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  3. Axiomatic Domain Theory in Categories of Partial Maps
  • Cited by 31
Publisher:
Cambridge University Press
Online publication date:
November 2009
Print publication year:
1996
Online ISBN:
9780511526565
DOI:
https://doi.org/10.1017/CBO9780511526565
Subjects:
Computer Science, Programming Languages and Applied Logic, Computing: General Interest
Series:
Distinguished Dissertations in Computer Science (14)
Information

Book description

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.

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 Source: Science of Computer Programming (1998)

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