Last Updated :2025/11/28

Curry-Howard correspondence

Proper noun
Japanese Meaning
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。
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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。

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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).

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Curry-Howard correspondence

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.

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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.

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