This thesis proposes a general framework for equational logic programming, called catf:gory­ based equational logic by placing the general principles underlying the design of the pro­ gramming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equational deduction to an arbitrary category satisfy­ ing certain natural conditions; completeness i...

In the early 80's, there was a number of papers on what should be called proofs by consistency. They describe how to perform inductive proofs, without using an explicit induction scheme, in the context of equational speciications and ground-convergent rewrite systems. The method was explicitly stated as a rst-order consistency proof in case of pure equational, constructor based, speciications. ...

We introduce the notion of an equational lifting monad: a commutative strong monad satisfying one additional equation (valid for monads arising from partial map classifiers). We prove that any equational lifting monad has a representation by a partial map classifier such that the Kleisli category of the former fully embeds in the partial category of the latter. Thus equational lifting monads pr...

We introduce the notion of an equational lifting monad: a commutative strong monad satisfying one additional equation (valid for monads arising from partial map classifiers). We prove that any equational lifting monad has a representation by a partial map classifier such that the Kleisli category of the former fully embeds in the partial category of the latter. Thus equational lifting monads pr...

We show that uni cation in certain extensions of shallow equational theories is decidable Our extensions generalize the known classes of shallow or standard equational theories In order to prove de cidability of uni cation in the extensions a class of Horn clause sets called sorted shallow equational theories is introduced This class is a natural extension of tree automata with equality constra...

For nite convergent term-rewriting systems the equational uniication problem is shown to be recursively independent of the equa-tional matching problem, the word matching problem, and the (simultaneous) 2 nd-order equational matching problem. We also present some new decidability results for simultaneous equational uniication and 2 nd-order equational matching.