Axiomatic Domain Theory in Categories of Partial Maps

First systematic account of axiomatic categorical domain theory and functional programming.

Marcelo P. Fiore (Author)

9780521602778, Cambridge University Press

Paperback, published 25 March 2004

256 pages
24.6 x 19 x 1.3 cm, 0.46 kg

' … the author succeeds in the difficult task of finding the right level of abstraction. Moreover, the exposition is very precise and technically outstanding.' Daniele Turi, Science of Computer Programming (1998)

Axiomatic categorical domain theory is crucial for understanding the meaning of programs and reasoning about them. This book is the first systematic account of the subject and studies mathematical structures suitable for modelling functional programming languages in an axiomatic (i.e. abstract) setting. In particular, the author develops theories of partiality and recursive types and applies them to the study of the metalanguage FPC; for example, enriched categorical models of the FPC are defined. Furthermore, FPC is considered as a programming language with a call-by-value operational semantics and a denotational semantics defined on top of a categorical model. To conclude, for an axiomatisation of absolute non-trivial domain-theoretic models of FPC, operational and denotational semantics are related by means of computational soundness and adequacy results. To make the book reasonably self-contained, the author includes an introduction to enriched category theory.

1. Introduction
2. Categorical preliminaries
3. Partiality
4. Order-enriched categories of partial maps
5. Data types
6. Recursive types
7. Recursive types in Cpo-categories
8. FPC
9. Computational soundness and adequacy
10. Summary and future research
Appendices
References
Indices.

Subject Areas: Mathematical theory of computation [UYA], Mathematical modelling [PBWH]