Abstract

Around thirty years ago, P. Martin-Lof [12] suggested that the intuitionistic theory of types, originally designed as a formal system for constructive mathematics, could be viewed as a programming language. The conclusion of this paper stresses the mutual benefit of relating constructive mathematics and computer programming. In one direction one gets a precise system of notations for both statements and proofs, and one obtains the computerization of abstract intuitionistic mathematics that was asked by Bishop [2]. In the other direction, computer programming “gets access to the whole conceptual apparatus of pure mathematics”.

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