Abstract

. For programming languages whose denotational semantics uses fixed points of domain constructors of mixed variance, proofs of correspondence between operational and denotational semantics (or between two different denotational semantics) often depend upon the existence of relations specified as the fixed 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 defined 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. 1 Introduction It is well known that various domain constructors can be extended to act on relations on domains. For example, given binary relations R and S on domains D and E, there is a binary relation R!S on the domain of continuous functions D!E given by: (f; g) 2 (R!S) if and onl...

Citations

363	LCF considered as a programming language - Plotkin - 1977
257	Semantics of programming languages: structures and techniques. Foundations of Computing - Gunter - 1992
102	R.D.: Parametricity and local variables - O’Hearn, Tennent - 1995
65	Recursive types reduced to inductive types - Freyd - 1990
60	Remarks on algebraically compact categories - Freyd - 1991
44	On the relation between direct and continuation semantics - Reynolds - 1974
39	A Co-induction Principle for Recursively Defined Domains - Pitts - 1994
26	Lectures on predomains and partial functions - Plotkin - 1985
21	Cosmadakis. Semantical paradigms: notes for an invited lecture - Meyer, C - 1988
15	Relational properties of recursively defined domains - Pitts - 1993
11	The Formal Semantics of Computer Languages and their Implementations - Milne - 1974
6	Algebraically Complete Categories. In A. Carboni et al (eds - Freyd - 1991