the Curry–Howard correspondence is the direct relationship between computer programs and mathematical proofs. It is also known as the Curry–Howard isomorphism...

Schönfinkel, for which Curry did much of the development. Curry is also known for Curry's paradox and the Curry–Howard correspondence. Named for him are three...

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

is strongly related to the consistency of a type system with Curry–Howard correspondence. To be sound, such a system must have uninhabited types. A type...

simply typed lambda calculus that has come to be known as the Curry–Howard correspondence. He has also been active in the theory of proof-theoretic ordinals...

The Curry–Howard correspondence is the interpretation of proofs-as-programs and formulae-as-types. The idea starting in 1934 with Haskell Curry and finalized...

material implication. In the Curry-Howard correspondence for intuitionistic logics, it can be realized through currying and uncurrying. Import-export...

limitations on computer memory. A deep result in proof theory, the Curry–Howard correspondence, states that a proof of functional correctness in constructive...

Brouwer–Heyting–Kolmogorov interpretation of constructive logic, the Curry–Howard correspondence between proofs and programs, and such logical systems as Per...

{\displaystyle P\to \mathbb {0} } . As the notation suggests, by the Curry–Howard correspondence, a term of type 0 {\displaystyle \mathbb {0} } is a false proposition...

exists". Because of this, and other work by Howard, propositions-as-types is known as the Curry–Howard correspondence. Loosely speaking, dependent types are...

with one constructor are isomorphic to a product type. In the Curry–Howard correspondence, product types are associated with logical conjunction (AND)...

cosine, in mathematics, a hyperbolic function, ch(x) = cosh(x) Curry–Howard correspondence, the relationship between computer programs and mathematical...

coincide with the empty type, which represents absurdum under the Curry–Howard correspondence The "undefined value" in quantum physics interpretations that...

therefore be known as the zero, never or empty type which, in the Curry–Howard correspondence, corresponds to falsity. However, when the bottom type is inhabited...

into a proof without Cut, and hence that Cut is admissible. The Curry–Howard correspondence between proofs and programs relates modus ponens to function...

is also used in SQL operations to form database queries. The Curry–Howard correspondence relates logical conjunction to product types. The membership...

evaluation strategies for typed lambda calculi. Natural deduction Curry–Howard correspondence Cut-elimination theorem Sequent calculus Prawitz 1965. von Plato...

logic (giving rise to connections between the two fields, e.g. Curry–Howard correspondence). The abstraction in the notion of judgment in mathematical logic...

relation. Judgment (mathematical logic) Type system Type theory Curry–Howard correspondence Sequent calculus Pierce, Benjamin C. (2002). Types and Programming...

Natural deduction Intuitionistic type theory BHK interpretation Curry–Howard correspondence Linear logic Game semantics Typed lambda calculus Typed and untyped...

neither true nor false"). In intuitionistic type theory, the Curry-Howard correspondence exhibits an equivalence of propositions and types, according...

be interpreted as a dialectic in this sense. For example, the Curry–Howard correspondence is such an adjunction or more generally the duality between closed...

generating an example of that object, a principle known as the Curry–Howard correspondence between proofs and algorithms. One reason that this particular...

{\big (}[(B\to C)\to C]\to D{\big )}\to (B\to D)} . Under the Curry-Howard correspondence, the last theorem here may also be justified by the lambda expression...

realizability is implemented in some proof assistants such as Coq. Curry–Howard correspondence Dialectica interpretation Harrop formula van Oosten 2000 A. Ščedrov...

The Curry–Howard correspondence is a relation between logical systems and programming languages. This theory established a precise correspondence between...

proof assistant based on the propositions-as-types paradigm (Curry–Howard correspondence), but unlike Rocq, has no separate tactics language, and proofs...

is strongly related to the consistency of a type system with Curry–Howard correspondence. To be sound, such a system must have uninhabited types. For...

interpretation describes the correspondence between natural deduction and lambda functions. Curry–Howard correspondence Logics for computability Van Atten...