Conversion from callcc to Continuation Passing Style (CPS) Tom - - PowerPoint PPT Presentation

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May 12, 2023 254 likes •646 views

Conversion from callcc to Continuation Passing Style (CPS) Tom Nikken Based on slides from Xavier Leroy, INRIA Type Theory and Coq May 8th 2018 Tom Nikken Conversion from callcc to CPS 1 / 16 Conversion to continuation-passing style (CPS)

SLIDE 1

Conversion from callcc to Continuation Passing Style (CPS)

Tom Nikken Based on slides from Xavier Leroy, INRIA Type Theory and Coq May 8th 2018

Tom Nikken Conversion from callcc to CPS 1 / 16

SLIDE 2

Conversion to continuation-passing style (CPS)

Goal: make explicit the handling of continuations. Input: a call-by-value functional language with callcc. Output: a pure functional language (no callcc). Uses: compilation of callcc, semantics, programming with continuations in Scheme, Haskell, ...

Tom Nikken Conversion from callcc to CPS 2 / 16

SLIDE 3

Illustration of CPS in Javascript

We need to save the continuation, in case we encounter a callcc Idea: turn everything into a function from its continuation to its value function id(x) { return x; }

Tom Nikken Conversion from callcc to CPS 3 / 16

SLIDE 4

Illustration of CPS in Javascript

We need to save the continuation, in case we encounter a callcc Idea: turn everything into a function from its continuation to its value function id(x, cont) { cont(x); }

Tom Nikken Conversion from callcc to CPS 3 / 16

SLIDE 5

Illustration of CPS in Javascript

function fact(n,cont) { if (n == 0) cont (1) ; else fact(n-1, function (t0) { cont(n * t0) }) ; }

Tom Nikken Conversion from callcc to CPS 4 / 16

SLIDE 6

Illustration of CPS in Javascript

function fact(n,cont) { if (n == 0) cont (1) ; else fact(n-1, function (t0) { cont(n * t0) }) ; } fact (5, function (n) { console.log(n) ; })

Tom Nikken Conversion from callcc to CPS 4 / 16

SLIDE 7

Now in the lambda calculus

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SLIDE 8

Now in the lambda calculus

... : (λ + callcc) → λ If a : τ, then a : (τ → answer) → answer, where: τ = τ for base types and τ1 → τ2 = τ1 → (τ2 → answer) → answer N = λk. k N x = λk. k x λx. a = λk. k (λx. a) f a = λk. f (λvf . a (λva. vf va k)) callcc f = λk. f (λvf . vf k k) throw a b = λk. a (λva. b (λvb. va vb))

Tom Nikken Conversion from callcc to CPS 5 / 16

SLIDE 9

Now in the lambda calculus

... : (λ + callcc) → λ If a : τ, then a : (τ → answer) → answer, where: τ = τ for base types and τ1 → τ2 = τ1 → (τ2 → answer) → answer N = λk. k N x = λk. k x λx. a = λk. k (λx. a) f a = λk. f (λvf . a (λva. vf va k)) callcc f = λk. f (λvf . vf k k) throw a b = λk. a (λva. b (λvb. va vb))

Tom Nikken Conversion from callcc to CPS 5 / 16

SLIDE 10

Remarks

callcc conversion duplicates k: one as argument to f and one to propagate the current continuation. Throw ignores k. Argument of application is always a value, so works for CBV and CBN.

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SLIDE 11

Exercise f x =β ?

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SLIDE 12