Equational logic is one of the most important domains of research in computer science. Specifications of types of data structures and assertions about the behaviour of programs are naturally written in equational form. Programs made of equations are called equational programs and appear in functional programming, logic programming and in most combinations of high level programming paradigms [19...

It is well known that bisimulation on μ-expressions cannot be finitely axiomatised in equational logic. Complete axiomatisations such as those of Milner and Bloom/Ésik necessarily involve implicational rules. However, both systems rely on features beyond pure equational Horn logic: either rules that are impure by involving non-equational side-conditions, or rules that are schematically infinita...

The purpose of this paper is threefold: to present a general abstract, yet practical, notion of equational system; to investigate and develop a theory of free constructions for such equational systems; and to illustrate the use of equational systems as needed in modern applications, specifically to the theory of substitution in the presence of variable binding and to models of name-passing proc...

We give complete, finite quasiequational axiomatisations to algebras of unary partial functions under the operations of composition, domain, antidomain, range and intersection. This completes the extensive programme of classifying algebras of unary partial functions under combinations of these operations. We look at the complexity of the equational theories and provide a nondeterministic polyno...

Higher-order uniication is equational uniication for-conversion. But it is not rst-order equational uniication, as substitution has to avoid capture. In this paper higher-order uniication is reduced to rst-order equational uniication in a suitable theory: the-calculus of explicit substitutions.