On Rewriting Terms with Strict Functions and Error Propagation

Partial functions play an essential role in the semantics of programs as a means to formalize non-terminating computations and computations terminating in an exception or error situation. However, when properly formalized, partial functions and errors often complicate underlying formalisms and reasoning systems. In this paper we focus on term rewriting systems, and discuss how partial functions and error propagation may be treated. In particular, we will be interested in strict functions because they arise from various implementation techniques. Reasoning with rewrite systems about such functions is nontrivial in the presence of errors due to the non-strict parameter passing semantics inherent in rewrite systems. In particular, rules formalizing strictness easily destroy rewrite rule confluence. We show how to mechanically extend rewrite rule systems so that strict parameter passing is imposed and so that convergent reasoning about terms which may turn out to be erroneous, becomes possible. Integration of non-strict functions will also be possible.