propositionsastypes
Propositions-as-types is a principle in logic and type theory that interprets logical propositions as types and proofs as programs. In this view, a proof of a proposition is a value of the corresponding type, and constructing a proof is the same as writing a program that inhabits the type. The approach is closely associated with the Curry–Howard correspondence, particularly in its intuitionistic form.
Historically, the idea arose from work by Haskell Curry and William Alvin Howard in the mid-20th century
Core correspondences include: a unit type corresponds to the proposition true; the empty type to false; product
In practice, propositions-as-types underpins modern proof assistants and languages with expressive type systems, such as Coq,
Limitations include the emphasis on constructive logic, as many classical results require additional axioms or non-constructive