On the Approximation of Denotational Mu-Semantics

A signature gives rise to a language L (Var) by extending with variables x 2 Var and binding constructs x and x, corresponding to least and greatest xed points respectively. The natural denotational models for such languages are bicomplete dcpos as monotone-algebras. We prove that several approximating denotational semantics have the usual compositional semantics as their limit. These results provide techniques for relating syntactic and semantic concepts such as in full abstraction or completeness proofs. In the presence of an involutive antitone map on a bicomplete dcpo D we may translate the language L (Var) into one with least xed points only such that meanings are preserved. This allows an approximative semantics where least and greatest xed points are simultaneously approximated byùnwindings' in the syntax, provided that the limit semantics is substitutive. We discuss the principal diiculties of simultaneous unwindings in the absence of such semantic negations.