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...

We introduce an abstract general notion of system of equations between terms, called Term Equational System, and develop a sound logical deduction system, called Term Equational Logic, for equational reasoning. Further, we give an analysis of algebraic free constructions that together with an internal completeness result may be used to synthesise complete equational logics. Indeed, as an applic...