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Order-enrichment for categories of partial maps

Published online by Cambridge University Press:  04 March 2009

Marcelo P. Fiore
Marcelo P. Fiore
Affiliation:
Department of Computer Science, Laboratory for Foundations of Computer Science, University of Edinburgh, The King's Buildings, Edinburgh EH9 3JZ, Scotland. Email mf@dcs.ed.ac.uk
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Abstract

Motivated by a desire to treat non-termination directly in the semantics of computation, the notion of approximation between programs is studied in the context of categories of partial maps. In particular, contextual approximation and specialisation are considered and shown to coincide. Moreover, after exhibiting the approximation between total maps as a primitive notion, from an arbitrary (or axiomatic) approximation order on total maps a computationally natural approximation order on partial maps is derived. The main technical contribution is a characterisation of when this approximation order between partial maps is domain-theoretic (in the sense that the category of partial maps Cpo-enriches) provided that the approximation order between total maps is also.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 5 , Issue 4 , December 1995 , pp. 533 - 562
Copyright
Copyright © Cambridge University Press 1995

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