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- John R. Longley
- 1995

We introduce the concept of logical full abstraction, generalising the usual equational notion. We consider the language PCF and two extensions with " parallel " operations. The main result is that, for standard interpretations, logical full abstraction is equivalent to equa-tional full abstraction together with universality; the proof involves constructing… (More)

- John R. Longley, Alex K. Simpson
- Mathematical Structures in Computer Science
- 1997

We propose a uniform way of isolating a subcategory of predomains within the category of modest sets determined by a partial combinatory algebra (PCA). Given a divergence on a PCA (which determines a notion of partiality), we identify a candidate category of predomains, the well-complete objects. We show that, whenever a single strong completeness axiom… (More)

- M P Fourman, J D Fleuriot, J R Longley, A Background
- 2000

Much research in computer science, ever since its inception, has been devoted the problem: " How can we be sure that a computer program is correct? " The general problem is extremely difficult, and the enormous variety of computer software in use demands a corresponding variety of approaches: e.g. structured design methods [YC86], automated testing [Ber91]… (More)

- M P Fourman, G D Plotkin, J R Longley, Gordon Plotkin
- 2007

He has contributed to the development of categorical logic Fou77], the application of category theory to semantics PF92, FT95], the promulgation and commercial exploitation of Standard ML, and the application of computer assisted formal reasoning to system design. As a founding Director of Abstract Hardware Limited, he was responsible for AHL's adoption and… (More)

- M P Fourman, G D Plotkin, J R Longley
- 2007

A. Background A1. Introduction One of the fundamental questions at the heart of computer science is: \What does it mean for an operation or function to be computable in principle?" For the case of functions on the natural numbers, the work of Church, Turing and Kleene in the 1930s yielded several mathematical characterizations of a good class of computable… (More)

- Mike Fourman, Gordon Plotkin, John Longley
- 2001

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