Axiomatic Domain Theory in Categories of Partial Maps

By: Marcelo P. Fiore

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Paperback | 9 August 2004

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256 Pages

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24.61 x 18.9 x 1.37

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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.

Industry Reviews

' ... 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)

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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Set Theory Computing & I.T.Computer Programming & Software Development Programming & Scripting Languages Topology Analytic Topology Software Engineering Computer Science Mathematical Theory of Computation

Applied Mathematics Mathematical Modelling

Introduction
Categorical preliminaries
Partiality
Order-enriched categories of partial maps
Data types
Recursive types
Recursive types in Cpo-categories
FPC
Computational soundness and adequacy
Summary and future research
Appendices
References
Indices
Table of Contents provided by Publisher. All Rights Reserved.

Axiomatic Domain Theory in Categories of Partial Maps

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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