Partial evaluation and ω-completeness of algebraic specifications

Abstract

Suppose P( x, y) is a program with two arguments, whose first argument has a known value c, but whose second argument is not yet known. Partial evaluation of P( c, y) results (or rather: should result) in a specialized residual program P c ( y) in which ‘as much as possible’ has been computed on the basis of c. In the literature on partial evaluation this is often more or less loosely expressed by saying that partial evaluation amounts to ‘making maximal use of incomplete information’. In this paper a precise meaning is given to this notion in the context of equational logic, initial algebra specification, and term rewriting systems. If maximal propagation of incomplete information is to be achieved within this context, as a first step it is necessary to add equations to the algebraic specification in question until it is ω-complete (if ever). The basic properties of ω-complete specifications are discussed and some examples of ω-complete specifications as well as of specifications that do not have a finite ω-complete enrichment are given.