Curry-Howard correspondence

Curry-Howard correspondence

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

• Curry-Howard isomorphism