We introduce rewriting with two sets of rules, the rst interpreted equa-tionally and the second not. A semantic view considers equational rules as deening an equational theory and reduction rules as deening a rewrite relation modulo this theory. An operational view considers both sets of rules as similar. We introduce suucient properties for these two views to be equivalent (up to diierent noti...

Pratt [22] defines action algebras as Kleene algebras with residuals. In [9] it is shown that the equational theory of *-continuous action algebras (lattices) is Π 1−complete. Here we show that the equational theory of relational action algebras (lattices) is Π 1−hard, and some its fragments are Π 1−complete. We also show that the equational theory of action algebras (lattices) of regular langu...

Equational theories of an algebra, i.e. the equivalence relation closed under translations and endomorphisms, are formalized. The correspondence between equational theories and term rewriting systems is discussed in the paper. We get as the main result that any pair of elements of an algebra belongs to the equational theory generated by a set A of axioms iff the elements are convertible w.r.t. ...

A longstanding open problem in lambda calculus is whether there exists a non-syntactical model of the untyped lambda calculus whose theory is exactly the least λ-theory λβ. In this paper we make use of the Visser topology for investigating the related question of whether the equational theory of a model can be recursively enumerable (r.e. for brevity). We introduce the notion of an effective mo...

ion Space The definition of an implementation link is as a representation map from an abstract theory to a concrete theory, wi th an abstraction function for mapping concrete objects to abstract objects. The diagram below shows an implementation link between bags and lists, where the abstract theory of bags and the concrete theories of lists are axiomatized using equational logic. Abstraction M...