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wcrichton's profile
Will Crichton
Will Crichton
Will Crichton
@wcrichton

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Will Crichton

@wcrichton

Articulating the ineffable. Programming language theory 🤝 cognitive psychology. PhD @Stanford

he/him
willcrichton.net
Joined September 2011

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    1. Will Crichton‏ @wcrichton 14 Dec 2020

      Combinatorics problem: you're arranging 10 people (A .. J) in a row. A and B must sit next to each other. How many arrangements? How could writing this problem as a program help scaffold the problem-solving process?

      5 replies 3 retweets 18 likes
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    2. Will Crichton‏ @wcrichton 14 Dec 2020

      It seems like there are two styles of programming, which I call "subtractive" and "additive" (like 3D printing). permutations('A' .. 'J').filter(λ p: 'AB' in p or 'BA' in p) ^ subtractive means enumerate all possibilities, then remove constraint violations.

      1 reply 0 retweets 4 likes
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    3. Will Crichton‏ @wcrichton 14 Dec 2020

      But subtractive is hard to reason about analytically -- how to compute len(..)? Then we rewrite additively: permutations(['AB'] + 'C' .. 'J') + permutations(['BA'] + 'C' .. 'J') Now we can easily derive the formula permutations(9) * 2.

      2 replies 0 retweets 2 likes
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    4. Will Crichton‏ @wcrichton 14 Dec 2020

      Maybe this is actually a compiler problem: how can you rewrite the subtractive program (which naturally falls out of the problem statement) into an additive one (which is easily countable)? i.e. how do you remove all conditional expressions?

      3 replies 0 retweets 6 likes
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    5. full internal subcategory of the sarahzrf topos‏ @sarah_zrf 14 Dec 2020
      Replying to @wcrichton

      hmm... makes me think of the examples ive seen about squiggol (https://en.wikipedia.org/wiki/Bird%E2%80%93Meertens_formalism …), which i know less about than i ought to 🤔

      1 reply 0 retweets 2 likes
    6. full internal subcategory of the sarahzrf topos‏ @sarah_zrf 14 Dec 2020
      Replying to @sarah_zrf @wcrichton

      this kind of dichotomy is also definitely very present when working in a proof assistant—i wonder whether it's been pinned down in the proof automation/engineering literature?

      1 reply 0 retweets 2 likes
      Will Crichton‏ @wcrichton 14 Dec 2020
      Replying to @sarah_zrf

      When I was learning Lean and writing proofs about lambda calculus, I first wrote axioms as functions. But I later realized I couldn't easily access exhaustiveness theorems (eg this proof must have been derived using rule A or B), so I rewrote functions as a single data type.

      3:15 PM - 14 Dec 2020
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      2 replies 0 retweets 1 like
        1. Will Crichton‏ @wcrichton 14 Dec 2020
          Replying to @wcrichton @sarah_zrf

          Seems kind of similar -- you have to carefully pick your representation to ensure downstream analysis will work.

          0 replies 0 retweets 1 like
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        1. full internal subcategory of the sarahzrf topos‏ @sarah_zrf 14 Dec 2020
          Replying to @wcrichton

          what do you mean exactly by "wrote axioms as functions"?

          1 reply 0 retweets 0 likes
        2. Will Crichton‏ @wcrichton 15 Dec 2020
          Replying to @sarah_zrf

          By axioms I actually mean inference rules. And it was something like: constant has_type : Expr → Typ → Prop axiom T_add : ∀ e1 e2 : Expr, (has_type e1 Typ.Num ∧ has_type e2 Typ.Num) → has_type (Expr.Add e1 e2) Typ.Num

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