Automath

Automath (automating mathematics) was a formal language, devised by Nicolaas Govert de Bruijn starting in 1967, for expressing complete mathematical theories in such a way that an included automated proof checker can verify their correctness. The Automath system included many novel notions that were later adopted and/or reinvented in areas such as typed lambda calculus and explicit substitution. Dependent types is one outstanding example. Automath was also the first practical system that exploited the Curry–Howard correspondence. Propositions were represented as sets (called "categories") of their proofs, and the question of provability became a question of non-emptiness (type inhabitation); de Bruijn was unaware of Howard's work, and stated the correspondence independently.