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Domain-Theoretic Foundations of Functional Programming

Overview

This textbook provides a basis for a PhD course on domain-theoretic semantics of functional programming languages and their meta-mathematical properties. It introduces basic domain theory and the technique of logical relations as developed by Scott and Plotkin. The solution of recursive domain equations is explained in detail.

A complete discussion of the famous full abstraction problem for PCF (a functional Kernel language due to Scott and Plotkin) is given including a ...

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Overview

This textbook provides a basis for a PhD course on domain-theoretic semantics of functional programming languages and their meta-mathematical properties. It introduces basic domain theory and the technique of logical relations as developed by Scott and Plotkin. The solution of recursive domain equations is explained in detail.

A complete discussion of the famous full abstraction problem for PCF (a functional Kernel language due to Scott and Plotkin) is given including a construction of the fully abstract Milner model using Kripke logical relations. A final chapter introduces computability in Scott domains and shows that this model is fully abstract and individual for appropriate extensions of PCF by parallel language constructs.

Key Features: Introduces both domain theory and logical relations techniques, Syntax-free construction of the fully abstract Milner model, Constructions and characterization of canonical solutions of recursive domain equations, Explains computability in domains and their relation to classical recursion theory.

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Product Details

  • ISBN-13: 9789812701428
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 12/28/2006
  • Pages: 132
  • Product dimensions: 6.10 (w) x 9.00 (h) x 0.60 (d)

Table of Contents


Preface     ix
Introduction     1
PCF and its Operational Semantics     13
The Scott Model of PCF     23
Basic Domain Theory     25
Domain Model of PCF     32
LCF - A Logic of Computable Functionals     34
Computational Adequacy     37
Milner's Context Lemma     43
The Full Abstraction Problem     45
Logical Relations     51
Some Structural Properties of the D[sigma]     57
Solutions of Recursive Domain Equations     65
Characterisation of Fully Abstract Models     77
Sequential Domains as a Model of PCF     87
The Model of PCF in S is Fully Abstract     95
Computability in Domains     99
Bibliography     117
Index     119
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