanation of policy improvement
    using a new proof principle, based on Banach's Fixpoint Theorem, that we call
    contraction coinduction.
  location: LT1310
  material: []
- tag: Talk
  date: '2018-05-17T13:00:00Z'
  speaker: Thorsten Altenkirch
  institute: Nottingham
  speakerurl: http://www.cs.nott.ac.uk/~txa/
  insturl: http://www.cs.nott.ac.uk/
  title: HoTT for sets
  abstract: |-
    Before getting lost in the realms of higher dimensions we should see wether we can interpret set-level HoTT. We know how to deal with functional extensionality and a static universe of propositions (see Observational Type Theory) but what about a dynamic universe of propositions, i.e. one reflecting HProps that also validates propositional extensionality. I will discuss the problems modelling this and a possible solution using globular setoids.

    The dynamic prop corresponds to a subobject classifier in a topos (in particular we get unique choice) while the static universe corresponds to a quasitopos I am told.
  location: LT1310
  material: []
- tag: Talk
  date: '2018-05-23T16:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: How Do We Model a Problem Like Mutable State?
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2018-05-16T11:00:00Z'
  speaker: Helle Hvid Hansen
  institute: TU Delft
  speakerurl: https://homepage.tudelft.nl/c9d1n/
  insturl: https://www.tudelft.nl/en/tpm/about-the-faculty/departments/engineering-systems-and-services/
  title: Long-Term Values in Markov Decision Processes, (Co)Algebraically
  abstract: |-
    In this talk, we study Markov decision processes (MDPs) with the discounted sums criterion from the perspective of coalgebra and algebra. Probabilistic systems, similar to MDPs but without rewards, have been extensively studied, also coalgebraically, from the perspective of program semantics. Here, we focus on the role of MDPs as models in optimal planning, where the reward structure is central. Our main contributions are: (i) a coinductive explanation of policy improvement using a new proof principle, based on Banach's Fixpoint Theorem, that we call contraction coinduction, and (ii) showing that the long-term value function of a policy can be obtained via a generalized notion of corecursive algebra, which takes boundedness into account.

    This is joint work with Frank Feys (Delft) and Larry Moss (Indiana).
  location: LT1310
  material: []
- tag: Talk
  date: '2018-05-30T11:00:00Z'
  speaker: Artjoms Šinkarovs and Peter Hancock
  institute: Heriot-Watt
  speakerurl: http://ashinkarov.github.io/
  insturl: ''
  title: Multi-Dimensional Arrays and their Types
  abstract: |-
    Though Multi-Dimensional Arrays (MDAs) seem conceptually straightforward, it's not easy to come up with a mathematical theory of arrays that can be used within optimising compilers.  We'd like to treat arrays as functions from indices to values with some domain restrictions.  It is desirable that these domain restrictions are specified in a compact form, and are equipped with closed algebraic operations like intersection, union, etc.  We are going to consider a few typical models like hyperrectangulars, grids and polyhedrons.

    When typing array operations, ideally we'd like to find a balance between tracking all the shapes of arrays and allowing for generic array operations.  This proves to be tricky, for reasons we'll explain.

    We will propose, tentatively, an analysis of MDAs in terms of container functors.  The aim is to supply concepts helpful when thinking about MDAs, e.g. when designing notations for coding with arrays.  Some intriguing gadgetry shows up.
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2018-05-04T11:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg
  insturl: ''
  title: The Dialectica Interpretation
  abstract: 'A proof interpretation translates proofs of one logical system into proofs
    of another (example: the double-negation interpretation of classical logic into
    constructive logic). This often reveals some information about the original system
    (e.g. classical logic is equiconsistent with constructive logic). G&ouml;del''s
    Dialectica interpretation (named after the journal it was published in) translates
    Heyting arithmetic (the constructive theory of the natural numbers, including
    induction) into System T (the quantifier-free theory of the simply typed lambda
    calculus with natural numbers) &mdash; quantifier complexity is traded for higher
    type complexity. Combining this translation with (a refined) double negation translation,
    one can extract System T programs from a proof of a forall-exists statement, even
    if this proof is using non-constructive priciples such as Markov''s Principle,
    Excluded Middle, or the Quantifier-Free Axiom of Choice. I''ve always found the
    Dialectica translation mystifying, so I''ll try to explain the intuition behind
    it.'
  location: LT1310
  material: []
- tag: Talk
  date: '2018-04-19T11:00:00Z'
  speaker: James Wood
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Midlands Graduate School Trip Report
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2018-04-12T11:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg
  insturl: ''
  title: Quotient Inductive-Inductive Types
  abstract: |-
    Higher inductive types (HITs) in Homotopy Type Theory (HoTT) allow the definition of datatypes which have constructors for equalities over the defined type. HITs generalise quotient types and allow to define types which are not sets in the sense of HoTT (i.e. do not satisfy uniqueness of equality proofs) such as spheres, suspensions and the torus. However, there are also interesting uses of HITs to define sets, such as the Cauchy reals, the partiality monad, and the internal, total syntax of type theory.  In each of these examples we define several types that depend on each other mutually, i.e. they are inductive-inductive definitions. We call those HITs quotient inductive-inductive types (QIITs).

    Although there has been recent progress on the general theory of HITs, there isn't yet a theoretical foundation of the combination of equality constructors and induction-induction, despite having many interesting applications. In the present paper we present a first step towards a semantic definition of QIITs. In particular, we give an initial-algebra semantics and show that this is equivalent to the section induction principle, which justifies the intuitively expected elimination rules.
  location: LT1415
  material: []
- tag: Talk
  date: '2018-03-28T12:30:00Z'
  speaker: Thorsten Altenkirch
  institute: Nottingham
  speakerurl: http://www.cs.nott.ac.uk/~txa/
  insturl: http://www.cs.nott.ac.uk/
  title: What is a category, actually?
  abstract: 'Let us revisit the definition of a category and define it in a way which
    has the advantage that we can generalize it to higher dimensions. Why am I interested
    in higher categories (or specifically (\infty,1)-categories)? I have a few problems
    in Homotopy Type Theory which I think can be solved using these beasts: the coherence
    problem for type theory in type theory (in the moment I cannot even define the
    standard model) and generalizing the Hungarian approach to Quotient Inductive
    Inductive Types (QIITs) to Higher Inductive Inductive Types (HIITs).'
  location: LT1310
  material: []
- tag: Talk
  date: '2018-03-21T15:00:00Z'
  speaker: Jamie Gabbay
  institute: Heriot-Watt
  speakerurl: http://www.gabbay.org.uk
  insturl: http://www.macs.hw.ac.uk/departments/computer-science.htm
  title: Equivariant ZFA and the foundations of nominal techniques
  abstract: |-
    The sets foundations of nominal techniques are usually taken to be Fraenkel-Mostowski set theory (which is ZFA + a finite support property).  I will argue that in many situations, a new foundation which I call Equivariant ZFA (EZFA) may be a better choice, because you can do everything in EZFA that you can do in FM and furthermore EZFA with Choice (EZFAC) is consistent whereas FM with Choice is not.
    <ul><li>I will define EZFA and how it interacts with Choice.</li><li>I will prove that EZFA is <em>equivalent</em> to ZFA.</li><li>I will then prove that EZFA is <em>not equivalent</em> to ZFA.</li><li>I will explain why I think EZFA(C) may be useful, why my last three papers were actually written in EZFAC, and finally I will discuss the implications this may have for mathematical foundations in general.</li></ul>
  location: LT1415
  material:
  - tag: Link
    address: http://www.gabbay.org.uk/papers.html#equzfn
    linkDescription: Paper the talk is based on
- tag: BasicTalk
  date: '2018-02-14T15:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg
  insturl: ''
  title: Domain Theory
  abstract: I will give an introduction to Domain Theory, focusing on motivation.
    I hope to cover recursive definitions, and solving domain equations using retraction
    pairs.
  location: LT1310
  material: []
- tag: Talk
  date: '2018-02-08T15:00:00Z'
  speaker: Alexander Kurz
  institute: Leicester
  speakerurl: http://www.cs.le.ac.uk/people/ak155/
  insturl: https://www2.le.ac.uk/departments/informatics
  title: Introduction to coalgebra
  abstract: ''
  location: LT1212
  material: []
- tag: DepartmentalSeminar
  date: '2018-02-07T15:00:00Z'
  speaker: Justin Hsu
  institute: UCL
  speakerurl: https://justinh.su/
  insturl: http://pplv.cs.ucl.ac.uk/welcome/
  title: From Couplings to Probabilistic Relational Program Logics
  abstract: Many program properties are relational, comparing the behavior of a program
    (or even two different programs) on two different inputs. While researchers have
    developed various techniques for verifying such properties for standard, deterministic
    programs, relational properties for probabilistic programs have been more challenging.
    In this talk, I will survey recent developments targeting a range of probabilistic
    relational properties, with motivations from privacy, cryptography, machine learning.
    The key idea is to meld relational program logics with an idea from probability
    theory, called a probabilistic coupling. The logics allow a highly compositional
    and surprisingly general style of analysis, supporting clean proofs for a broad
    array of probabilistic relational properties.
  location: LT1415
- tag: Talk
  date: '2018-04-06T11:00:00Z'
  speaker: James Chapman
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/james.chapman
  insturl: ''
  title: Setoids and Quotients
  abstract: 'In preparation for Fred''s talk about "Quotient Inductive-Inductive Types"
    next week I will introduce quotients and setoids in type theory and some of the
    issues surrounding them. The use of setoids is discouraged by many doctors and
    can lead to a contagious and incurable condition: relation preservation. Quotients
    on the other hand are dangerous if not correctly handled and can lead to unsightly
    things appearing where they shouldn''t such as inhabitants of the excluded middle.'
  location: LT1310
  material: []
- tag: Talk
  date: '2018-03-14T15:00:00Z'
  speaker: Joe Collins
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Quantum Computing with ZX Calculus
  abstract: |-
    Quantum mechanics is dope, so it makes sense that making a computer using the principles of quantum mechanics would also be pretty sick. However, the formalism that is used by physicists, called a Hilbert space, is not specialised for this purpose. In particular, it is
    1) Difficult to prove properties about programs for quantum computers
    2) Difficult to see what is these programs are actually doing

    Thankfully, category theory is very cool! Using ZX calculus, we can talk about quantum computing in a much clearer manner. I will be introducing some fundamental quantum mechanics and ZX calculus, and then using ZX calculus I will talk about Shor's algorithm.
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2018-03-07T10:00:00Z'
  endDate: '2018-03-07T17:00:00Z'
  title: SPLS
  url: ''
  location: Level 5, School of Computing Science, University of Glasgow
  locationurl: ''
  description: ''
- tag: Talk
  date: '2018-02-21T15:00:00Z'
  speaker: Jan de Muijnck-Hughes
  institute: Glasgow
  speakerurl: http://jfdm.github.io/
  insturl: https://www.gla.ac.uk/schools/computing/
  title: A Type-System for describing the Structural Topology of System-on-a-Chip
    Architectures
  abstract: |-
    The protocols that describe the interactions between IP Cores on System-on-a-Chip architectures are well-documented. These protocols described not only the structural properties of the physical interfaces but also the behaviour of the emanating signals. However, there is a disconnect between the design of SoC architectures, their formal description, and the verification of their implementation in known hardware description languages.

    Within the Border Patrol project we are investigating how to capture and reason about the structural and behavioural properties of SoC architectures using state-of-the-art advances in programming language research. Namely, we are investigating using dependent types and session types for the description of hardware communication.

    In this talk I will discuss my work in designing a linked family of languages that captures and reasons about the topological structure of a System-on-a-Chip. These languages provide correct-by-construction guarantees over the interaction protocols themselves; the adherence of a component that connects using said protocols; and the validity of the specified connections. These guarantees are provided through abuse of indexed monads to reason about resource usage; and general (ab)use of dependent types as presented in Idris.

    I will not cover all aspects of the languages but will concentrate my talk detailing the underlying theories that facilitate the correct-by-construction guarantees.
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2018-03-09T16:00:00Z'
  speaker: Alasdair Lambert and Ben Price
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Kan extensions
  abstract: ''
  location: LT1310
  material: []
- tag: CancelledTalk
  date: '2018-02-14T15:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: TBA
  abstract: ''
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2018-02-07T15:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg
  insturl: ''
  title: The adjoint functor theorem
  abstract: 'Adjoint functors arise everywhere, but how do we find them? It is a fun
    exercise to prove that right adjoints preserve limits, and, dually, that left
    adjoints preserve colimits. An adjoint functor theorem is a statement that (under
    certain conditions) the converse holds: a functor which preserves limits is a
    right adjoint. I will discuss the General Adjoint Functor Theorem, and why Peter
    Johnstone considers it fundamentally useless.'
  location: LT1310
  material: []
- tag: Talk
  date: '2018-01-31T15:00:00Z'
  speaker: Kevin Dunne
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Reflections on the PhD process
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2018-01-24T15:00:00Z'
  speaker: Jurriaan Rot
  institute: Radboud University Nijmegen
  speakerurl: http://jurriaan.me/
  insturl: http://www.ru.nl/icis/
  title: Coinduction and the Companion
  abstract: The coinductive proof method can be enhanced by several techniques, often
    referred to as up-to-techniques. I will talk about the basic theory of coinduction-up-to,
    and a little about the more recent notion of companion. This companion is the
    largest valid up-to technique for a given predicate, and gives a nice way of working
    with coinduction up-to.
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2018-01-16T16:00:00Z'
  endDate: '2018-01-16T17:00:00Z'
  title: MSP101 Planning session
  url: ''
  location: LT1310
  locationurl: ''
  description: ''
- tag: Talk
  date: '2017-12-08T16:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: Dijkstra Monads
  abstract: One monad to the tune of another.
  location: LT1310
  material: []
- tag: Talk
  date: '2017-10-27T16:00:00Z'
  speaker: Johannes Marti
  institute: Universität Bremen
  speakerurl: http://johannesmarti.com/
  insturl: http://www.informatik.uni-bremen.de/tdki/
  title: Size-Matters in the Modal mu-Calculus
  abstract: |-
    I talk about three methods for measuring the size of formulas in the modal mu-calculus and explore how the choice between them influences the complexity of computations on formulas. Especially, I focus on the guarded transformation, which is a simple syntactic transformation on formulas that is commonly assumed to be polynomial but has recently been shown to require exponential time.

    I will complain about the mess in the literature and present two of our (Clemens, Yde and me) own preliminary results:

    1) There is a polynomial guarded transformation if we measure the input formula in the number of its subformulas and measure the output formula in the size of its closure.

    2) If there is a polynomial guarded transformation where we measure the input formula in the size of its closure then there is a polynomial algorithm for solving parity games. Hence finding such a transformation is at least as hard as solving parity games, which is commonly believed to be quite hard.

    We employ an automata-theoretic approach that relates the different measures for the size of a formula to different constraints on the transition structure of an automaton corresponding to the formula.

    This is a very technical talk but there will be many pictures!
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2017-10-11T12:00:00Z'
  endDate: '2017-10-11T17:00:00Z'
  title: SPLS
  url: http://simonjf.com/spls-oct2017/
  location: Informatics Forum, Edinburgh
  locationurl: ''
  description: ''
- tag: Talk
  date: '2017-09-22T16:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Bidirectional Martin-L&ouml;f 1971
  abstract: 'Per Martin-L&ouml;f''s 1971 Theory of Types is the ancestor of the type
    systems used today in Agda, Coq, Idris, NuPRL, and many other variations on the
    theme of dependent types. Its principal virtue is its simplicity: it has very
    few moving parts (but they move quite a lot). Its well known principal vice is
    its inconsistency: you can write a looping program inhabiting any type (thus ''proving''
    any proposition). I''ll be talking about the design principles for constructing
    dependent type systems which are bidirectional &mdash; clearly split into a type  checking
    part and a type synthesis part. By following these principles, it gets easier
    to establish good safety properties of these systems. In particular, I''ll sketch
    how to keep type safety ("well typed programs don''t go wrong") separate from
    normalization ("all computations terminate"). Martin-L&ouml;f''s 1971, reformulated
    bidirectionally, makes a good example, because it''s small and type-safe, but
    not normalizing.'
  location: LT1310
  material: []
- tag: Talk
  date: '2017-09-29T16:00:00Z'
  speaker: Ben Price
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/benjamin.price
  insturl: ''
  title: Worlds
  abstract: |-
    Building on last week's introduction to Martin-L&ouml;f 1971, we describe a toy type theory which not only accounts for what type terms have, but also where they live. This extra information can be interpreted as where (physically) data lives, at what phase (typechecking vs runtime) it exists, when it exists, or who has access to the data.

    In return for caring about these "worlds" describing where data lives, we get applications to distributed computing and erasure for efficient code generation, with future work to consider productivity and security.
  location: LT1310
  material: []
- tag: Talk
  date: '2017-10-06T16:00:00Z'
  speaker: Peter Hancock
  institute: ''
  speakerurl: http://docs.hancock.fastmail.fm/
  insturl: ''
  title: Tetration
  abstract: |-
    In ghci, you can write something like <div class='centered'><tt>let two f = f . f in two two two two (+1) 0</tt></div> and it will print "65536". If you write something like <div class='centered'><tt>let two f = f . f ; four = two . two in four ($ two) id (+1) 0</tt></div> it will print "Occurs check: cannot construct the infinite type: a ~ a -> a".

    Can haskell not count to four?(*)

    The topic is the compact representation of unfeasibly large numbers using a pure (Glaswegian?) universe.  Some excursions into the hinterland of the topic are likely.

    By the way, tetration is the function m n |-> n ^ .. ^ n with m n's.

    (*) No doubt mad haskell mambo or pragma exists that will trick it into counting up to four.  I will reward the most amusing/revolting demonstration with a large (reasonably priced) malt whisky.
  location: LT1310
  material: []
- tag: Talk
  date: '2017-10-13T16:00:00Z'
  speaker: Simone Barlocco
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Coalgebraic Learning
  abstract: 'Automata learning is a well known technique to infer a finite state machine
    from a set of observations. One important algorithm for automata learning is the
    L* algorithm by Dana Angluin. In this 101 I will present a new perspective on
    L* using ideas from coalgebra and modal logic. After a brief recap of how L* works,
    I will describe a generalisation of the L* algorithm to the coalgebraic level.
    I will conclude my talk with two concrete instances of the general framework:
    the learning of Mealy machines and of bisimulation quotients of probabilistic
    transition systems. Joint work with Clemens Kupke.'
  location: LT1310
  material: []
- tag: Talk
  date: '2017-11-03T16:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: Measuring the sizes of trees
  abstract: I'll talk about a way of measuring the sizes of trees using weighted tree
    automata, in a compositional way that works well with pattern matching. This is
    based on some work by Georg Moser and Martin Hofmann.
  location: LT1310
  material: []
- tag: Talk
  date: '2017-11-17T16:00:00Z'
  speaker: Ross Duncan
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/ross.duncan
  insturl: ''
  title: Deep Learning
  abstract: I'll explain the first concepts of Deep Learning. This is an advert for
    a reading group on the topic which will run over the next few weeks.
  location: LT1310
  material: []
- tag: CancelledTalk
  date: '2017-12-15T16:00:00Z'
  speaker: James/Fred
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: TBA
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2017-11-10T16:00:00Z'
  speaker: Alasdair Lambert
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Infinite Iteration of Games
  abstract: My talk will be based on our recent paper "A Compositional Treatment of
    Iterated Open Games". In this paper we introduce a new operator on open games
    to capture the concept of subgame perfect equilibrium as well as providing final
    coalgebra semantics of infinite games.
  location: LT1310
  material: []
- tag: CancelledTalk
  date: '2017-12-22T16:00:00Z'
  speaker: Fred/James
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: TBA
  abstract: ''
  location: LT1310
  material: []
- tag: CancelledTalk
  date: '2017-11-24T16:00:00Z'
  speaker: Neil Ghani
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/neil.ghani
  insturl: ''
  title: TBA
  abstract: ''
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2017-12-01T16:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Hereditary substitution
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2017-12-06T13:00:00Z'
  speaker: Chung-Kil Hur
  institute: Seoul National University
  speakerurl: http://sf.snu.ac.kr/gil.hur/
  insturl: http://sf.snu.ac.kr/
  title: The Power of Parameterization in Coinductive Proof
  abstract: "In this talk, I will present a simple yet powerful principle for coinductive
    reasoning, which we call \"parameterized coinduction\". More specifically, it
    is as simple as the Knaster-Tarski theorem without requiring any syntactic checking,
    yet as powerful as Coq's syntactic guarded coinduction supporting incremental
    reasoning. As an important consequence, parameterized coinduction can easily support
    complex nested induction-coinduction. \n\nWe also implemented the parameterized
    coinduction as the Coq library called \"paco\", which can be found at:\n\n<a href='http://plv.mpi-sws.org/paco'>http://plv.mpi-sws.org/paco</a>\n\nThis
    is joint work with Georg Neis, Derek Dreyer and Viktor Vafeiadis, and was presented
    at POPL'13. "
  location: LT1415
  material: []
- tag: SpecialEvent
  date: '2017-09-14T11:40:00Z'
  endDate: '2017-09-14T12:40:00Z'
  title: MSP101 Planning session
  url: ''
  location: LT1310
  locationurl: ''
  description: ''
- tag: Talk
  date: '2017-09-11T14:00:00Z'
  speaker: Andrea Vezzosi
  institute: Chalmers
  speakerurl: http://www.cse.chalmers.se/~vezzosi/
  insturl: http://www.chalmers.se/en/departments/cse/Pages/default.aspx
  title: Adding Cubes to Agda
  abstract: |-
    Cubical Type Theory (CTT) provides an extension of Martin-L&ouml;f Type Theory (MLTT) where we can interpret the univalence axiom while preserving the canonicity property, i.e. every closed term actually computes to a value. The typing and equality rules of CTT come as a fairly well-behaved extension of the ones of MLTT and the denotational model and prototype implementation help clarifying the system further.

    Given the above it felt reasonable to introduce the features of CTT into a more mature proof assistant like Agda, and this talk reports the status of this endeavour. In short:
    <ul><li>The univalence axiom is proven as a theorem and we successfully tested its computational behavior on small examples.</li><li><tt>comp</tt> computes for any parametrized data or record types, including coinductive ones, but it is stuck for inductive families.</li><li>The interaction of the path type and copatterns gives extensionality principles for coinductive records.</li><li>The interval <tt>I</tt> is an actual type, we also have restriction types <tt>A[&phi; &mapsto; u]</tt> and types for partial elements <tt>Partial &phi; A</tt>. Their sort makes sure <tt>comp</tt> does not apply to them.</li></ul>
    Examples are collected at <a href='https://github.com/Saizan/cubical-demo'>https://github.com/Saizan/cubical-demo</a>.
  location: LT1101 (Board room)
  material: []
- tag: Talk
  date: '2017-09-06T14:00:00Z'
  speaker: Ross Duncan
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/ross.duncan
  insturl: ''
  title: Binding and Substitution in String Diagrams
  abstract: In the categorical semantics of (e.g.) the simply typed lambda calculus
    substitution of a variable by a term is achieved by composing morphisms.  What
    is the equivalent notion in diagrammatic languages?  What even is a "variable"
    in this context?  I'll sketch some (pretty) rough ideas for the beginnings of
    a “functional language” of diagrams including substitution, binding, and pattern
    matching.  It turns out to all be about operads and co-operads.
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2017-07-10T10:00:00Z'
  endDate: '2017-07-10T17:00:00Z'
  title: Open Games Workshop
  url: http://msp.cis.strath.ac.uk/opengames-2017/
  location: LT1415
  locationurl: ''
  description: ''
- tag: Talk
  date: '2017-07-05T14:00:00Z'
  speaker: Noam Zeilberger
  institute: Birmingham
  speakerurl: http://noamz.org/
  insturl: http://www.cs.bham.ac.uk/
  title: Some enumerative, topological, and algebraic aspects of linear lambda calculus
  abstract: Enumeration of graphs on surfaces (or "maps") is an active topic of research
    in combinatorics, with links to wide-ranging domains such as algebraic geometry,
    knot theory, and mathematical physics. In the last few years, it has also been
    found that map enumeration is related to the combinatorics of lambda calculus,
    with various well-known families of maps in 1-to-1 correspondence with various
    natural families of linear lambda terms. In the talk I will begin by giving a
    brief survey of these enumerative connections, then use those to motivate a closer
    look at the surprisingly rich topological and algebraic properties of linear lambda
    calculus.
  location: LT1415
  material: []
- tag: Talk
  date: '2017-06-15T14:00:00Z'
  speaker: Stuart Gale
  institute: MSP
  speakerurl: http://www.bishboria.com/
  insturl: ''
  title: Informal introduction to knot theory and the unknotting problem
  abstract: |-
    This is an informal talk on the interesting properties I've found when playing with the unknotting problem (knot simplification moves that help to establish whether any given knot is a loop in complicated disguise, or something really knotted).

    I'll discuss the syntax that I've used for annotating knots that leads to a(n almost) syntax based method for unknotting, but that hints further at unknotting in a more interesting way by using an unintentional property of the syntax.

    I'll present some examples of the problems with representing knots and how the syntax and reduction rules help, in my opinion, to make unknotting more tangible.
  location: LT1310
  material: []
- tag: Talk
  date: '2017-06-29T14:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: Syntax and semantics of Quantitative Type Theory
  abstract: |-
    At last year's WadlerFest celebration, Conor presented a dependent type theory where variables are tagged with information about how they are used. Variable usage tagging has been developed in the non dependent setting, starting with Girard's Linear Logic, and culminating with recent work in contextual effects, coeffects, and quantitative type theories. The subtlety with dependent types lies in how to account for the difference between usage in types and terms. Conor's system handles this by treating usage in types as a "zero" usage, so that it doesn't affect the usage in terms. This is a departure from previous "linear" type theories that maintains a strict separation between usage controlled information, which types cannot depend on, and unrestricted information, which types can depend on.

    Conor presented a syntax and typing rules for the system, as well as an erasure property that exploits the difference between "not used" and "used", but doesn't do anything with the finer usage information available. I'll present a collection of models for the system that fully exploit the usage information. This will give interpretations of type theory in resource constrained computational models, Geometry of Interaction models, and imperative models. To maintain order, I will gather all these notions of model under a new concept of "Quantitative Category with Families", a generalisation of the standard "Category with Families" class of models of dependent types.
  location: LT1310
  material: []
- tag: Talk
  date: '2017-06-08T14:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg
  insturl: ''
  title: TYPES 2017 Trip report
  abstract: I'll tell you about the most interesting talks, ideas and gossip that
    came out of the TYPES conference in BudaPest last week.
  location: LT1310
  material: []
- tag: Talk
  date: '2017-07-27T14:00:00Z'
  speaker: Matteo Cavaliere
  institute: Edinburgh
  speakerurl: https://sites.google.com/site/researchcavaliere/
  insturl: http://www.synthsys.ed.ac.uk/
  title: The Rise and Fall of Cooperative Communities
  abstract: |-
    Social, biological and economic networks grow and decline with recurrent fragmentation and re-formation, often explained in terms of external perturbations. I will present a model of dynamical networks and evolutionary game theory that explains these phenomena as consequence of imitation and endogenous conflicts between "cooperators" and "cheaters". Cooperators promote well-connected prosperous (but fragile)  networks and cheaters cause the network to fragment and lose its prosperity. Once the network is fragmented it can be reconstructed by a new invasion of cooperators, leading to recurrent cycles of formation and fragmentation observed, for instance, in bacterial communities and socio-economic networks. In the last part of the talk, I will briefly introduce my current works on the role of individual decision-making in cooperative communities and the possibility of synthetic biology to address these ideas in microbial communities.

    References

    M. Cavaliere, S. Sedwards, C.E. Tarnita, M.A. Nowak, A. Csikasz-Nagy.
    Prosperity is Associated with Instability in Dynamical Networks.
    Journal of Theoretical Biology, 299, 2012.

    Plasticity Facilitates Sustainable Growth in the Commons.
    M. Cavaliere, J.F. Poyatos.
    Journal of the Royal Society Interface, 10, 2013.

    Eco-Evolutionary Feedbacks can Rescue Cooperation in Microbial Populations.
    C. Moreno-Fenoll, M. Cavaliere, E. Martinez-Garcia, J.F. Poyatos.
    Scientific Reports, 7, 2017.
  location: LT1415
  material: []
- tag: Talk
  date: '2017-06-01T14:00:00Z'
  speaker: Rob Myers
  institute: ''
  speakerurl: ''
  insturl: ''
  title: 'Optimal nondeterminism: explaining the Kameda-Weiner algorithm'
  abstract: The Kameda-Weiner algorithm takes a machine (nondeterministic finite automaton)
    as input, and provides an optimal machine (state-minimal nondeterministic finite
    automaton) as output. In this talk I will discuss work which provides a clear
    explanation of it, by translating the various syntactic constructs into more meaningful
    order-theoretic ones, and then composing them together to prove correctness.
  location: LT1310
  material: []
- tag: Talk
  date: '2017-05-25T11:00:00Z'
  speaker: Clemens Kupke
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/clemens.kupke
  insturl: ''
  title: Learning via Coalgebraic Logic
  abstract: |-
    A key result in computational learning theory is Dana Angluin's L* algorithm that describes how to learn a regular language, or a deterministic finite automaton (DFA), using membership and equivalence queries. In my talk I will present a generalisation of this algorithm using ideas from coalgebra and modal logic &mdash; please note, however, that prior knowledge of these topics will not be required.

    In the first part of my talk I will recall how the L* algorithm works and establish a link to the notion of a filtration from modal logic. Furthermore I will provide a brief introduction to coalgebraic modal logic. In the second part of my talk I will present a generalisation of Angluin's original algorithm from DFAs to coalgebras for an arbitrary finitary set functor T in the following sense: given a (possibly infinite) pointed T-coalgebra that we assume to be regular (i.e. having an equivalent finite representation) we can learn its finite representation by (i) asking "logical queries" (corresponding to membership queries) and (ii) making conjectures to which a teacher has to reply with a counterexample (equivalence queries). This covers (known variants of) the original L* algorithm and  algorithms for learning Mealy and Moore machines. Other examples are infinite streams, trees and bisimulation quotients of various types of transition systems.

    Joint work with Simone Barlocco.
  location: LT1310
  material: []
- tag: Talk
  date: '2017-05-18T15:00:00Z'
  speaker: Thorsten Altenkirch
  institute: Nottingham
  speakerurl: http://www.cs.nott.ac.uk/~txa/
  insturl: http://www.cs.nott.ac.uk/
  title: The joy of QIITs
  abstract: |-
    Quotient inductive inductive types (QIITS) are set-truncated mutually defined higher inductive types. I am going to discuss two applications of QIITs:

    1. define an internal syntax of Type Theory without reference to untyped preterms;
    2. define a version of the partiality monad that doesn't require countable choice.

    On the one hand I think that these applications are interesting because they represent applications of HoTT which have nothing to do with homotopy theory; on the other hand they are clearly not very higher order (in the sense of truncation levels) but can be defined in the set-truncated fragment of HoTT. Hence my question: what are interesting applications of higher types which are not directly related to synthetic homotopy theory?

    This talk is based on joint work with Paolo Capriotti, Nils Anders Danielsoon, Gabe Dijkstra, Ambrus Kaposi and Nicolai Kraus.
  location: LT1310
  material: []
- tag: Talk
  date: '2017-04-20T14:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: Modular Datalog
  abstract: ''
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2017-05-04T14:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Differential Operators
  abstract: |-
    A traditional source of complaint from CS undergraduates (especially in the USA, but in other places, too) is that they are made to learn too much standard issue mathematics with little apparent relevance to computation. Differential calculus (with its usual presentational focus on physical systems) is often picked upon as the archetype. What we see in action is the fragile male ego: they are not so quick to complain about the unimportance of things they do not find difficult. All of which makes more delicious the irony that differential operators have a key role to play in understanding discrete structures, such as automata, datatypes, execution stacks, and plenty more.

    The basic idea is as follows: to put your finger over any single K in the pair of words <div class='centered'>BREKEKEKEX KOAXKOAX</div> you must choose either to put your finger over a single K in BREKEKEKEX and pair with KOAXKOAX intact, or to leave BREKEKEKEX intact and cover a K in KOAXKOAX. You have just followed Leibniz's rule for differentiating a product (with respect to K), and computed a one-hole context for a K in a data structure.

    Newton, of course, would point out that such derivatives arise as the limit of a divided difference, a concept worthy of study in more generality. I would point out that divided differences are often definable, even in situtations when neither division nor difference makes much apparent sense. Notably, Brzozowski's derivative for regular languages is a divided difference (even though it is not Leibniz's derivative).

    I'll work mainly with containers (which look a lot like power series) but make sure there are plenty of concrete examples. In practice, it becomes rather useful to compute derivatives by pattern matching on types, which is especially funny as symbolic differentiation is the first example in the literature of computing anything by pattern matching at all.
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2017-04-05T10:00:00Z'
  endDate: '2017-04-05T17:00:00Z'
  title: CLAP
  url: http://homepages.inf.ed.ac.uk/cheunen/clapscotland/
  location: Strathclyde, room LT1415
  locationurl: ''
  description: ''
- tag: SpecialEvent
  date: '2017-04-10T09:00:00Z'
  endDate: '2017-04-10T17:00:00Z'
  title: ALCOP2017
  url: https://personal.cis.strath.ac.uk/clemens.kupke/ALCOP2017/
  location: Strathclyde, Room MC301 (McCance Building)
  locationurl: http://www.strath.ac.uk/maps/mccancebuilding/
  description: ''
- tag: DepartmentalSeminar
  date: '2017-02-22T15:00:00Z'
  speaker: Andrea Bracciali
  institute: Stirling
  speakerurl: http://www.cs.stir.ac.uk/~abb/
  insturl: http://www.cs.stir.ac.uk/
  title: An introduction to Blockchains
  abstract: Blockchains, i.e. decentralised, distributed data structures which can
    also carry executable code for a non-standard execution environment, introduce
    new models of computation. Decentralised, here, means, informally speaking, "without
    central control", e.g. a currency without a (central) bank, but much more. Blockchains
    support the recently introduced virtual currencies, a la Bitcoin, and a new class
    of decentralised applications, including smart contracts. In this talk we will
    introduce the main aspects of a blockchain, with particular reference to the Bitcoin
    blockchain as a paradigmatic case of such a new model of computation, and also
    touching on smart contracts. No previous knowledge of bitcoin/blockchain required
    for this introductory talk.
  location: LT1415
- tag: DepartmentalSeminar
  date: '2017-02-15T13:00:00Z'
  speaker: Chris Heunen
  institute: Edinburgh
  speakerurl: http://homepages.inf.ed.ac.uk/cheunen/
  insturl: http://www.ed.ac.uk/informatics/
  title: Semantics for probabilistic programming
  abstract: Statistical models in e.g. machine learning are traditionally expressed
    in some sort of flow charts. Writing sophisticated models succinctly is much easier
    in a fully fledged programming language. The programmer can then rely on generic
    inference algorithms instead of having to craft one for each model. Several such
    higher-order functional probabilistic programming languages exist, but their semantics,
    and hence correctness, are not clear. The problem is that the standard semantics
    of probability theory, given by measurable spaces, does not support function types.
    I will describe how to get around this.
  location: LT1415
- tag: Talk
  date: '2017-02-06T14:00:00Z'
  speaker: Ohad Kammar
  institute: Oxford
  speakerurl: http://www.cs.ox.ac.uk/people/ohad.kammar/main.html
  insturl: http://www.cs.ox.ac.uk/
  title: 'On the expressive power of user-defined effects: effect handlers, monadic
    reflection, delimited control without answer-type-modification'
  abstract: |-
    We compare the expressive power of three programming abstractions for user-defined computational effects: Bauer and Pretnar's effect handlers, Filinski's monadic reflection, and delimited control. This comparison allows a precise discussion about the relative merits of each programming abstraction.

    We present three calculi, one per abstraction, extending Levy's call-by-push-value. These comprise syntax, operational semantics, a natural type-and-effect system, and, for handlers and reflection, a set-theoretic denotational semantics. We establish their basic meta-theoretic properties: adequacy, soundness, and strong normalisation. Using Felleisen's notion of a macro translation, we show that these abstractions can macro-express each other, and show which translations preserve typeability.  We use the adequate finitary set-theoretic denotational semantics for the monadic calculus to show that effect handlers cannot be macro-expressed while preserving typeability either by monadic reflection or by delimited control. We supplement our development with a mechanised Abella formalisation.

    Joint work with Yannick Forster, Sam Lindley, and Matija Pretnar.
  location: LT1415
  material: []
- tag: Talk
  date: '2017-04-27T14:00:00Z'
  speaker: Kevin Dunne
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: What I, Dunne, done in my PhD
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2017-03-30T14:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg
  insturl: ''
  title: Cubical adventures in Connecticut
  abstract: I'll report on my attempts to design a cubical type theory together with
    Dan Licata and Ed Morehouse during my visit to Wesleyan University, Middletown,
    Connecticut. We had something which seemed quite promising, but that falls apart
    just short of the finish line; I'll tell you about it in the hope of miraculous
    rescue from the audience. However, I'll start from basics so that everyone has
    a chance to join in in the fun. Mentions of Donald Trump will be kept to a minimum.
  location: LT1310
  material: []
- tag: Talk
  date: '2017-03-23T14:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: Blockchain discussion
  abstract: ''
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2017-03-16T14:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: Operational and Denotational Semantics for PCF
  abstract: PCF is the prototypical functional programming language, with two data
    types (naturals and booleans), lambda-abstraction and recursion. PCF was introduced
    by Gordon Plotkin in his seminal "LCF Considered as a Programming Language" paper
    from 1977. Despite PCF's simplicity, its semantics is theoretically interesting.
    I will introduce PCF, its operational semantics, the "standard" domain-theoretic
    denotational semantics and show that the two agree on closed programs. Finally,
    I will discuss observational equivalence for PCF and show that the denotational
    semantics fails to be "fully abstract".
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2017-03-09T14:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Indexed Containers/Interaction Structures
  abstract: ''
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2017-03-02T14:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: Separation Logic and Hoare Logic
  abstract: 'Hoare Logic is a logic for proving properties of programs of the form:
    if the initial state satisfies a precondition, then the final state satisfies
    a postcondition. Hoare logic proofs are structured around the structure of the
    program itself, making the system a compositional one for reasoning about pieces
    of programs. I''ll introduce Hoare Logic for a little imperative language with
    WHILE loops. I''ll then motivate Separation Logic, which enriches Hoare Logic
    with a Frame Rule for local reasoning. '
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2017-02-23T14:00:00Z'
  speaker: James Chapman
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/james.chapman
  insturl: ''
  title: Blockchain
  abstract: I will try to follow on from yesterday's introduction by getting to nitty
    gritty of bitcoin/blockchain. I won't assume attendance of the seminar but will
    try not to repeat it!
  location: LT1415
  material: []
- tag: BasicTalk
  date: '2017-02-16T14:00:00Z'
  speaker: Clemens Kupke
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/clemens.kupke
  insturl: ''
  title: Automata on infinite words
  abstract: In this 101 I plan to discuss omega-automata, i.e., finite automata that
    operate on infinite words/streams. These automata form an important tool for the
    specification and verification of the ongoing, possibly infinite behaviour of
    a system. In my talk I will provide the standard definition(s) of omega-automata
    and highlight what makes omega-automata difficult from a coalgebraic perspective.
    Finally, I am going to discuss the work by Ciancia & Venema that provides a first
    coalgebraic representation of a particular type of omega-automata, so-called Muller
    automata.
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2017-02-09T14:00:00Z'
  speaker: Simone Barlocco
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Automata learning
  abstract: Automata learning is a well known technique to infer a finite state machine
    from a set of observations. One important algorithm for automata learning is the
    L* algorithm by Dana Angluin. In this 101, I will explain how the L* algorithm
    works via an example. Afterwards, I will discuss the ingredients of the algorithm
    both in the standard framework by Angluin and in a recently developed categorical/coalgebraic
    framework by Jacobs & Silva. Lastly, I plan to outline the proof of the minimality
    of the automaton that is built by the learning algorithm.
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2017-02-02T14:00:00Z'
  speaker: Johannes Marti
  institute: MSP
  speakerurl: http://johannesmarti.com/
  insturl: ''
  title: First-order logic
  abstract: In this 101 I outline the syntax and semantics of classical first order
    predicate logic. I try to also mention some of the characteristic properties of
    first order logic such as compactness, the L&ouml;wenheim-Skolem theorem or locality
    properties in finite model theory.
  location: LT1310
  material: []
- tag: Talk
  date: '2017-01-26T14:00:00Z'
  speaker: Conor McBride, James Chapman, and Bob Atkey
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: 'La Vie Parisienne: POPL trip report'
  abstract: "  Our POPL attendees will tell us about their favourite talks, the latest
    research gossip and show us their most scenic photos from POPL in Paris."
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2017-01-19T14:00:00Z'
  speaker: Johannes Marti
  institute: MSP
  speakerurl: http://johannesmarti.com/
  insturl: ''
  title: Automata and games for fixpoint logics
  abstract: I explain how we can use automata and games to understand the behaviour
    of modal fixpoint logics.
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2017-01-12T11:40:00Z'
  endDate: '2017-01-12T12:40:00Z'
  title: MSP101 Planning session
  url: ''
  location: LT1310
  locationurl: ''
  description: ''
- tag: DepartmentalSeminar
  date: '2016-12-14T16:00:00Z'
  speaker: Sam Lindley
  institute: Edinburgh
  speakerurl: http://homepages.inf.ed.ac.uk/slindley/
  insturl: http://www.ed.ac.uk/informatics/
  title: Do be do be do
  abstract: "We explore the design and implementation of Frank, a strict functional
    programming language with a bidirectional effect type system designed from the
    ground up around a novel variant of Plotkin and Pretnar's effect handler abstraction.\n\nEffect
    handlers provide an abstraction for modular effectful programming: a handler acts
    as an interpreter for a collection of commands whose interfaces are statically
    tracked by the type system. However, Frank eliminates the need for an additional
    effect handling construct by generalising the basic mechanism of functional abstraction
    itself. A function is simply the special case of a Frank <i>operator</i> that
    interprets no commands.\n\nMoreover, Frank's operators can be <i>multihandlers</i>
    which simultaneously interpret commands from several sources at once, without
    disturbing the direct style of functional programming with values.\n\nEffect typing
    in Frank employs a novel form of effect polymorphism which avoid mentioning effect
    variables in source code. This is achieved by propagating an <i>ambient ability</i>
    inwards, rather than accumulating unions of potential effects outwards.\n\nI'll
    give a tour of Frank through a selection of concrete examples.\n\n(Joint work
    with Conor McBride and Craig McLaughlin) "
  location: LT1415
- tag: SpecialEvent
  date: '2016-11-30T12:00:00Z'
  endDate: '2016-11-30T17:00:00Z'
  title: CLAP
  url: http://homepages.inf.ed.ac.uk/cheunen/clapscotland/
  location: Strathclyde
  locationurl: ''
  description: ''
- tag: Talk
  date: '2016-11-02T14:00:00Z'
  speaker: Phil Scott
  institute: University of Ottawa
  speakerurl: http://www.site.uottawa.ca/~phil/
  insturl: http://engineering.uottawa.ca/eecs/
  title: An introduction to many-valued logics and effect algebras
  abstract: |-
    The algebras of many-valued Lukasiewicz logics (MV algebras) as well as the theory of quantum measurement (Effect algebras) have undergone considerable development in the 1980s and 1990s; they now constitute important research fields, with connections to several contemporary areas of mathematics, logic, and theoretical computer science.

    Both subjects have recently attracted considerable interest among groups of researchers in categorical logic and foundations of quantum computing. I will give a leisurely introduction to MV algebras (and their associated logics), as well as the more general world of effect algebras. If time permits, we will also illustrate some new results (with Mark Lawson, Heriot-Watt) on coordinatization of some concrete MV-algebras using inverse semigroup theory.
  location: LT1415
  material: []
- tag: SpecialEvent
  date: '2016-11-09T12:00:00Z'
  endDate: '2016-11-09T17:00:00Z'
  title: SPLS
  url: https://msp-strath.github.io/spls-16/
  location: Room 301, McCance building, Strathclyde
  locationurl: http://www.strath.ac.uk/maps/mccancebuilding/
  description: ''
- tag: Talk
  date: '2016-09-28T15:00:00Z'
  speaker: Guillaume Allais
  institute: Radboud University Nijmegen
  speakerurl: http://gallais.org
  insturl: ''
  title: Towards a Generic Treatment of Syntaxes with Binding
  abstract: |-
    The techniques used by the generic programming community have taught us that we can greatly benefit from exposing the common internal structure of a family of objects. One can for instance derive once and for all a wealth of iterators from an abstract characterisation of recursive datatypes as fixpoints of functors.

    Our previous work on type and scope preserving semantics and their properties has made us realise that numerous semantics of the lambda calculus can be presented as instances of the fundamental lemma associated to an abstract notion of 'Model'. This made it possible to avoid code duplication as well as prove these semantics' properties generically.

    Putting these two ideas together, we give an abstract description of syntaxes with binding making both their recursive and scoping structure explicit. The fundamental lemma associated to these syntaxes can be instantiated to provide the user with proofs that its language is stable under renaming and substitution as well as provide a way to easily define various evaluators.
  location: LT1310
  material: []
- tag: Talk
  date: '2016-09-15T15:00:00Z'
  speaker: Jules Hedges
  institute: Oxford
  speakerurl: http://www.cs.ox.ac.uk/people/julian.hedges/home.html
  insturl: http://www.cs.ox.ac.uk/
  title: Morphisms of open games
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2016-12-14T11:00:00Z'
  speaker: Alasdair Lambert
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Compositional Game Theory
  abstract: I will be discussing composition in a model of economic game theory and
    methods for representing the impact of choice on subsequent games. Time permitting
    I will also work through some games using this model.
  location: LT1310
  material: []
- tag: Talk
  date: '2016-12-07T11:00:00Z'
  speaker: Jamie Gabbay
  institute: Heriot-Watt
  speakerurl: http://www.gabbay.org.uk
  insturl: http://www.macs.hw.ac.uk/departments/computer-science.htm
  title: Nominal filters and semantics of predicate logic
  abstract: |-
    A <dfn>filter</dfn> P is a consistent deductively closed set of predicates. A filter is <dfn>prime</dfn> when
    <div class='centered'>(&phi; &or; &psi;) &isin; P &rArr; (&phi; &isin; P &or; &psi; &isin; P)</div>In words: if phi-or-psi is in P then phi is in P or psi is in P. Primeness gives soundness for disjunction.

    Using this it is not hard to construct a semantics to propositional logic in which a predicate &phi; "means" the set of prime filters containing it.  This is a standard "trick" for building semantics and is an extremely useful proof-method.

    I have developed a semantics for predicate logic and also for the lambda-calculus based on similar notions of filter, but in a <i>nominal</i> context &mdash; meaning that filters are developed using Fraenkel-Mostowski (FM) set theory instead of Zermelo-Fraenkel (ZF) set theory.  What matters here is that FM sets have additional name structure over ZF sets, and this additional structure can be exploited to give semantics to the extra structure that predicates have over propositions, and in particular the additional name structure lets us write down primeness conditions for soundness for universal quantification.

    The resulting semantics is rich and interesting.  In a sentence: nominal techniques help us to extend the notion of Stone representation and duality from propositional logic to full first-order logic (also with equality, if we wish, and also to other logics and calculi with variables and quantifiers).

    I will give a detailed description of the filter-style conditions involved, and discuss some of what I think they tell us about predicates and quantification in logic and computation.  More information can also be found in two papers here:
    <a href='http://www.gabbay.org.uk/papers.html#semooc'>http://www.gabbay.org.uk/papers.html#semooc</a>
    <a href='http://www.gabbay.org.uk/papers.html#repdul'>http://www.gabbay.org.uk/papers.html#repdul</a>
  location: LT1310
  material: []
- tag: Talk
  date: '2016-11-23T11:00:00Z'
  speaker: Yde Venema
  institute: ILLC, Amsterdam
  speakerurl: https://staff.science.uva.nl/y.venema/
  insturl: http://www.illc.uva.nl/
  title: Some model theory for the modal mu-calculus
  abstract: |-
    We discuss a number of semantic properties pertaining to formulas of the modal mu-calculus. For each of these properties we provide a corresponding syntactic fragment, in the sense that a mu-calculus formula \phi has the given property iff it is equivalent to a formula \phi' in the corresponding fragment. Since this formula \phi' will always be effectively obtainable from \phi, as a corollary, for each of the properties under discussion, we prove that it is decidable in elementary time whether a given mu-calculus formula has the property or not.

    The properties that we study have in common that they all concern the dependency of the truth of the formula at stake, on a single proposition letter p. In each case the semantic condition on \phi will be that \phi, if true at a certain state in a certain model, will remain true if we restrict the set of states where p holds, to a special subset of the state space. Important examples include the properties of complete additivity and (Scott) continuity, where the special subsets are the singletons and the finite sets, respectively.

    Our proofs for these characterisation results will be automata-theoretic in nature; we will see that the effectively defined maps on formulas are in fact induced by rather simple transformations on modal automata.
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2016-11-16T11:00:00Z'
  speaker: Johannes Marti
  institute: MSP
  speakerurl: http://johannesmarti.com/
  insturl: ''
  title: Modal logic
  abstract: |-
    Modal logic provides a simple, yet surprisingly powerful, language for specifying properties of coalgebras. In this talk I introduce the basic modal logic that is interpreted on relational structures. My aim is to provide an idea how modal logic relates to other logics, such as first-order and intuitionistic logic, and to the duality between algebraic and coalgebraic structures.

    If time permits, I might also give a very informal warm-up for the modal mu-calculus which is the topic of next week's talk.
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2016-11-09T10:30:00Z'
  speaker: Stuart Gale
  institute: MSP
  speakerurl: http://www.bishboria.com/
  insturl: ''
  title: Meta-theory of lambda-calculi
  abstract: |-
    I'll give a standard overview of Simply Typed Lambda Calculus (STLC) (syntax, typing and computation rules) in a well-typed setting, and then modify it to show STLC in a bidirectional setting.

    Afterwards I'll show Strong Confluence (Church-Rosser theorem) in the bidirectional setting.
  location: LT1310
  material: []
- tag: Talk
  date: '2016-11-02T11:00:00Z'
  speaker: Ben Price
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/benjamin.price
  insturl: ''
  title: System F and proof-relevant parametricity
  abstract: |-
    I shall give a brief introduction to System F.
    I will then explain how to capture our intuition about polymorphic functions behaving uniformly by relational parametricity, and talk about ongoing work to find a notion of proof-relevant parametricity.
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2016-10-26T11:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg
  insturl: ''
  title: Data types and initial-algebra semantics
  abstract: I will give a basic introduction to data types and initial-algebra semantics.
    The meaning of a data type is given as the initial object in a category of types
    with the corresponding constructors. Initiality immediately allows the modelling
    of a non-dependent recursion principle. I'll show how this can be upgraded to
    full dependent elimination, also known as induction, by using the uniqueness of
    the mediating arrow; in fact, induction is equivalent to recursion plus uniqueness.
    All possibly unfamiliar terms in this abstract will also be explained.
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2016-10-19T11:00:00Z'
  speaker: Clemens Kupke
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/clemens.kupke
  insturl: ''
  title: A first introduction to coalgebra
  abstract: 'The core subject of Computer Science is "generated behaviour" (quiz:
    who said this?). Coalgebra provides the categorical formalisation of generated
    behaviour. I am planning to provide a first, very basic introduction to coalgebra.
    This will consist of two parts: i) coinduction & corecursion as means to define
    & reason about the (possibly) infinite behaviour of things; ii)modal logics for
    coalgebras.'
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2016-10-12T11:00:00Z'
  speaker: Neil Ghani
  institute: MSP
  speakerurl: http://personal.cis.strath.ac.uk/neil.ghani
  insturl: ''
  title: Category Theory
  abstract: ''
  location: LT1310
  material: []
- tag: BasicTalk
  date: '2016-10-05T11:00:00Z'
  speaker: Ross Duncan
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/ross.duncan
  insturl: ''
  title: Rewriting, and operads
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2016-09-28T11:00:00Z'
  speaker: James Chapman
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/james.chapman
  insturl: ''
  title: ICFP trip report
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2016-09-21T11:00:00Z'
  speaker: Kevin Dunne
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Eventual image functors
  abstract: |-
    For a category C we consider the endomorphism category End(C) and the subcategory of automorphisms Aut(C) -> End(C). It has been observed that for C the category of finite sets, finite dimensional vector spaces, or compact metric spaces this inclusion functor admits a simultaneous left and right adjoint.

    We give general criteria for the existence of such adjunctions for a broad class of categories which includes FinSet, FinVect and CompMet as special cases. This is done using the language of factorisation systems and by introducing a notion of eventual image functors which provide a general method for constructing adjunctions of this kind.
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2016-09-14T11:40:00Z'
  endDate: '2016-09-14T12:40:00Z'
  title: MSP101 Planning session
  url: ''
  location: LT1310
  locationurl: ''
  description: ''
- tag: Talk
  date: '2016-08-24T16:00:00Z'
  speaker: Philippa Cowderoy
  institute: ''
  speakerurl: http://flippac.org
  insturl: ''
  title: Information Effects for Understanding Type Systems
  abstract: 'Or: how someone else found the maths to justify my dogma'
  location: LT1415
  material:
  - tag: PDF
    slideName: 2016-08-24_cowderoy.pdf
    comment: 'Philippa says: beware, slightly wordy slides!'
  - tag: File
    path: 2016-08-24_cowderoy/STLC.hs
    fileDescription: Haskell implementation for simply-typed lambda calculus
- tag: Talk
  date: '2016-07-01T14:00:00Z'
  speaker: Kevin Dunne
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: A New Perspective On Observables in the Category of Relations
  abstract: Practice talk for Quantum Interactions.
  location: LT1415
  material: []
- tag: Talk
  date: '2016-07-01T14:00:00Z'
  speaker: Ross Duncan
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/ross.duncan/
  insturl: ''
  title: Interacting Frobenius Algebras are Hopf
  abstract: |-
    Practice talk for LICS.

    Theories featuring the interaction between a Frobenius algebra and a Hopf algebra have recently appeared in several areas in computer science: concurrent programming, control theory, and quantum computing, among others. Bonchi, Sobocinski, and Zanasi have shown that, given a suitable distribution law, a pair of Hopf algebras forms two Frobenius algebras. Coming from the perspective of quantum theory, we take the opposite approach, and show that interacting Frobenius algebras form Hopf algebras. We generalise \cite{Bonchi2014a} by including non-trivial dynamics of the underlying object &ndash; the so-called phase group &ndash; and investigate the effects of finite dimensionality of the underlying model, and recover the system of Bonchi et al as a subtheory in the prime power dimensional case. We show that the presence of a non-trivial phase group means that the theory cannot be formalised as a distributive law.
  location: LT1415
  material: []
- tag: SpecialEvent
  date: '2016-06-06T09:00:00Z'
  endDate: '2016-06-06T17:00:00Z'
  title: Quantum Physics and Logic 2016
  url: http://qpl2016.cis.strath.ac.uk/
  location: McCance building, Strathclyde
  locationurl: http://www.strath.ac.uk/maps/mccancebuilding/
  description: ''
- tag: Talk
  date: '2016-06-01T12:00:00Z'
  speaker: Kevin Dunne
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Interacting Frobenius algebras
  abstract: |-
    Practice talk for QPL.

    Theories featuring the interaction between a Frobenius algebra and a Hopf algebra have recently appeared in several areas in computer science: concurrent programming, control theory, and quantum computing, among others. Bonchi, Sobocinski, and Zanasi (2014) have shown that, given a suitable distributive law, a pair of Hopf algebras forms two Frobenius algebras. Here we take the opposite approach, and show that interacting Frobenius algebras form Hopf algebras. We generalise (BSZ 2014) by including non-trivial dynamics of the underlying object &ndash; the so-called phase group &ndash; and investigate the effects of finite dimensionality of the underlying model. We recover the system of Bonchi et al as a subtheory in the prime power dimensional case, but the more general theory does not arise from a distributive law.
  location: LT1310
  material: []
- tag: Talk
  date: '2016-05-04T11:00:00Z'
  speaker: Kevin Dunne
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Factorisation Systems and Algebra
  abstract: I'll show how to generalise some results from algebra (think groups, rings,
    R-modules etc.) to a categorical setting using factorisation systems and an appropriate
    notion of finiteness on the objects of a category.
  location: LT1310
  material: []
- tag: Talk
  date: '2016-04-27T11:00:00Z'
  speaker: Guillaume Allais
  institute: Radboud University Nijmegen
  speakerurl: http://gallais.org
  insturl: ''
  title: Typing with Leftovers
  abstract: ''
  location: LT1310
  material: []
- tag: DepartmentalSeminar
  date: '2016-04-19T16:00:00Z'
  speaker: Andreas Abel
  institute: Chalmers and Gothenburg University
  speakerurl: http://www.cse.chalmers.se/~abela/
  insturl: http://www.chalmers.se/en/departments/cse/Pages/default.aspx
  title: Formal languages, coinductively formalized
  abstract: |-
    Formal languages and automata are taught to every computer science student. However, the student will most likely not see the beautiful coalgebraic foundations.

    In this talk, I recapitulate how infinite trees can represent formal languages (sets of strings). I explain Agda's coinduction mechanism based on copatterns and demonstrate that it allows an elegant representation of the usual language constructions like union, concatenation, and Kleene star, with the help of Brzozowski derivatives. We will also investigate how to reason about equality of languages using bisimulation and coinductive proofs.
  location: LT1415
- tag: SpecialEvent
  date: '2016-04-14T10:30:00Z'
  endDate: '2016-04-14T17:00:00Z'
  title: Categories, Logic, and Physics, Scotland
  url: http://homepages.inf.ed.ac.uk/cheunen/clapscotland/
  location: " School of Informatics, Edinburgh"
  locationurl: ''
  description: ''
- tag: Talk
  date: '2016-03-31T10:30:00Z'
  speaker: ''
  institute: ''
  speakerurl: ''
  insturl: ''
  title: Presentations by candidates for the 'Coalgebraic Foundations of Semi-Structured
    Data' RA position
  abstract: ''
  location: LT1415
  material: []
- tag: DepartmentalSeminar
  date: '2016-03-23T16:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: A static analyser for concurrent Java
  abstract: |-
    ThreadSafe is a static analysis tool for finding bugs in concurrent Java code that has been used by companies across the world to analyse and find bugs in large mission industrial applications. I will talk about how ThreadSafe works, and our experiences in applying static analysis technology to the "real world".

    ThreadSafe is available from <a href='http://www.contemplateltd.com/'>http://www.contemplateltd.com/</a>
  location: LT1415
- tag: DepartmentalSeminar
  date: '2016-05-25T15:30:00Z'
  speaker: Neil Ghani
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/neil.ghani/
  insturl: ''
  title: A Compositional Approach to Game Theory
  abstract: |-
    I will sketch an alternative approach to economic game theory based upon the computer science idea of compositionality: concretely we i) give a number of operators for building up complex and irregular games from smaller and simpler games; and ii) show how the Nash equilibrium of these complex games can be defined recursively from their simpler components. We apply compositional reasoning to sophisticated games where agents must reason about how their actions affect future games and how those future games effect the utility they receive. This forces us into a second innovation &mdash; we augment the usual lexicon of games with a dual notion to utility because, in order for games to accept utility, this utility must be generated by other games. Our third innovation is to represent our games as string diagrams so as to give a clear visual interface to manipulate them. Our fourth, and final, innovation is a categorical formalisation of these intuitive diagrams which ensures our reasoning about them is fully rigorous.

    The talk will be general so as appeal to as wide an audience as possible. In particular, no knowledge of category theory will be assumed!
  location: LT908
- tag: Talk
  date: '2016-03-17T11:00:00Z'
  speaker: Nicolas Behr
  institute: Edinburgh
  speakerurl: http://www.inf.ed.ac.uk/people/staff/Nicolas_Behr.html
  insturl: http://wcms.inf.ed.ac.uk/lfcs/
  title: On the rule algebraic reformulation of graph rewriting
  abstract: |-
    Motivated by the desire to understand the combinatorics of graph rewriting systems, it proved necessary to invent a formulation of graph rewriting itself that is not based on category theoretic structures as in the traditional framework, but on the concept of diagrammatic combinatorial Hopf algebras and reductions thereof. In this talk, I will present how the classical example of the Heisenberg-Weyl algebra of creation and annihilation of indistinguishable particles, which can alternatively be interpreted as the algebra of discrete graph rewriting, gave the initial clues for this novel framework. In hindsight, to pass from the special case of discrete graph rewriting to the case of general graph rewriting required every aspect of the framework of diagrammatic combinatorial Hopf algebras as a guideline for the construction, yet none of the traditional category theoretic ideas, whence one might indeed consider this reformulation as an independent formulation of graph rewriting.

    The new framework results in a number of surprising results even directly from the formulation itself: besides the two main variants of graph rewriting known in the literature (DPO and SPO rewriting), there exist two more natural variants in the new framework. For all four variants, graph rewriting rules are encoded in so-called rule diagrams, with their composition captured in the form of diagrammatic compositions followed by one of four variants of reduction operations. Besides the general structure theory of the resulting algebras aka the rule algebras, one of the most important results to date of this framework in view of applications is the possibility to formulate stochastic graph rewriting systems in terms of the canonical representations of the rule algebras. Notably, this is closely analogous to the formulation of chemical reaction systems in terms of the canonical representation of the Heisenberg-Weyl algebra aka the bosonic Fock space. The presentation will not assume any prior knowledge of the audience on the particular mathematics required for this construction, and will be given on the whiteboard. The work presented is the result of a collaboration with Vincent Danos and Ilias Garnier (ENS Paris/LFCS University of Edinburgh), and (in an earlier phase) with Tobias Heindel (University of Copenhagen).
  location: LT1310
  material: []
- tag: Talk
  date: '2016-03-03T11:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: Comprehensive Parametric Polymorphism
  abstract: |-
    In this talk, we explore the fundamental category-theoretic structure needed to model relational parametricity (i.e., the fact that polymorphic programs preserve all relations) for the polymorphic lambda calculus (a.k.a. System F). Taken separately, the notions of categorical model of impredicative polymorphism and relational parametricity are well-known (lambda2-fibrations and reflexive graph categories, respectively). Perhaps surprisingly, simply combining these two structures results in a notion that only enjoys the expected properties in case the underlying category is well-pointed. This rules out many categories of interest (e.g. functor categories) in the semantics of programming languages.

    To circumvent this restriction, we modify the definition of fibrational model of impredicative polymorphism by adding one further ingredient to the structure: comprehension in the sense of Lawvere. Our main result is that such comprehensive models, once further endowed with reflexive-graph-category structure, enjoy the expected consequences of parametricity. This is proved using a type-theoretic presentation of the category-theoretic structure, within which the desired consequences of parametricity are derived. Working in this type theory requires new techniques, since equality relations are not available, so that standard arguments that exploit equality need to be reworked.

    This is joint work with Neil Ghani and Alex Simpson, and a dry run for a talk in Cambridge the week after.
  location: LT1310
  material: []
- tag: Talk
  date: '2016-01-26T15:00:00Z'
  speaker: Aleks Kissinger
  institute: Nijmegen
  speakerurl: http://www.cs.ru.nl/A.Kissinger/
  insturl: http://www.ru.nl/ds/
  title: Rewriting modulo symmetric monoidal structure
  abstract: |-
    String diagrams give a powerful graphical syntax for morphisms in symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and control theory.

    An important role in many such approaches is played by equational theories of diagrams, which can be oriented and used as rewrite systems. In this talk, I'll lay the foundations for this form of rewriting by interpreting diagrams combinatorially as typed hypergraphs and establish the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting of hypergraphs, subject to a soundness condition called convexity, on the other. This result rests on a more general characterisation theorem in which we show that typed hypergraph DPO rewriting amounts to diagram rewriting modulo the laws of SMCs with a chosen special Frobenius structure.

    If there's time, I'll also discuss some of the results we have in developing the rewrite theory of hypergraphs for SMCs, namely termination proofs via graph metrics and strongly convex critical pair analysis.
  location: LT1310
  material: []
- tag: Talk
  date: '2016-01-26T10:30:00Z'
  speaker: John Power
  institute: Bath
  speakerurl: http://www.bath.ac.uk/comp-sci/contacts/academics/john_power/
  insturl: http://www.bath.ac.uk/comp-sci/
  title: Enriched Lawvere Theories
  abstract: In this talk, we consider extending Lawvere theories to allow enrichment
    in a base category such as CMonoid, Poset or Cat. In doing so, we see that we
    need to alter the formulation in a fundamental way, using the notion of cotensor,
    a kind of limit that is hidden in the usual accounts of ordinary category theory
    but is fundamental to enriched category theory. If time permits, we will briefly
    consider the specific issues that arise when one has two-dimensional structure
    in the enriching category, as exemplified by Poset and Cat.
  location: LT1310
  material: []
- tag: Talk
  date: '2016-01-25T10:30:00Z'
  speaker: John Power
  institute: Bath
  speakerurl: http://www.bath.ac.uk/comp-sci/contacts/academics/john_power/
  insturl: http://www.bath.ac.uk/comp-sci/
  title: Lawvere Theories
  abstract: 'In 1963, Bill Lawvere characterised universal algebra in category theoretic
    terms. His formulation being category theoretic was not its central contribution:
    more fundamental was its presentation independence. Three years later, monads
    were proposed as another category theoretic formulation of universal algebra.
    Overall, the former are technically better but the relationship is particularly
    fruitful and the latter are more prominent, cf Betamax vs VHS. So we study Lawvere
    theories carefully in the setting of universal algebra and in relation to monads.'
  location: LT1310
  material: []
- tag: Talk
  date: '2016-02-25T11:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Excuse My Extrusion
  abstract: |-
    I have recently begun to learn about the Cubical Type Theory of Coquand et al., as an effective computational basis for Voevodsky's Univalent Foundations, inspired by a model of type theory in cubical sets. It is in some ways compelling in its simplicity, but in other ways intimidating in its complexity. In order to get to grips with it, I have begun to develop my own much less subtle variation on the theme. If I am lucky, I shall get away with it. If I am unlucky, I shall have learned more about why Cubical Type Theory has to be as subtle as it is.

    My design separates Coquand's all-powerful "compose" operator into smaller pieces, dedicated to more specific tasks, such as transitivity of paths. Each type path Q : S = T, induces a notion of value path s {Q} t, where either s : S, or s is •, "blob", and similarly, t : T or t = •. A "blob" at one end indicates that the value at that end of the path is not mandated by the type. This liberalisation in the formation of "equality" types allows us to specify the key computational use of paths between types, extrusion:

    if Q : S = T and s : S, then s ⌢• Q : s {Q} •

    That is, whenever we have a value s at one end of a type path Q : S = T, we can extrude that value across the type path, getting a value path which is s at the S end, but whose value at the T end is not specified in advance of explaining how to compute it. Extrusion gives us a notion of coercion-by-equality which is coherent by construction. It is defined by recursion on the structure of type paths. Univalence can be added to the system by allowing the formation of types interpolating two equivalent types, with extrusion demanding the existence of the corresponding interpolant values, computed on demand by means of the equivalence.

    So far, there are disconcerting grounds for optimism, but the whole of the picture has not yet emerged: I may just have pushed the essential complexity into one corner, or the whole thing may be holed below the waterline. But if it does turn out to be nonsense, it will be nonsense for an interesting reason.
  location: LT1310
  material: []
- tag: Talk
  date: '2016-02-18T14:00:00Z'
  speaker: Clemens Kupke
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/clemens.kupke/
  insturl: ''
  title: Coalgebraic Dynamic Logics
  abstract: I will present work in progress on a (co)algebraic framework that allows
    to uniformly study dynamic modal logics such as Propositional Dynamic Logic (PDL)
    and Game Logic (GL). Underlying our framework is the basic observation that the
    program/game constructs of PDL/GL arise from monad structure, and that the axioms
    of these logics correspond to compatibility requirements between the modalities
    and this monad structure. So far we have a general soundness and completeness
    result for PDL-like logics wrt T-coalgebras for a monad T. I will discuss our
    completeness theorem, its limitations and plans for extending our results. [For
    the latter we might require the help of koalas, wallabies and wombats.]
  location: LT1310
  material: []
- tag: Talk
  date: '2016-02-11T11:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: Introduction to (infinity, 1)-categories
  abstract: 'Infinity-categories simultaneously generalise topological spaces and
    categories. Intuitively, a (weak) infinity-category should have objects, morphisms,
    2-morphisms, 3-morphisms, ... and identity morphisms and composition which is
    suitably unital and associative up to a higher (invertible) morphism (the number
    1 in (infinity, 1)-category means that k-morphisms for k &gt; 1 are invertible)
    . The trouble begins when one naively tries to make these coherence conditions
    precise; already 4-categories famously requires <a href=''http://math.ucr.edu/home/baez/trimble/tetracategories.html''>51
    pages to define explicitly</a>. Instead, one typically turns to certain "models"
    of infinity-categories that encode all this data implicitly, usually as some kind
    of simplicial object with additional properties. I will introduce two such models:
    quasicategories and complete Segal spaces. If time allows, I will also discuss
    hopes and dreams about internalising these notions in Type Theory, which should
    give a satisfactory treatment of category theory in Type Theory without assuming
    Uniqueness of Identity Proofs.'
  location: LT1310
  material: []
- tag: Talk
  date: '2016-02-04T11:00:00Z'
  speaker: Neil Ghani
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/neil.ghani/
  insturl: ''
  title: Two Constructions on Games
  abstract: I've been working with Jules Hedges on a compositional model of game theory.
    After briefly reminding you of the model, I'll discuss where we are at &ndash;
    namely the definition of morphisms between games, and the treatment of choice
    and iteration of games. I'm hoping you will be able to shed some light on this
    murky area. There is a draft paper if anyone is interested.
  location: LT1310
  material: []
- tag: Talk
  date: '2016-01-28T11:00:00Z'
  speaker: Kevin Dunne
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Introduction to sheaves
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2016-01-21T11:00:00Z'
  speaker: Guillaume Allais
  institute: MSP
  speakerurl: http://gallais.org
  insturl: ''
  title: 'Overview: A Type Theory for Probabilistic and Bayesian Reasoning'
  abstract: "The probabilistic calculus introduced in the eponymous paper by Robin
    Adams and Bart Jacobs is inspired by quantum theory by considering that conditional
    probabilities can be seen as side-effect-free measurements. A type-theoretic treatment
    of this semantic observation leads, once equipped with suitable computation rules,
    to the ability to do exact conditional inference.\n\nI will present the type theory
    and the accompanying computation rules proposed in the paper and discuss some
    of the interesting open questions I will be working on in the near future. "
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2016-01-13T13:40:00Z'
  endDate: '2016-01-13T14:40:00Z'
  title: MSP101 Planning session
  url: ''
  location: LT1310
  locationurl: ''
  description: ''
- tag: Talk
  date: '2015-12-02T11:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: Introduction to coherence spaces, and how to use them for dependent session
    types
  abstract: |-
    Coherence spaces are a simplification of Scott domains, introduced by Girard to give a semantics to the polymorphic lambda-calculus. While investigating the structure of coherence spaces, Girard noticed that the denotation of the function type in coherence spaces can be decomposed into two independent constructions: a linear ("use-once") function space, and a many-uses-into-one-use modality. And so Linear Logic was discovered.

    Coherence spaces are interesting because they model computation at a low level in terms of interchange of atomic 'tokens' of information. This makes them a useful tool for understanding several different computational phenomena.

    In this talk, I'll show how coherence spaces naturally model session types, via Wadler's interpretation of Classical Linear Logic as a session-typed pi-calculus, and how that interpretation extends to an interpretation of a dependently typed version of session types.
  location: LT1310
  material: []
- tag: Talk
  date: '2015-11-18T11:00:00Z'
  speaker: Bram Westerbaan
  institute: Nijmegen
  speakerurl: http://bram.westerbaan.name/home/
  insturl: http://www.ru.nl/icis/
  title: The categorical structure of von Neumann algebras
  abstract: I would like to speak about the categorical structure of the category
    of von Neumann algebras, with as morphisms normal, completely positive, unital
    linear maps.  For some years my colleagues and I have worked on identifying basic
    structures in this category, and while surprisingly many things do not exist or
    do not work in this category (it's not a topos or even an extensive category,
    there's no epi-mono factorisation system, there is no dagger, colimits &mdash;
    if they exist at all &mdash; are horrendous...), we did find some structure (the
    products behave reasonable in some sense, there is a 'quotient', and 'comprehension',
    and we have a universal property for the minimal Stinespring dilation, and a universal
    property for M_2&mdash;the qubit).  There is no deep category theory involved
    by any standards, and I promise I will spare you the functional analysis, so it
    should be a light talk.
  location: LT1310
  material: []
- tag: Talk
  date: '2015-11-11T11:00:00Z'
  speaker: Clemens Kupke
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/clemens.kupke/
  insturl: ''
  title: The Power of Coalitions
  abstract: Due to popular demand I am going to give a brief introduction to Marc
    Pauly's Coalition Logic, a propositional modal logic that allows to reason about
    the power of coalitions in strategic games. I will provide motivation and basic
    definitions. Furthermore I am planning to discuss how the logic can be naturally
    viewed as a coalgebraic logic and what we gain from the coalgebraic perspective.
    Finally &mdash; if (preparation) time permits &mdash; I am going to say how the
    logic can be applied to the area of mechanism design.
  location: LT1310
  material: []
- tag: Talk
  date: '2015-10-22T15:00:00Z'
  speaker: Viktor Winschel
  institute: ETH Zurich
  speakerurl: http://www.vikwin.de/
  insturl: http://www.irme.ethz.ch/
  title: Semantics for Social Systems where Theory about the System Changes the System
  abstract: 'In societies the notion of a law is not given by nature. Instead social
    dynamics are driven by the theories the citizens have about the dynamics of the
    social system. Obviously self-referential mathematical structures, developed in
    computer science, are candidates to be applied in social sciences for this foundational
    issue. We will see a prototypical game theoretical problem where several computer
    scientific tools can help to discuss these structures. It is a long standing problem
    in economics and of human kind and their scarce recourses: "should we go to a
    bar that is always so overcrowded"?'
  location: LT1415
  material: []
- tag: Talk
  date: '2015-10-06T15:00:00Z'
  speaker: Alessandra Palmigiano
  institute: TU Delft
  speakerurl: http://www.appliedlogictudelft.nl/alessandra-palmigiano/
  insturl: http://www.appliedlogictudelft.nl/
  title: Proof-theoretic semantics for dynamic logics
  abstract: |-
    Research in the proof theory of dynamic logics has recently gained momentum. However, features which are essential to these logics prevent standard proof-theoretic methodologies to apply straightforwardly. In this talk, I will discuss the main properties proof systems should enjoy in order to serve as suitable environments for an inferential theory of meaning (proof-theoretic semantics). Then, I'll identify the main challenges to the inferential semantics research agenda posed by the very features of dynamic logics which make them so appealing and useful to applications. Finally, I'll illustrate a methodology generating multi-type display calculi, which has been successful on interesting case studies (dynamic epistemic logic, propositional dynamic logic, monotone modal logic).

    References

    1. S. Frittella, G. Greco, A. Kurz, A. Palmigiano, V. Sikimić, A Proof-Theoretic Semantic Analysis of Dynamic Epistemic Logic, Journal of Logic and Computation, Special issue on Substructural logic and information dynamics (2014), DOI:10.1093/logcom/exu063.

    2. S. Frittella, G. Greco, A. Kurz, A. Palmigiano, V. Sikimić, Multi-type Display Calculus for Dynamic Epistemic Logic, Journal of Logic and Computation, Special issue on Substructural logic and information dynamics (2014), DOI:10.1093/logcom/exu068.

    3. S. Frittella, G. Greco, A. Kurz, A. Palmigiano, Multi-type Display Calculus for Propositional Dynamic Logic, Special issue on Substructural logic and information dynamics (2014), DOI:10.1093/logcom/exu064.

    4. S. Frittella, G. Greco, A. Kurz, A. Palmigiano, V. Sikimić, Multi-type Sequent Calculi, Proc. Trends in Logic XIII, A. Indrzejczak,  J. Kaczmarek, M. Zawidski eds, p 81-93, 2014.

    5. G. Greco, A. Kurz, A. Palmigiano, Dynamic Epistemic Logic Displayed,  Proc.  Fourth International Workshop on Logic, Rationality and Interaction (LORI 2013) Eds: Huaxin Huang, Davide Grossi, Olivier Roy eds, 2013.
  location: LT1415
  material:
  - tag: PDF
    slideName: 2015-10-06_palmigiano.pdf
    comment:
- tag: Talk
  date: '2015-09-25T16:00:00Z'
  speaker: Pierre Lescanne
  institute: ENS Lyon
  speakerurl: http://perso.ens-lyon.fr/pierre.lescanne/
  insturl: http://www.ens-lyon.fr/LIP/PLUME/
  title: Coinduction, Equilibrium and Rationality of Escalation
  abstract: Escalation is the behavior of players who play forever in the same game.  Such
    a situation is a typical field for application of coinduction which is the tool
    conceived for reasoning in infinite mathematical structures. In particular, we
    use coinduction to study formally the game called <i>dollar auction</i>, which
    is considered as the paradigm of escalation.  Unlike what is admitted since 1971,
    we show that, provided one assumes that the other agent will always stop, bidding
    is rational, because it results in a subgame perfect equilibrium.  We show that
    this is not the only rational strategy profile (the only subgame perfect equilibrium).  Indeed
    if an agent stops and will stop at every step, whereas the other agent keeps bidding,
    we claim that he is rational as well because this corresponds to another subgame
    perfect equilibrium.  In the infinite dollar auction game the behavior in which
    both agents stop at each step is not a Nash equilibrium, hence is not a subgame
    perfect equilibrium, hence is not rational.  Fortunately, the notion of rationality
    based on coinduction fits with common sense and experience.  Finally the possibility
    of a rational escalation in an arbitrary game can be expressed as a predicate
    on games and the rationality of escalation in the dollar auction game can be proved
    as a theorem which we have verified in the proof assistant COQ.  In this talk
    we will recall the principles of infinite extensive games and use them to introduce
    coinduction and equilibria (Nash equilibrium, subgame perfect equilibrium).  We
    will show how one can prove that the two strategy profiles presented above are
    equilibria and how this leads to a "rational" escalation in the dollar auction.  We
    will show that escalation may even happen in much simpler game named 0,1-game.
  location: LT1415
  material: []
- tag: Talk
  date: '2015-10-28T11:00:00Z'
  speaker: Ross Duncan
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/ross.duncan/
  insturl: ''
  title: Interacting Frobenius Algebras Are Hopf
  abstract: |-
    Commutative Frobenius algebras play an important role in both Topological Quantum Field Theory and Categorical Quantum Mechanics;  in the first case they correspond to 2D TQFTs, while in the second they are non-degenerate observables.  I will consider the case of "special" Frobenius algebras, and their associated group of phases.  This gives rise to a free construction from the category of abelian groups to the PROP generated by this Frobenius algebra.  Of course a theory with only one observable is not very interesting.  I will consider how two such PROPs should be combined, and show that if the two algebras (i) jointly form a bialgebra and (ii) their units are "mutually real"; then they jointly form a Hopf algebra.  This gives a "free" model of a pair of strongly complementary observables.  I will also consider which unitary maps must exist in such models.

    Slides are <a href='http://personal.strath.ac.uk/ross.duncan/talks/2015/vienna.pdf'>here</a> if you want a preview.
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2015-10-21T12:30:00Z'
  endDate: '2015-10-21T17:00:00Z'
  title: SPLS
  url: http://simonjf.com/spls-oct2015/
  location: Edinburgh
  locationurl: ''
  description: ''
- tag: Talk
  date: '2015-10-14T11:00:00Z'
  speaker: Guillaume Allais
  institute: MSP
  speakerurl: http://gallais.org
  insturl: ''
  title: Type and Scope Preserving Semantics
  abstract: |-
    We introduce a notion of type and scope preserving semantics  generalising Goguen and McKinna's "Candidates for Substitution" approach to defining one traversal generic enough to be instantiated to renaming first and then substitution. Its careful distinction of environment and model values as well as its variation on a structure typical of a Kripke semantics make it capable of expressing renaming and substitution but also various forms of Normalisation by Evaluation as well as, perhaps more surprisingly, monadic computations such as a printing function.

    We then demonstrate that expressing these algorithms in a common framework yields immediate benefits: we can deploy some logical relations generically over these instances and obtain for instance the fusion lemmas for renaming, substitution and normalisation by evaluation as simple corollaries of the appropriate fundamental lemma. All of this work has been formalised in Agda.
  location: LT1310
  material:
  - tag: PDF
    slideName: 2015-10-21_gallais.pdf
    comment:
  - tag: Link
    address: https://github.com/gallais/type-scope-semantics
    linkDescription: Github repository with paper and sources
- tag: SpecialEvent
  date: '2015-10-07T12:00:00Z'
  endDate: '2015-10-07T17:00:00Z'
  title: STP
  url: http://staff.computing.dundee.ac.uk/christopherwarburton/stp/2015/10/
  location: Dundee
  locationurl: ''
  description: ''
- tag: Talk
  date: '2015-09-30T11:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: ICFP trip report
  abstract: ''
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2015-09-23T11:30:00Z'
  endDate: '2015-09-23T12:30:00Z'
  title: MSP101 Planning session
  url: ''
  location: LT1310
  locationurl: ''
  description: ''
- tag: Talk
  date: '2015-09-16T11:00:00Z'
  speaker: Giovanni Ciná
  institute: Amsterdam
  speakerurl: https://sites.google.com/site/homepagegcina/
  insturl: http://www.illc.uva.nl/
  title: Contextuality, path logic and a modal logic for Social Choice Theory
  abstract: 'Social Choice functions are procedures used to aggregate the preferences
    of individuals into a collective decision. We outline two recent abstract approaches
    to SCFs: a recent sheaf treatment of Arrow''s Theorem by Abramsky and a modal
    logic studied by Ulle Endriss and myself. We show how to relate the categorical
    modelling of Social Choice problems to said work in Modal Logic. This insight
    prompts a number of research questions, from the relevance of sheaf-like condition
    to the modelling of properties of SCFs on varying electorates.'
  location: LT1310
  material: []
- tag: Talk
  date: '2015-09-02T11:00:00Z'
  speaker: Ross Duncan
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/ross.duncan/
  insturl: ''
  title: Concurrent games
  abstract: ''
  location: LT1310
  material:
  - tag: Whiteboard
    dirName: 2015-09-02_Ross
- tag: Talk
  date: '2015-08-13T15:00:00Z'
  speaker: Jeremy Siek
  institute: Indiana University
  speakerurl: http://wphomes.soic.indiana.edu/jsiek/
  insturl: http://lambda.soic.indiana.edu/home
  title: The Polymorphic Blame Calculus and Parametricity
  abstract: The Polymorphic Blame Calculus (PBC) of Ahmed et al. (2011) combines polymorphism,
    as in System F, with type dynamic and runtime casts, as in the Blame Calculus.
    The PBC is carefully designed to ensure relational parametricity, that is, to
    ensure that type abstractions do not reveal their abstracted types. The operational
    semantics of PBC uses runtime sealing and syntactic barriers to enforce parametricity.
    However, it is an open question as to whether these mechanisms actually guarantee
    parametricity for the PBC. Furthermore, there is some question regarding what
    parametricity means in the context of the PBC, as we have examples that are morally
    parametric but not technically so. This talk will review the design of the PBC
    with respect to ensuring parametricity and hopefully start a discussion regarding
    what parametricity should mean for the PBC.
  location: LT1415
  material:
  - tag: PDF
    slideName: 2015-08-13_siek.pdf
    comment:
- tag: Talk
  date: '2015-08-26T11:00:00Z'
  speaker: Kevin Dunne
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Comonadic Cellular Automata II
  abstract: This is a sequel to my last 101 where I spoke about describing cellular
    automata as algebras of a comonad on Set. I'll describe how we can make sense
    of "generalised cellular automata" (probabilistic/non-deterministic/quantum, for
    example) as comonads on other categories via distributive laws of monads and comonads.
  location: LT1310
  material: []
- tag: Talk
  date: '2015-07-23T11:00:00Z'
  speaker: Ross Duncan
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/ross.duncan/
  insturl: ''
  title: Free interacting observables
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2015-05-26T16:00:00Z'
  speaker: Paul Levy
  institute: Birmingham
  speakerurl: http://www.cs.bham.ac.uk/~pbl/
  insturl: http://www.cs.bham.ac.uk/
  title: Final coalgebras from corecursive algebras
  abstract: |-
    We give a technique to construct a final coalgebra out of modal logic.  An element of the final coalgebra is a set of modal formulas.  The technique works for both the finite and the countable powerset functors.  Starting with a corecursive algebra, we coinductively obtain a suitable subalgebra.  We see - first with an example, and then in the general setting of modal logic on a dual adjunction - that modal theories form a corecursive algebra, so that this construction may be applied.

    We generalize the framework to categories other than Set, and look at examples in Poset and in the opposite category of Set.
  location: LT1415
  material: []
- tag: Talk
  date: '2015-05-13T11:00:00Z'
  speaker: Federico Orsanigo
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Two-dimensional proof-relevant parametricity
  abstract: |-
    Relational parametricity is a fundamental concept within theoretical computer science and the foundations of programming languages, introduced by John Reynolds. His fundamental insight was that types can be interpreted not just as functors on the category of sets, but also as equality preserving functors on the category of relations. This gives rise to a model where polymorphic functions are uniform in a suitable sense; this can be used to establish e.g. representation independence, equivalences between programs, or deriving useful theorems about programs from their type alone.

     The relations Reynolds considered were proof-irrelevant, which from a type theoretic perspective is a little limited. As a result, one might like to extend his work to deal with proof-relevant, i.e. set-valued relations. However naive attempts to do this fail: the fundamental property of equality preservation cannot be established. Our insight is that just as one uses parametricity to restrict definable elements of a type, one can use parametricity of proofs to ensure equality preservation. The idea of parametricity for proofs can be formalised using the idea of 2-dimensional logical relations. Interestingly, these 2-dimensional relations have clear higher dimensional analogues where (n+1)-relations are fibered over a n-cube of n-relations. Thus the story of proof relevant logical relations quickly expands into one of higher dimensional structures similar to the cubical sets which arises in Homotopy Type Theory. Of course, there are also connections to Bernardy and Moulin's work on internal parametricity.
  location: LT1310
  material: []
- tag: DepartmentalSeminar
  date: '2015-05-08T15:00:00Z'
  speaker: Svante Linusson
  institute: KTH, Stockholm
  speakerurl: https://people.kth.se/~linusson/
  insturl: https://www.kth.se/en/sci/institutioner/math
  title: The probability of the Alabama paradox
  abstract: |-
    There exists various possible methods to distribute seats proportionally between states (or parties) in a parliament. Hamilton's method (also known as the method of largest reminder) was abandoned in the USA because of some drawbacks, in particular the possibility of the Alabama paradox, but it is still in use in many other countries.

    In recent work (joint with Svante Janson) we give, under certain assumptions, a closed formula for the probability that the Alabama paradox occurs given the vector p_1,...,p_m of relative sizes of the states.

    From the theorem we deduce a number of consequences. For example it is shown that the expected number of states that will suffer from the Alabama paradox is asymptotically bounded above by 1/e. For random (uniformly distributed) relative sizes p_1,...,p_m the expected number of states to suffer from the Alabama paradox converges to slightly more than a third of this, or approximately 0.335/e=0.123, as m -> infinity.

     I will assume no prior knowledge of electoral mathematics, but begin by giving a brief background to various methods suggested and used for the distribution of seats proportionally in a parliament (it's all in the rounding).
  location: LT1415
- tag: Talk
  date: '2015-05-06T11:00:00Z'
  speaker: Jules Hedges
  institute: Queen Mary University of London
  speakerurl: http://www.eecs.qmul.ac.uk/~julesh/
  insturl: http://theory.eecs.qmul.ac.uk/
  title: Game theory in string diagrams
  abstract: We define a category whose morphisms are 'games relative to a continuation',
    designed to allow games to be built recursively from simple components. The resulting
    category has interesting structure similar to (but weaker than) compact closed,
    and comes with an associated string diagram language.
  location: LT1310
  material: []
- tag: Talk
  date: '2015-04-29T11:00:00Z'
  speaker: Bob Atkey
  institute: MSP
  speakerurl: http://bentnib.org
  insturl: ''
  title: An Introduction to Differential Privacy
  abstract: |-
    Let's say you have a database of people's private information. For SCIENCE, or some other reason, you want to let third parties query your data to learn aggregate information about the people described in the database. However, you have a duty to the people whose information your database contains not to reveal any of their individual personal information. How do you determine which queries you will let third parties execute, and those you will not?

    "Differential Privacy" defines a semantic condition on probabilistic queries that identifies queries that are safe to execute, up to some "privacy budget".

    I'll present the definition of differential privacy, talk a bit about why it is better than some 'naive' alternatives (e.g., anonymisation), and also describe how the definition can be seen as an instance of relational parametricity.

    A good place to read about the definition of differential privacy is the book "The Algorithmic Foundations of Differential Privacy" by Cynthia Dwork and Aaron Roth.
  location: LT1310
  material:
  - tag: Link
    address: 'http://www.cis.upenn.edu/~aaroth/Papers/privacybook.pdf '
    linkDescription: "<em>The Algorithmic Foundations of Differential Privacy</em>
      by Cynthia Dwork and Aaron Roth"
- tag: DepartmentalSeminar
  date: '2015-03-20T15:00:00Z'
  speaker: Chris Heunen
  institute: Oxford
  speakerurl: http://www.cs.ox.ac.uk/people/chris.heunen/
  insturl: http://www.cs.ox.ac.uk/
  title: Approximating transition systems
  abstract: Classical computation, invertible computation, probabilistic computation,
    and quantum computation, form increasingly more sophisticated labelled transition
    systems. How can we approximate a transition system by less sophisticated ones?
    Considering all ways to get probabilistic information out of a quantum system
    leads to domain-theoretic ideas, that also apply in the accompanying Boolean logic.
    I will survey to what extent these domains characterise the system, leading with
    examples from quantum theory, in a way that is accessible to a broad audience
    of computer scientists, mathematicians, and logicians.
  location: LT1415
- tag: DepartmentalSeminar
  date: '2015-04-29T15:00:00Z'
  speaker: Uli Kraehmer
  institute: University of Glasgow
  speakerurl: http://www.maths.gla.ac.uk/~ukraehmer/
  insturl: http://www.maths.gla.ac.uk/
  title: Cyclic homology from mixed distributive laws
  abstract: |-
    In pure mathematics, cyclic homology is an invariant of associative algebras that is motivated by algebra, topology and even mathematicial physics. However, when studied from an abstract point of view it turns out to be an invariant of a pair of a monad and a comonad that are related by a mixed distributive law, and I speculate that this could lead to some potential applications in computer science.

    (based on joint work with Niels Kowalzig and Paul Slevin)
  location: LT1415
- tag: Talk
  date: '2015-04-22T14:00:00Z'
  speaker: Guillaume Allais
  institute: MSP
  speakerurl: http://gallais.org
  insturl: ''
  title: 'Patterns to avoid: (dependent) stringly-typed programming'
  abstract: |-
    Type : Set
    Type = String -> Bool
  location: LT1310
  material:
  - tag: Link
    address: https://github.com/gallais/STRINaGda
    linkDescription: Github repository
- tag: Talk
  date: '2015-03-11T11:00:00Z'
  speaker: Peter Hancock
  institute: ''
  speakerurl: ''
  insturl: ''
  title: Collapsing
  abstract: <p>The topic comes from theory of infinitary proofs, and cut-elimination.  In
    essence it is about nicely-behaved maps from higher "infinities" to lower ones,
    as the infinitary proofs are er, infinite, and can be thought of as glorified
    transfinite iterators. What might nice behaviour mean?</p><p>You can think of
    it as how to fit an uncountable amount of beer into a bladder whose capacity is
    merely countable. (Or maybe even finite.)</p><p>The most ubiquitous form of infinity
    is the regular cardinal, iepassing from a container F to F + (mu F -> _), where
    mu is the W-type operation.  I'll "explain" regular collapsing as being all about
    diagonalisation.</p>
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2015-03-04T14:00:00Z'
  endDate: '2015-03-04T15:00:00Z'
  title: A HoTT-Date with Thorsten Altenkirch
  url: http://msp.cis.strath.ac.uk/hott-afternoon/
  location: LT1415
  locationurl: ''
  description: ''
- tag: SpecialEvent
  date: '2015-02-18T12:00:00Z'
  endDate: '2015-02-18T17:00:00Z'
  title: SPLS @ Strathclyde
  url: ''
  location: Royal College Building, room RC512
  locationurl: http://www.strath.ac.uk/maps/royalcollegebuilding/
  description: ''
- tag: Talk
  date: '2015-02-11T11:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Totality versus Turing Completeness?
  abstract: 'I gave an <a href=''http://www.dcs.gla.ac.uk/research/spls/Mar12/''>SPLS
    talk</a>, which was mostly propaganda, about why people should stop claiming that
    totality loses Turing completeness. There was some technical stuff, too, about
    representing a recursive definition as a construction in the free monad whose
    effect is calling out to an oracle for recursive calls: that tells you what it
    is to be recursive without prejudicing how to run it. I''m trying to write this
    up double-quick as a paper for the miraculously rubbery MPC deadline, with more
    explicit attention to the monad morphisms involved. So I''d be grateful if you
    would slap down the shtick and make me more morphic. The punchline is that the
    Bove-Capretta domain predicate construction is a (relative) monad morphism from
    the free monad with a recursion oracle to the (relative) monad of Dybjer-Setzer
    Induction-Recursion codes. But it''s worth looking at other monad morphisms (especially
    to the Delay monad) along the way.'
  location: LT1415
  material: []
- tag: Talk
  date: '2015-01-28T16:30:00Z'
  speaker: Tarmo Uustalu
  institute: Institute of Cybernetics, Tallinn
  speakerurl: http://www.cs.ioc.ee/~tarmo/
  insturl: http://cs.ioc.ee/
  title: Runners for your computations
  abstract: 'What structure is required of a set so that computations in a given notion
    of computation can be run statefully this with set as the state space? Some answers:
    To be able to serve stateful computations, a set must carry the structure of a
    lens; for running interactive I/O computations statefully, a "responder-listener"
    structure is necessary etc. I will observe that, in general, to be a runner of
    computations for an algebraic theory (defined as a set equipped with a monad morphism
    between the corresponding monad and the state monad for this set) is the same
    as to be a comodel of this theory, ie a coalgebra of the corresponding comonad.
    I will work out a number of instances. I will also compare runners to handlers.'
  location: LT1415
  material: []
- tag: Talk
  date: '2015-01-22T11:00:00Z'
  speaker: James Chapman
  institute: Institute of Cybernetics, Tallinn
  speakerurl: http://cs.ioc.ee/~james/
  insturl: http://cs.ioc.ee/
  title: Termination, later
  abstract: |-
    It would be a great shame if dependently-typed programming (DTP) restricted us to only writing very clever programs that were a priori structurally recursive and hence obviously terminating. Put another way, it is a lot to ask of the programmer to provide the program and its termination proof in one go, programmers should also be supported in working step-by-step. I will show a technique that lowers the barrier of entry, from showing termination to only showing productivity up front, and then later providing the opportunity to show termination (convergence). I will show an example of a normaliser for STLC represented in Agda as a potentially non-terminating but nonetheless productive corecursive function targeting the coinductive delay monad.

    (Joint work with  Andreas Abel)
  location: LT1310
  material: []
- tag: Talk
  date: '2014-12-17T11:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: Worlds, Types and Quantification
  abstract: 'I''ve managed to prove a theorem that I''ve been chasing for a while.
    The trouble, of course, was <em>stating</em> it. I''ll revisit the motivation
    for extending type systems with an analysis of not just <em>what</em> things are
    but <em>where</em>, <em>when</em>, <em>whose</em>, etc. The idea is that typed
    constructions occur in one of a preordered set of worlds, with scoping restricted
    so that information flows only "upwards" from one world to another. Worlds might
    correspond to "at run time" and "during typechecking", or to computation in distinct
    cores, or in different stages, etc. What does the dependent function space mean
    in this setting? For a long time, I thought that each world had its own universal
    quantifier, for abstracting over stuff from that world. Failure to question this
    presumption is what led to failure to state a theorem I could prove. By separating
    quantifiers from worlds, I have fixed the problem. I''ll show how to prove the
    key fact: if I can build something in one world and then move it to another, then
    it will also be a valid construction once it has arrived at its destination.'
  location: LT1310
  material: []
- tag: Talk
  date: '2014-12-10T11:00:00Z'
  speaker: Aleks Kissinger
  institute: Oxford
  speakerurl: http://www.cs.ox.ac.uk/people/aleks.kissinger/about.html
  insturl: http://www.cs.ox.ac.uk/activities/quantum/
  title: ZX and PROPs
  abstract: ''
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2014-12-03T14:00:00Z'
  endDate: '2014-12-03T15:00:00Z'
  title: HoTT reading group @ Strathclyde
  url: http://homepages.inf.ed.ac.uk/s1225336/hott-reading-group/
  location: LT1310
  locationurl: ''
  description: 'We will read the paper <a href=''http://drops.dagstuhl.de/opus/volltexte/2014/4628/pdf/7.pdf''>A
    Model of Type Theory in Cubical Sets</a> by <a href=''http://www.ii.uib.no/~bezem/''>Marc
    Bezem</a>, <a href=''http://www.cse.chalmers.se/~coquand/''>Thierry Coquand</a>
    and <a href=''http://www.cse.chalmers.se/~simonhu/''>Simon Huber</a>. Thierry''s
    <a href=''http://www.cse.chalmers.se/~coquand/comp.pdf''>Variation on cubical
    sets</a> might also be useful. <em>Administrative details</em>: meet for lunch
    at 12am for those who want to, reading group starts at 2pm.'
- tag: Talk
  date: '2014-11-19T12:00:00Z'
  speaker: Neil Ghani and Clemens Kupke
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Arrow's Theorem and Escalation
  abstract: Neil and Clemens will report back from the <a href='http://www.cs.le.ac.uk/people/akurz/lsb.html'>Lorentz
    Center Workshop on Logics for Social Behaviour</a>.
  location: LT1310
  material: []
- tag: Talk
  date: '2014-11-26T11:00:00Z'
  speaker: Ross Duncan
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/ross.duncan/
  insturl: ''
  title: Diagrammatic languages for monoidal categories
  abstract: Monoidal categories are essentially 2-dimensional things, so why on earth
    would we represent them using a linear string of symbols?  I'll talk about how
    to use string diagrams for monoidal categories, graph rewriting for reasoning
    within them, and how the syntax can be extended to handle certain kinds of infinitary
    expressions with the infamous !-box.  If there's time I'll finish with some half-baked
    (eh... basically still looking for the on switch of the oven...) ideas of how
    to generalise them.
  location: LT1310
  material: []
- tag: Talk
  date: '2014-11-06T09:00:00Z'
  speaker: Kevin Dunne
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Comonadic Cellular Automata
  abstract: Kevin will be giving an informal talk about some of the stuff he has been
    learning about. He'll give the definition of a cellular automaton and then talk
    about how this definition can be phrased in terms of a comonad.
  location: LT1310
  material: []
- tag: Talk
  date: '2014-11-05T11:00:00Z'
  speaker: Shin-ya Katsumata
  institute: Kyoto University
  speakerurl: http://www.kurims.kyoto-u.ac.jp/~sinya/index-e.html
  insturl: http://www.kurims.kyoto-u.ac.jp/en/index.html
  title: Logical Relations for Monads by Categorical TT-Lifting
  abstract: |-
    Logical relations are widely used to study various properties of typed lambda calculi. By extending them to the lambda calculus with monadic types, we can gain understanding of the properties on functional programming languages with computational effects. Among various constructions of logical relations for monads, I will talk about a categorical TT-lifting, which is a semantic analogue of Lindley and Stark's leapfrog method.

    After reviewing some fundamental properties of the categorical TT-lifting, we apply it to the problem of relating two monadic semantics of a call-by-value functional programming language with computational effects. This kind of problem has been considered in various forms: for example, the relationship between monadic style and continuation passing style representations of call-by-value programs was studied around '90s. We give a set of sufficient conditions to solve the problem of relating two monadic semantics affirmatively. These conditions are applicable to a wide range of such problems.
  location: Boardroom (LT1101d)
  material: []
- tag: Talk
  date: '2014-10-27T14:00:00Z'
  speaker: Dominic Orchard
  institute: Imperial College London
  speakerurl: http://www.cl.cam.ac.uk/~dao29/
  insturl: http://mrg.doc.ic.ac.uk/
  title: Constructing analysis-directed semantics
  abstract: 'All kinds of semantics are syntax directed: the semantics follows from
    the syntax. Some varieties of semantics are syntax and type directed. In this
    talk, I''ll discuss syntax, type, <em>and</em> analysis directed semantics (analysis-directed
    semantics for short!), for analyses other than types. An analysis-directed semantics
    maps from terms coupled with derivations of a static program analysis into some
    semantic domain. For example, the simply-typed lambda calculus with an effect
    system maps to the category generated by a strong parametric effect monad (due
    to Katsumata) and a bounded-linear logic-like analysis (described as a coeffect
    systems) maps to a category generated by various structures related to monoidal
    comonads. I''ll describe a general technique for building analysis-directed semantics
    where semantic objects and analysis objects have the same structure and are coupled
    by lax homomorphisms between them. This aids proving semantic properties: the
    proof tree of an equality for two program analyses implies the rules needed to
    prove equality of the programs'' denotations.'
  location: Boardroom (LT1101d)
  material: []
- tag: Talk
  date: '2014-11-12T11:00:00Z'
  speaker: Peter Hancock
  institute: ''
  speakerurl: ''
  insturl: ''
  title: Lambda-abstraction and other diabolical contrivances
  abstract: The topic is the unholy trinity of eta, zeta, and xi. I'll indicate how
    Curry managed to give a finite combinatorial axiomatisation of this nastiness,
    by anticipating (almost-but-not-<em>quite</em>) McBride et al's applicative functors.
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2014-10-29T12:00:00Z'
  endDate: '2014-10-29T17:00:00Z'
  title: SICSA CSE Meeting on Effects and Coeffects Systems and their use for resource
    control
  url: http://staff.computing.dundee.ac.uk/marcogaboardi/effcoeff.html
  location: Dundee
  locationurl: ''
  description: ''
- tag: Talk
  date: '2014-10-22T11:00:00Z'
  speaker: Neil Ghani
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/neil.ghani/
  insturl: ''
  title: Higher dimensional parametricity and its cubical structure
  abstract: "Neil will talk about partial progress made during the summer on higher
    dimensional parametricity and the cubical structures that seem to arise. \nDetails
    will be kept to a minimum and, of course, concepts stressed."
  location: LT1310
  material: []
- tag: SpecialEvent
  date: '2014-10-15T12:00:00Z'
  endDate: '2014-10-15T17:00:00Z'
  title: SPLS
  url: http://www.macs.hw.ac.uk/~rs46/spls-hwu-q3-2014/
  location: Heriot Watt
  locationurl: ''
  description: ''
- tag: Talk
  date: '2014-10-08T11:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/conor.mcbride/
  insturl: ''
  title: '"Real-world data" and dependent types'
  abstract: Conor has offered to talk to us about what he has been thinking about
    recently. He says this includes models, views, and dependent types.
  location: LT1310
  material: []
- tag: Talk
  date: '2014-10-01T11:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: Initial algebras via strong dinaturality, internally
  abstract: |2-
      Or: My summer with Steve
    Or: How Christine and Frank were right, after all
    Or: Inductive types for the price of function extensionality and impredicative Set

     Christine Paulin-Mohring and Frank Pfenning suggested to use impredicative encodings of inductive types in the Calculus of Constructions, but this was later abandoned, since it is "well-known" that induction principles, i.e. dependent elimination,  can not be derived for this encoding. It now seems like it is  possible to give a variation of this encoding for which the  induction principle is derivable after all. The trick is to use  identity types to cut down the transformations of type  (Pi X : Set) . (F(X) -> X) -> X to the ones that are internally strongly dinatural, making use of a formula for a "generalised Yoneda Lemma" by Uustalu and Vene.
  location: LT1310
  material: []
- tag: Talk
  date: '2014-08-15T15:00:00Z'
  speaker: Fredrik Nordvall Forsberg
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/
  insturl: ''
  title: Internal parametricity
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2014-05-28T11:00:00Z'
  speaker: Ohad Kammar
  institute: Cambridge
  speakerurl: http://www.cl.cam.ac.uk/~ok259/
  insturl: http://www.cl.cam.ac.uk/
  title: Graphical algebraic foundations for monad stacks
  abstract: |-
    Ohad gave an informal overview of his current draft, with the following abstract:

    Haskell incorporates computational effects modularly using sequences of monad transformers, termed monad stacks. The current practice is to find the appropriate stack for a given task using intractable brute force and heuristics. By restricting attention to algebraic stack combinations, we provide a linear-time algorithm for generating all the appropriate monad stacks, or decide no such stacks exist. Our approach is based on Hyland, Plotkin, and Power's algebraic analysis of monad transformers, who propose a graph-theoretical solution to this problem. We extend their analysis with a straightforward connection to the modular decomposition of a graph and to cographs, a.k.a. series-parallel graphs.

    We present an accessible and self-contained account of this monad-stack generation problem, and, more generally, of the decomposition of a combined algebraic theory into sums and tensors, and its algorithmic solution. We provide a web-tool implementing this algorithm intended for semantic investigations of effect combinations and for monad stack generation.
  location: LT1310
  material: []
- tag: Talk
  date: '2014-05-21T11:00:00Z'
  speaker: Clemens Kupke
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/clemens.kupke/
  insturl: ''
  title: Coalgebraic Foundations of Databases
  abstract: " This 101 is intended to be a brainstorming session on possible links
    between the theory of coalgebras and the theory of databases. I will outline some
    ideas in this direction and I am looking forward to your feedback."
  location: LT1310
  material: []
- tag: Talk
  date: '2014-05-14T11:00:00Z'
  speaker: Guillaume Allais
  institute: MSP
  speakerurl: https://gallais.org
  insturl: ''
  title: Resource aware contexts and proof search for IMLL
  abstract: |-
    In Intuitionistic Multiplicative Linear Logic, the right introduction rule for tensors implies picking a 2-partition of the set of assumptions and use each component to inhabit the corresponding tensor's subformulas. This makes a naive proof search algorithm intractable. Building a notion of resource availability in the context and massaging the calculus into a more general one handling both resource consumption and a notion of "leftovers" of a subproof allows for a well-structured well-typed by construction proof search mechanism.

     Here is an <a href='http://gallais.org/code/LinearProofSearch/poc.LinearProofSearch.html'>Agda file</a> implementing the proof search algorithm.
  location: LT1310
  material: []
- tag: Talk
  date: '2014-04-07T11:00:00Z'
  speaker: Jamie Gabbay
  institute: Heriot-Watt
  speakerurl: http://www.gabbay.org.uk
  insturl: http://www.macs.hw.ac.uk/departments/computer-science.htm
  title: Nominal sets
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2014-04-02T11:00:00Z'
  speaker: Thorsten Altenkirch
  institute: Nottingham
  speakerurl: http://www.cs.nott.ac.uk/~txa/
  insturl: http://www.cs.nott.ac.uk/
  title: Towards cubical type theory
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2014-03-19T11:00:00Z'
  speaker: Guillaume Allais
  institute: MSP
  speakerurl: http://www.gallais.org
  insturl: ''
  title: The selection monad transformer
  abstract: Guillaume presented parts of Hedges' paper <a href='http://www.eecs.qmul.ac.uk/~julesh/papers/monad_transformers.pdf'>Monad
    transformers for backtracking search</a> (accepted to <a href='http://www.cs.bham.ac.uk/~pbl/msfp2014/'>MSFP
    2014</a>). The paper extends Escardo and Oliva's work on the selection and continuation
    monads to the corresponding monad transformers, with applications to backtracking
    search and game theory.
  location: LT1310
  material: []
- tag: Talk
  date: '2014-03-05T15:00:00Z'
  speaker: Stuart Hannah
  institute: Strathclyde Combinatorics
  speakerurl: https://personal.cis.strath.ac.uk/stuart.a.hannah/
  insturl: http://combinatorics.cis.strath.ac.uk/
  title: Lagrange inversion
  abstract: Stuart spoke about Lagrange inversion, a species-theoretic attempt to
    discuss the existence of solutions to equations defining species.
  location: LT1310
  material: []
- tag: Talk
  date: '2014-02-28T14:00:00Z'
  speaker: Neil Ghani
  institute: MSP
  speakerurl: https://personal.cis.strath.ac.uk/neil.ghani/
  insturl: ''
  title: Species
  abstract: Neil spoke about how adding structured quotients to containers gives rise
    to a larger class of data types.
  location: LT1310
  material: []
- tag: Talk
  date: '2014-02-19T11:00:00Z'
  speaker: Tim Revell
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Synthetic Differential Geometry
  abstract: 'Tim gave a brief introduction to Synthetic Differential Geometry. This
    is an attempt to treat smooth spaces categorically so we can extend the categorical
    methods used in the discrete world of computer science to the continuous work
    of physics. '
  location: LT1310
  material: []
- tag: Talk
  date: '2014-02-12T11:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: http://strictlypositive.org/
  insturl: ''
  title: Worlds
  abstract: 'Conor talked about worlds (aka phases, aka times, ...): why one might
    bother, and how we might go about equipping type theory with a generic notion
    of permitted information flow.'
  location: LT1310
  material: []
- tag: Talk
  date: '2014-02-05T11:00:00Z'
  speaker: Miles Gould
  institute: Edinburgh
  speakerurl: http://homepages.inf.ed.ac.uk/mgould1/
  insturl: http://www.inf.ed.ac.uk/
  title: Operads
  abstract: 'Miles has kindly agreed to come through and tell us about Operads, thus
    revisiting the topic of his PhD and the city in which he did it. '
  location: LT1310
  material: []
- tag: Talk
  date: '2014-01-22T11:00:00Z'
  speaker: Lorenzo Malatesta
  institute: MSP
  speakerurl: ''
  insturl: ''
  title: Overview of (extensions of) inductive-recursive definitions
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2014-01-08T11:00:00Z'
  speaker: Conor McBride
  institute: MSP
  speakerurl: http://strictlypositive.org/
  insturl: ''
  title: On the recently found inconsistency of the univalence axiom in current Agda
    and Coq
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2013-12-18T11:00:00Z'
  speaker: Ross Duncan
  institute: MSP
  speakerurl: http://personal.strath.ac.uk/ross.duncan/
  insturl: ''
  title: Quantum Mechanics
  abstract: ''
  location: LT1310
  material: []
- tag: Talk
  date: '2013-11-20T11:00:00Z'
  speaker: Robin Adams
  institute: MSP visitor
  speakerurl: http://www.cs.rhul.ac.uk/~robin/
  insturl: ''
  title: Classical Type Theories
  abstract: |-
    In 1987, Felleisen showed how to add control operators (for things like exceptions and unconditional jumps) to the untyped lambda-calculus.  In 1990, Griffin idly wondered what would happen if one did the same in a typed lambda calculus.  The answer came out: the inhabited types become the theorems of classical logic.

     I will present the lambda mu-calculus, one of the cleanest attempts to add control operators to a type theory.  We'll cover the good news: the inhabited types are the tautologies of minimal classical logic, and Godel's Double Negation translation from classical to intuitionistic logic turns into the CPS translation.

    And the bad news: control operators don't play well with other types. Add natural numbers (or some other inductive type), and you get inconsistency. Add Sigma-types, and you get degeneracy (any two objects of the same type are definitionally equal).  It gets worse: add plus-types, and you break Subject Reduction.
  location: LT1310
  material: []
- tag: Talk
  date: '2013-11-13T11:00:00Z'
  speaker: Guillaume Allais
  institute: MSP
  speakerurl: http://www.gallais.org
  insturl: ''
  title: Continuation Passing Style
  abstract: 'I chose to go through (parts of) Hatcliff and Danvy''s paper <a href=''http://dl.acm.org/citation.cfm?id=178053''>
    "A Generic Account of Continuation-Passing Styles"</a> (POPL 94) which gives a
    nice factorization of various CPS transforms in terms of:  <ul>   <li>embeddings
    from STLC to Moggi''s computational meta-language       (either call-by-value,
    call-by-name, or whatever you can come       up with)</li>   <li>followed by a
    generic CPS transform transporting terms from ML       back to STLC</li> </ul>
    Here is <a href=''http://gallais.org/code/GenericCPS/definitions.html''>an Agda
    file</a> containing what we had the time to see.'
  location: LT1310
  material: []