Equivalences and transformations of recursive definitions

Abstract

This work presents a unified theory of recursive program schemes, context-free grammars, grammars on arbitrary algebraic structures (and actually of recursive definitions of all kind) in terms of regular systems of equations. Several equivalence relations on regular systems (depending on sets of equational axioms) are defined. They are systematically investigated and characterized (in some cases) in terms of system transformations by folding, unfolding and rewriting according to the equational algebraic laws.