A Conservative Look at Term Deduction Systems with Variable Binding

Abstract

We set up a formal framework to describe term deduction systems, such as transition system specifications in the style of Plotkin, and conditional term rewriting systems. This framework has the power to express many-sortedness, general binding mechanisms and substitutions, among other notions such as negative premises and unary predicates on terms. The framework is used to present a conservativity format in operational semantics, which states sufficient criteria to ensure that the extension of a transition system specification with new rules does not affect the behaviour of the original terms. Furthermore, we show how general theorems in structured operational semantics can be transformed into results in conditional term rewriting. We apply this approach to the conservativity theorem, which yields a result that is useful in the field of abstract data types.