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A Generalization of the Curry-Howard Correspondence (1612.02816v1)
Published 8 Dec 2016 in cs.LO and math.CT
Abstract: We present a variant of the calculus of deductive systems developed in (Lambek 1972, 1974), and give a generalization of the Curry-Howard-Lambek theorem giving an equivalence between the category of typed lambda-calculi and the category of cartesian closed categories and exponential-preserving morphisms that leverages the theory of generalized categories (Schoenbaum 2016). We discuss potential applications and extensions.