The marriage of effects and monads (Wadler) Curry–Howard correspondence. A proof written as a functional program: the proof of commutativity of addition on natural numbers in the proof assistant Coq. nat_ind stands for mathematical induction, eq_ind for substitution of equals and f_equal for taking the same function on both sides of the equality.
Earlier theorems are referenced showing m = m + 0 and S (m + y) = m + S y. In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs.
Origin, scope, and consequences[edit] Podcast on Curry-Howard. Church's Thesis and Functional Programming. Journal of Functional Programming. Ttfp.pdf (application/pdf-Objekt) Applicative.pdf (application/pdf-Objekt)