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14 votes
3 answers
907 views

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 ...
4 votes
0 answers
83 views

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 ...
7 votes
1 answer
200 views

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....
8 votes
3 answers
762 views

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 ...
2 votes
0 answers
105 views

"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 <...
3 votes
0 answers
184 views

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-...
0 votes
2 answers
638 views

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

I'm looking at the following tutorial on delimited (or composable) continuations: http://community.schemewiki.org/?composable-continuations-tutorial The author(s) propose the following "rewrite ...
8 votes
1 answer
498 views

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 ...
0 votes
1 answer
80 views

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 ...
12 votes
0 answers
163 views

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 ...
12 votes
2 answers
646 views

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 $$\...
4 votes
2 answers
370 views

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 ...