Axiomatic Domain Theory in Categories of Partial Maps

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, ...

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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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Editorial Reviews

From the Publisher
"...this bookis well-written, and it represents a significant contribution to axiomatic domain theory. It certainly deserves the recognition as a distinguished dissertation in computer science." Guo-Qiang Zhang, Mathematical Reviews
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Product Details

Table of Contents

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.

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