Studies of a Theory of Specifications with Built-in Program Extraction

Authors:
Paula Severi;Nora Szasz
Affiliations:
Department of Mathematics, School of Sciences, Universidad de la República, Montevideo, Uruguay. e-mail: severi@cmat.edu.uy;Department of Computing Science, School of Engineering, Universidad de la República, Montevideo, Uruguay. e-mail: nora@fing.edu.uy
Venue:
Journal of Automated Reasoning
Year:
2001

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Abstract

We present a Theory of Specifications based on Martin-Löf's type theory, with rules for simultaneously constructing programs and their correctness proofs. The theory contains types for representing specifications whose corresponding notion of implementation is that of a pair formed by a program and a correctness proof. The rules of the theory are such that in implementations the program parts appear mixed together with the proof parts. A confluent and normalizing computational relation performs the task of separating programs from proofs. As a consequence, every implementation computes to a pair composed of a program and a proof of its correctness, and so the program extraction procedure is immediate.