Computational Adequacy via `Mixed' Inductive De nitions

For programming languages whose denotational semantics uses xed points of domain constructors of mixed variance, proofs of correspondence between operational and denotational semantics (or between two diierent denotational semantics) often depend upon the existence of relations speciied as the xed point of non-monotonic operators. This paper describes a new approach to constructing such relations which avoids having to delve into the detailed construction of the recursively deened domains themselves. The method is introduced by example, by considering the proof of computational adequacy of a denotational semantics for expression evaluation in a simple, untyped functional programming language.