the Curry–Howard correspondence. The Wikibook Haskell has a page on the topic of: The Curry–Howard isomorphism Howard on Curry-Howard The Curry–Howard Correspondence...

new type constructor Π {\displaystyle \Pi } corresponds via the Curry-Howard isomorphism to a universal quantifier, and the system λP as a whole corresponds...

constructions can be considered an extension of the Curry–Howard isomorphism. The Curry–Howard isomorphism associates a term in the simply typed lambda calculus...

the concept of local completeness in natural deduction, via the Curry–Howard isomorphism. For the untyped lambda calculus, β-reduction as a rewriting rule...

(without explicit type annotations) is undecidable. Under the Curry–Howard isomorphism, System F corresponds to the fragment of second-order intuitionistic...

is rarely used to derive general mathematical results. In the Curry–Howard isomorphism, proof by exhaustion and case analysis are related to ML-style...

corresponding to theorems in classical logic. According to the Curry–Howard isomorphism, lambda calculus on its own can express theorems in intuitionistic...

systems based on higher-order typed lambda calculus through a Curry–Howard isomorphism, cut elimination algorithms correspond to the strong normalization...

closely related to mathematical logic and proof theory via the Curry–Howard isomorphism and they can be considered as the internal language of certain...

possible in any APL-like language with user-defined operators. The Curry–Howard isomorphism implies a connection between logic and programming: every proof...

cannot be deduced from the deduction theorem alone. Under the Curry–Howard isomorphism, Peirce's law is the type of continuation operators, e.g. call/cc...

(2007). "Classical Logic and Control Operators". Lectures on the Curry-Howard isomorphism (1st ed.). Boston, MA: Elsevier. ISBN 978-0444520777. "The CONT...

logic S4 called Constructive Modal Logic CS4. There is an extended Curry–Howard isomorphism between IPC and simply-typed lambda calculus. BHK interpretation...

combinators and the corresponding logical axioms is an instance of the Curry–Howard isomorphism. There may be multiple ways to do a reduction. All are equivalent...

Brouwer–Hilbert controversy Computability logic Constructive logic Curry–Howard isomorphism Foundations of mathematics Fuzzy logic Game semantics Intuition...

other calculi, like System F, the problem is even undecidable. Curry–Howard isomorphism Pawel Urzyczyn (1997). "Inhabitation in typed lambda-calculi (A...

Sørensen, Morten Heine B.; Urzyczyn, Pawel (1998), Lectures on the Curry-Howard Isomorphism, CiteSeerX 10.1.1.17.7385 Bove, Ana; Dybjer, Peter (2008). Dependent...

(2006). "Pure type systems and the lambda cube". Lectures on the Curry–Howard isomorphism. Elsevier. doi:10.1016/S0049-237X(06)80015-7. ISBN 0-444-52077-5...

through the BHK interpretation, its connection to logic by the Curry–Howard isomorphism, and its connections to Category theory. Terms usually belong to...

explain certain phenomena in natural language. In mathematics, the Curry–Howard isomorphism between computer programs and mathematical proofs relates continuation-passing...

strict notion of currying and uncurrying is in the closed monoidal categories, which underpins a vast generalization of the Curry–Howard correspondence...

This correspondence is called the Curry–Howard isomorphism. Prior type theories had also followed this isomorphism, but Martin-Löf's was the first to...

express arbitrary propositions in higher-order logic. Through the Curry–Howard isomorphism, then, well-typed programs in these languages become a means of...

Morten Heine Sørensen; Paweł Urzyczyn (2006). Lectures on the Curry-Howard isomorphism. Elsevier. pp. 206–207. ISBN 978-0-444-52077-7. Shramko, Y.; Wansing...

logic, i.e., the implicational propositional calculus, via the Curry–Howard isomorphism: terms correspond precisely to proofs in natural deduction, and...

manifesto Morten Heine Sørensen, Paweł Urzyczyn, Lectures on the Curry–Howard isomorphism, Elsevier, 2006, ISBN 0-444-52077-5, pp 98-99 R. P. Nederpelt,...

follows that Peirce's law cannot be intuitionistically derived. See Curry–Howard isomorphism for the general context of what this implies in type theory. The...

normal form.[citation needed] This idea lies at the basis of the Curry–Howard isomorphism, and of intuitionistic type theory. His inversion principle lies...

Church–Rosser theorem Simply typed lambda calculus Typed lambda calculus Curry–Howard isomorphism Calculus of constructions Constructivist analysis Lambda cube System...

η-conversion (eta conversion) in the lambda calculus, using the Curry–Howard isomorphism. By local completeness, we see that every derivation can be converted...