Curry-Howard correspondence

proper noun

A thesis which claims the existence of an analogy or correspondence between — on the one hand — constructive mathematical proofs and programs (especially functions of a typed functional programming language), and — on the other hand — between formulae (proven by the aforementioned proofs) and types (of the aforementioned functions).

“Gerhard Gentzen's calculus of natural deduction is the first formalism of structural proof theory, and is the cornerstone of the Curry-Howard correspondence relating logic to functional programming.ᵂᴾ”

Similar
Curry-Howard isomorphism
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Meanings

proper noun
  1. A thesis which claims the existence of an analogy or correspondence between — on the one hand — constructive mathematical proofs and programs (especially functions of a typed functional programming language), and — on the other hand — between formulae (proven by the aforementioned proofs) and types (of the aforementioned functions).

    Gerhard Gentzen's calculus of natural deduction is the first formalism of structural proof theory, and is the cornerstone of the Curry-Howard correspondence relating logic to functional programming.ᵂᴾ

    Synonyms: Curry-Howard isomorphism

Synonyms & antonyms

proper nounA thesis which claims the existence of an analogy or correspondence between — on the one hand — constructive mathematical proofs and programs (especially functions of a typed functional programming language), and — on the other hand — between formulae (proven by the aforementioned proofs) and types (of the aforementioned functions).

Similar
Curry-Howard isomorphism
Also see
curry-howard isomorphism
Cite this entry
APA

Curry-Howard correspondence. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Curry-Howard%20correspondence

MLA

“Curry-Howard correspondence.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Curry-Howard%20correspondence. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Curry-Howard correspondence,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Curry-Howard%20correspondence.

Source: Curry-Howard correspondence on Wiktionary, CC BY-SA 4.0.