Full Abstraction and Semantic Equivalence demonstrates an original theory that uses the same inclusive predicates to show semantic equivalence and to construct fully abstract, extensional submodels. Previous general techniques for proving semantic equivalence, through the construction of inclusive predicates, have foundered due to their complexity and the lack of any counter-examples. In this book, Mulmuley has been able to construct a counterexample through diagonalization; moreover, he has discovered a technique to prove semantic equivalences that has the advantage of being mechanizable. This system, called Inclusive Predicate Logic (IPL), can almost automatically prove the existence of most of the inclusive predicates which arise in practice. Mulmuley also demonstrates that one can construct a fully abstract algebraic model of typed lambda calculus which is a submodel of the classical model, if the classical model is based on complete lattices. Beyond this, the book shows that theory can extend to the case of a language that has reflexive (recursively defined) types-as do most of the "real" programming languages.
ContentsIntroduction to Domain Theory • The Problem of Inclusive Predicate Existence • Fully Abstract Submodels of Typed Lambda Calculi • Fully Abstract Submodels in the Presence of Reflexive Types • A Mechanizable Theory for Existence Proofs • IPL Implementation • Conclusion
Full Abstraction and Semantic Equivalence is a winner of the 1986 ACM Doctoral Dissertation Award.