Adapting Proofs-as-Programs

This monograph details several important advances in the area known as the proofs-as-programs paradigm, a set of approaches to developing programs from proofs in constructive logic. It serves the dual purpose of providing a state-of-the-art overview of the field and detailing tools and techniques to stimulate further research. One of the book's central themes is a general, abstract framework for developing new systems of program synthesis by adapting proofs-as-programs to new contexts, which the authors call the Curry--Howard Protocol. This protocol is used to provide two novel applications for industrial-scale, complex software engineering: contractual imperative program synthesis and structured software synthesis. These applications constitute an exemplary justification for the applicability of the protocol to different contexts.The book is intended for graduate students in computer science or mathematics who wish to extend their background in logic and type theory as well as gain experience working with logical frameworks and practical proof systems. In addition, the proofs-as-programs research community, and the wider computational logic, formal methods and software engineering communities will benefit. The applications given in the book should be of interest for researchers working in the target problem domains. TOC:Part I. Prologue.- Introduction.- Part II. Generalizing Proofs-as-Programs.- Functional Program Synthesis.- The Curry--Howard protocol.- Part III. Imperative Proofs-as-Programs.- Intuitionistic Hoare Logic.- Properties of Intuitionistic Hoare Logic.- Proofs-as-Imperative-Programs.- Part IV. Structured Proofs-as-Programs.- Reasoning about Structured Specifications.- Proof-theoretic Properties of SSL.- Structured Proofs-as-Programs.- Generic Specifications.- Structured Program Synthesis.- Part V. Epilogue.- Conclusions: Toward Constructive Logic as a Practical 4GL.- Part VI. Appendix.- A: Constructive Logic.- References.- Index.