Chapter

Types for Proofs and Programs

Volume 806 of the series Lecture Notes in Computer Science pp 108-126

Date:

Logic of refinement types

  • Susumu HayashiAffiliated withDepartment of Applied Mathematics and Informatics, Ryukoku University

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Abstract

Refinement types are subsets of ordinary types, which are intended to be specifications of programs. Ordinary types correspond to constructive propositions by Curry-Howard isomorphism. Refinement types correspond to “classical” propositions by a semantics resembling interpretations of logics in categorical/algebraic logic. In this paper, we will study the logic of refinement types in the type system ATTT which was introduced in [9] as a framework for an “optimized” Curry-Howard isomorphism.