Axiomatic Domain Theory in Categories of Partial Maps

Axiomatic Domain Theory in Categories of Partial Maps

by Marcelo P. Fiore
     
 

ISBN-10: 052157188X

ISBN-13: 9780521571883

Pub. Date: 08/08/1996

Publisher: Cambridge University Press

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

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Overview

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.

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Product Details

ISBN-13:
9780521571883
Publisher:
Cambridge University Press
Publication date:
08/08/1996
Series:
Distinguished Dissertations in Computer Science Series
Pages:
254
Product dimensions:
6.85(w) x 9.72(h) x 0.75(d)

Table of Contents

Preface
1Introduction1
2Categorical Preliminaries17
3Partiality34
4Order-Enriched Categories of Partial Maps52
5Data Types77
6Recursive Types106
7Recursive Types in Cpo-Categories133
8FPC147
9Computational Soundness and Adequacy170
10Summary and Further Research191
App. A. Lemma 8.4.4202
App. B. Theorem 8.6.6205
App. C. Lemma 9.1.3212
App. D. Propositions D.0.1 and D.0.2222
Bibliography226
Index233
Symbol Index238

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