Graph reducibility of term rewriting systems

Abstract

Term rewriting is generally implemented using graph rewriting for efficiency reasons. Graph rewriting allows sharing of common structures thereby saving both time and space. This implementation is sound in the sense that computation of a normal form of a graph yields a normal form of the corresponding term. However, certain properties of term rewriting systems are not reflected in their graph rewriting implementations. Weak normalization is one such property. An undesirable side effect of this is that it may be impossible to compute a normal form of a normalizable term. In this paper, we present some sufficient conditions for preservation of weak normalization and discuss the implication of the results to modularity.