Questions tagged [curry-howard]

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Connection between strong normalization of the simply typed λ-calculus, and cut elimination for propositional logic

What is the precise connection between: strong normalization of the simply typed $\lambda$-calculus, and cut elimination for (intuitionistic) propositional logic (limited to implication) in “sequent ...
Gro-Tsen's user avatar
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1 vote
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Do game semantics for logic have Curry-Howard-like correspondence with game semantics for programming languages?

Both for logic and PLs do have notion of game semantics. Both are defined by two-player dialogue game, but players are different. In first case it is game between Verifyer and Falsifyer and in second ...
uhbif19's user avatar
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How can we establish that Gödel's completeness theorem corresponds to an interactive disassembler?

I have came across an idea from Jean-Louis Krivine, in this article written in French (page 7 to 10), where he dresses up an equivalence between an operating system and an axiomatic system: A utility ...
Aramya's user avatar
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1 vote
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What is the model of computation that corresponds (in the manner of Curry-Howard) to the deduction rule of resolution?

The Curry-Howard Correspondence is well-documented for the isomorphism which associates the intuitionistic natural deduction proof calculus (logic side) with the type system for the simply typed ...
jpt4's user avatar
  • 81
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
9 votes
2 answers

Why is the Curry-Howard isomorphism?

The Curry-Howard isomorphism is the correspondence between type systems (like for the simply typed lambda calculus) and proof systems (like natural deduction). More precisely, types resemble ...
JoJoModding's user avatar
4 votes
0 answers

What logic do refinement types correspond to?

I'm interested in applicability of refinement types to theorem-proving hence the questions about their logical expressiveness. Let's say, we have a type system which corresponds to some logic ...
oquechy's user avatar
  • 41
0 votes
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Curry Howard Isomorphism and cut elimination

I am currently reading about the proof for the isomorphism between Gentzen's sequent calculus $G$ and the simply typed lambda calculus $\lambda(\rightarrow,\times)$. The proof assumes the cut-free ...
David Lehnherr's user avatar
8 votes
1 answer

Type-theoretic interpretation of Skolemization

What is the type-theoretic interpretation / equivalent of Skolemization? Skolemization converts some formula into Skolem normal form. The two formulae are equisatisfiable with each other. Or, to say ...
Manuel Jacob's user avatar
9 votes
2 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
1 vote
0 answers

Equality Theorems with Type Theoretic Proof

I am investigating how I might be able to translate even commonplace equalities/ inequalities via the so-called Curry-Howard Correspondance - from a generic, set theoretic plus AOC foundation - into a ...
Krpcannon's user avatar
3 votes
2 answers

Languages that lack contraction, weakening or exchange

When learning about generalized arrows, a question arised to me: Are there any languages (or potential languages) that lack one or more of the structural rules: contraction, weakeing and exchange? ...
Petr's user avatar
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3 votes
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Motivation for Dependent Type

By the Curry-Howard Isomorphism we view propositions (or theorems if true/inhabited) as types. But take the type $\mathbb{N} \implies \mathbb{N} \implies \mathbb{N} $. We have as witnesses to this ...
Krpcannon's user avatar
20 votes
2 answers

Is there a typed lambda calculus which is consistent and Turing complete?

Is there a typed lambda calculus where the corresponding logic under the Curry-Howard correspondence is consistent, and where there are typeable lambda expressions for every computable function? This ...
Morgan Thomas's user avatar
14 votes
1 answer

Simply typed lambda calculus and higher order logic

What is the relation between simply typed lambda calculus and higher order logic? Under Curry-Howard it seems that simply typed lambda calculus corresponds to propositional logic. How is it related ...
lambda2's user avatar
  • 195
3 votes
2 answers

Can Curry-Howard prove a theorem from the types in your program, that has nothing to do with your program? [closed]

The following link states: Curry-Howard means that any type can be interpreted as a theorem in some logical system, and any term can be interpreted as a proof of its type. This does not mean that ...
hawkeye's user avatar
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