Domain-Theoretic Foundations of Functional Programming

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 universal for appropriate extensions of PCF by parallel language constructs.

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PCF and Its Operational Semantics; The Scott Model of PCF; Computational Adequacy; Milner's Context Lemma; The Full Abstraction Problem; Logical Relations; Some Structural Properties of the D ; Solutions of Recursive Domain Equations; Characterisation of Fully Abstract Models; Sequential Domains as a Model of PCF; The Model of PCF in S is Fully Abstract; Computability in Domains.

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