add Sequence node

[k4b7]

A Sequence node can be either finite or infinite. If it's infinite it can also have a general term, e.g.

{
  type: "Sequence",
  kind: "finite" | "infinite",
  terms: [ Expression ],
  general: null | Expression,
}

[k4b7]

• 2, 3, 5, 7 (finite sequence)
• 2, 3, 5, 7, ... (infinite sequence)
• a_n = 3n + 1 (definition of a sequence)
• a_n = a_(n-1) - 1 (recursive definition of a sequence)
• x = -2, 2 (multiple solutions for x)
• x = \pm 2 (multiple solutions for x)
• A = { 2, 3, 5, 7 } (set with finite elements)
• A = { 2, 3, 5, 7, ... } (infinite set containing all primes)

Since there's lots of ways of defining a set, maybe it makes sense for the contents of a set to be a Sequence, or something like x | x > 5, x \in R or x < -5 U x > 5. It's totally valid to union or intersect relations b/c they represent all of solution of themselves.

[aliang8]

• 2, 3, 5, 7 ...

{ 
  type: "Sequence",
  kind: "finite", 
  terms: [ x | x is prime ], <- given 2, 3, 5, 7, ... how do we recognize the nature of the sequence?
} 

• a_n = 3n + 1

In this scenario, do we assume that a definition of a sequence occurs when the left side of an equation has a subscript?

[k4b7]

Recognizing the nature of a sequence like 2, 3, 5, 7, ... or even something link 1, 3, 9, 27, ... is outside of the scope of the AST should be responsible for.

With things like a_n = 3n + 1, I think we can parse them as

{
  type: 'Apply',
  op: 'eq',
  args: [ a_n, 3n + 1 ],
}