English Dictionary

Curry-Howard correspondence

固有名詞

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).

日本語の意味

カリー・ハワード対応は、構成的数学的証明とプログラム（特に型付き関数型プログラミング言語の関数）との間、さらに証明された論理式とそのプログラムにおける型との間に対応関係が存在するという類推または主張を表す概念・定理です。

The Curry-Howard correspondence reveals a deep connection between constructive mathematical proofs and typed functional programs, asserting that proofs correspond to programs and propositions correspond to types.

証明とプログラムの対応は、構成的数学の証明と型付き関数型プログラムとの間に深い関係があることを示し、証明がプログラムに、命題が型に対応することを主張する。

意味（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