Term Rewriting

Abstract

In the area of system specifications, rewriting techniques have been developed for two main applications: prototyping algebraic specifications of userdefined data types and theorem proving related to program verification. A formulation of term rewriting was proposed first by Evans [Eva51] and later by Knuth and Bendix [KB70]. Originally its main purpose was for generating canonical term rewriting systems,which can be used as decision procedures for proving the validity of equalities in some equational theories. Since then, in addition to the validity problem of equational logic, term rewriting has also been applied to inductive theorem proving, checking consistency and completeness of equational or conditional specifications, first-order theorem proving, unification theory, geometry theorem proving, etc. Through various implementations and experiments in automated theorem proving, it has been demonstrated that simplification of formulas by rewriting is indeed an effective way of pruning the search space. On the other hand, with the emergence of equationally specified abstract data types in the late 1970’s, term rewriting has also gained considerable popularity as a bridge between programming language theory and program verification. Several specification languages or programming environments, such as LARCH, OBJ, ASF, RAP, MAUDE, ELAN, to cite a few, are using rewriting as their basic evaluation mechanism. Rewriting techniques are also used in functional programming languages such as ML.