Curry-Howard Correspondence
Version 1.0.0 · Updated 2026-07-28
CORE DEFINITION
The Curry-Howard correspondence is a close relationship between computer programs and mathematical proofs; it is also called the Curry-Howard isomorphism, formulas-as-types correspondence, or propositions-as-types correspondence. It is a generalization of the syntactic similarity between formal logic systems and mathematical operations. It is considered to have been independently discovered by American mathematician Haskell Curry and logician William Alvin Howard.
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The Curry-Howard correspondence is a close relationship between computer programs and mathematical proofs; it is also called the Curry-Howard isomorphism, formulas-as-types correspondence, or propositions-as-types correspondence. It is a generalization of the syntactic similarity between formal logic systems and mathematical operations. It is considered to have been independently discovered by American mathematician Haskell Curry and logician William Alvin Howard.
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Program types correspond to logical propositions, and programs themselves correspond to proofs of those propositions; the two are structurally isomorphic. Writing code is writing proofs, and computation and reasoning are essentially unified.
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- zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E6%9F%AF%E9%87%8C-%E9%9C%8D%E5%8D%8E%E5%BE%B7%E5%AF%B9%E5%BA%94verified
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