Adapting Proofs-as-Programs: The Curry-Howard Protocol

Description

This book ?nds new things to do with an old idea. The proofs-as-programs paradigm constitutes a set of approaches to developing programs from proofs in constructive logic. It has been over thirty years since the paradigm was ?rst conceived. At that time, there was a belief that proofs-as-programs had the - tential for practical application to semi-automated software development. I- tial applications were mostly concerned with ?ne-grain, mathematical program synthesis. For various reasons, research interest in the area eventually tended toward more theoretic issues of constructive logic and type theory. However, in recent years, the situation has become more balanced, and there is increasingly active research in applying constructive techniques to industrial-scale, complex software engineering problems. Thismonographdetailsseveralimportantadvancesinthisdirectionofpr- tical proofs-as-programs. One of the central themes of the book is a general, abstract framework for developing new systems of program synthesis by adapting proofs-as-programs to new contexts. Framework-oriented approaches that facilitate analogous - proaches to building systems for solving particular problems have been popular and successful. Thesemethodsarehelpful asthey providea formal toolbox that enablesa“roll-your-own”approachtodevelopingsolutions.Itishopedthatour framework will have a similar impact. The framework is demonstrated by example. We will give two novel - plications of proofs-as-programs to large-scale, coarse-grain software engine- ing problems: contractual imperative program synthesis and structured p- gram synthesis. These applications constitute an exemplary justi?cation of the framework. Also, in and of themselves, these approaches to synthesis should be interesting for researchers working in the target problem domains. Front Matter....Pages 1-1 Introduction....Pages 3-21 Front Matter....Pages 23-23 Functional Program Synthesis....Pages 25-75 The Curry-Howard Protocol....Pages 77-89 Front Matter....Pages 91-94 Intuitionistic Hoare Logic....Pages 95-134 Properties of Intuitionistic Hoare Logic....Pages 135-164 Proofs-as-Imperative-Programs....Pages 165-213 Front Matter....Pages 215-215 Reasoning about Structured Specifications....Pages 217-252 Proof-theoretic Properties of SSL....Pages 253-295 Structured Proofs-as-Programs....Pages 297-339 Generic Specifications....Pages 341-365 Structured Program Synthesis....Pages 367-389 Front Matter....Pages 391-391 Conclusions: Toward Constructive Logic as a Practical 4GL....Pages 393-396