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Tweak some wording in the 2+2=4 notebook
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Lines changed: 49 additions & 32 deletions

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‎notebooks/An introduction to compositionality via "two plus two is four".ipynb‎

Lines changed: 49 additions & 32 deletions
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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"collapsed": true
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"outputs": [],
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"collapsed": false
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"collapsed": false
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"collapsed": true
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"source": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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"metadata": {},
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"outputs": [],
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"source": [
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"def isfun(x): # I called it this because `is` is a reserved word in python.\n",
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"metadata": {},
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"outputs": [],
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"source": [
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"f = isfun(2)\n",
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"f(3)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"(isfun(2))(2) # note that isfun(2,2) won't work, because the function takes only one argument."
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"cell_type": "code",
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"execution_count": null,
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"collapsed": false
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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"cell_type": "code",
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"execution_count": null,
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"(two * (plus * two)) * (is_V * five)"
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"((two * (plus * two)) * (is_V * five))[0].content.derivation"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Notice that, in a way, the lambda notebook calculation is _not concerned_ with whether the resulting expression is true. It is trivial to see that one of the above two expressions is true and one is false, but what the lambda notebook is calculating is a reduction to a **meta-language** expression of some kind. In this case, the meta-language is (apparently) a simple fragment of arithmetic. In this sense, both of the above results are exactly what I suggested we should want. The denotation of each of these sentence is a truth value, and what truth value it is (0 or 1) will depend on how the meta-language expression is interpreted."
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"In this case, the calculation was able to determine actual truth-values for these derivations. But it is useful to know how it did this -- and in particular, to see what the *truth-conditions* of this sentence are."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"((two * (plus * two)) * (is_V * five))[0].content.derivation"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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"collapsed": true
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"outputs": [],
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"source": [
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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"collapsed": true
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"outputs": [],
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"source": [
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"r = ((two * (plus * two)) * (is_V * four))\n",
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"r.tree()"
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"r.tree(derivations=True)"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"collapsed": false
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"collapsed": true
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"outputs": [],
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"source": [
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.1"
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"version": "3.6.2"
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}
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},
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"nbformat": 4,

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