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Synopsis
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.