High performance Simplification-Based Automated Deduction

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, 23]. First order logic can be expressed equationally [20]. This formulation makes it possible to express logic programming equationally and to employ the computational model of equational languages in logic programming [7]. Set theory can also be expressed equationally [33], enabling one to reason about query languages and optimization in data bases [11].