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Description of the CPS transformation for the typed lambda-calculus

Is there somewhere a precise but hopefully readable account of how the CPS (=continuation-passing-style) transformation applies to the typed lambda-calculus? (Say, simply-typed with product and sum ...
Gro-Tsen's user avatar
  • 841
7 votes
1 answer

Can you regain the Church-Rosser property in languages with continuations?

I'm aware that if you naively add continuations to a language, the Church-Rosser property no longer holds. For example, suppose we have some variant of the STLC with basic arithmetic and integer types....
idka's user avatar
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8 votes
3 answers

What's the logical counterpart to jumps with arguments on CPS terms?

It's well known that the CPS (continuation-passing style) translation often employed in compilers corresponds to double negation translation under the Curry-Howard isomorphism. Though often the target ...
paulotorrens's user avatar
2 votes
0 answers

"finally" for algebraic effects and handlers

In Java in addition to catch there is also finally, this is very important to make sure resources get cleaned up. I believe <...
Labbekak's user avatar
  • 701
3 votes
0 answers

Type System Of $\lambda\mu$-Calculus

reading this paper on CPS-tranformation from the $\lambda\mu$-calculus, I'm a bit confused about the type system presented: Why second-order formulas in the types? Is this according to the Curry-...
fweth's user avatar
  • 139
14 votes
3 answers

How do continuations represent negations (under the Curry–Howard correspondence)?

Under the Curry–Howard correspondence, types can be thought of as propositions, and values inhabiting a type can be thought of as proofs that the corresponding proposition is true. (E.g., the ...
greatBigDot's user avatar
0 votes
2 answers

reset and shift only one level deep (delimited continuations)? [closed]

I'm looking at the following tutorial on delimited (or composable) continuations: The author(s) propose the following "rewrite ...
Reb.Cabin's user avatar
  • 117
8 votes
1 answer

What is the formal definitions of the reduction related to the "call/cc" (call with the current continuation) operator?

In lambda calculus or in combinatory logic we formally define reduction/expansion rules for terms (and in their typed variants reductions must preserve the type). Then we can talk about properties of ...
Petr's user avatar
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0 votes
1 answer

Seeking for a game for modelling a problem using game thoery [closed]

I have a problem which I want to formulate it as a game, using game theory. In this problem there is several agents, we can consider the agents as the employees of different offices, these agents have ...
Mary's user avatar
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12 votes
0 answers

Are the types that show monads are more powerful than continuations revealing something of fundamental importance?

In 1992 in the paper Imperative Functional Programming, Simon Peyton Jones and Philip Wadler write: So monads are more powerful than continuations, but only because of the types! It is not clear ...
hawkeye's user avatar
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12 votes
2 answers

Continuation passing transform of binary functions

Recall the continuation passing transform (CPS transform) which takes $A$ to $\beta A \mathrel{{:}{=}} R^{R^A}$ (where $R$ is fixed) and $f : A \to B$ to $\beta f : \beta A \to \beta B$ defined by $$\...
Andrej Bauer's user avatar
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4 votes
2 answers

Reversing the CPS transformation?

A quick Google search didn't turn up anything obvious, so I'm asking here. Converting direct style programs to continuation-passing style is a well-studied program transformation. However, I'm ...
Neel Krishnaswami's user avatar