Automatic program transformation viewed as theorem proving

Abstract

We identify the problem of automatic recursion removal using the unfold/fold methodology (2) to the problem of finding a ɛ-pattern-matcher σ for two terms t and s, i.e.so that σt=_ɛs. We propose a new method to solve this equation based on a technique of dynamic completion of a term rewriting system for the property $t = _\varepsilon s \Rightarrow t\mathop \to \limits^* _R s$. This method presentssome advantages because it enables us to work with incomplete theories and limits the number of superpositions we must do during the process of completion.