Adapting Proofsasprograms

by John Newsome Crossley, John Newsome Crossley, Martin Wirsing

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 bookbs 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.

Genres: Computer Science

Kindle Edition

First published January 1, 2005

About the author

John Newsome Crossley, DPhil, MA (Oxon), (born 1937, Yorkshire, England) is a British-Australian mathematician and logician who writes in the field of logic in computer science, history of mathematics and medieval history. He is involved in the field of mathematical logic in Australia and South East Asia.

As of 2010, Crossley is Emeritus Professor of Logic at Monash University, Australia where he has been connected since 1968. Crossley studied at Oxford University where he received his DPhil and MA (Mathematics) in 1963. His early career was spent at Oxford where he was the first university lecturer in mathematical logic and was a Fellow of All Souls College, Oxford. He is still a Quondam Fellow there. He was offered a Readership position and following a lecturing visit to Monash University in 1968, he was elected to a Chair in Pure Mathematics. He accepted this position and as of 2010, Crossley continues to be active at Monash University where he serves through its Faculty of Information Technology.

Crossley has written books in logic, mathematics and computer science. He is known as the lead author of the book What is Mathematical Logic. Co-written by some of his students, the book popularised the subject to the interested layman. Many of Crossley's doctoral students have gone on to be professors themselves and have written books in the field of mathematics or computing, including Peter Aczel, Wilfrid Hodges, John Lane Bell and Rod Downey.

Crossley is also an avid photographer. In 1974 he first exhibited his photographs in Melbourne and again 2005 he exhibited Composition and Context, a collection of photographs shot by Crossley around the world that illustrates the title and theme of the exhibition. A number of these photographs since have appeared in publications in Australia, Britain and the Philippines.