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Axiomatic Domain Theory in Categories of Partial Maps

$42.00 USD

Part of Distinguished Dissertations in Computer Science

  • Date Published: March 2011
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511822674

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About the Authors
  • 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.

    • First systematic account of axiomatic categorical treatment of domain theory
    • Thorough and up-to-date treatment of the semantics of recursive types
    • Contains introduction to enriched category theory
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    Reviews & endorsements

    ' … 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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    Product details

    • Date Published: March 2011
    • format: Adobe eBook Reader
    • isbn: 9780511822674
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • 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.

  • Author

    Marcelo P. Fiore, University of Edinburgh

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