Infinitary Term Graph Rewriting

Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by avoiding duplication. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can be used to reason about lazy evaluation. In this paper, we combine term graph rewriting and infinitary term rewriting thereby addressing both components of lazy evaluation: non-strictness and sharing. Moreover, we show how our theoretical underpinnings, based on a metric space and a complete semilattice, provides a unified framework for both term rewriting and term graph rewriting. This makes it possible to study the correspondences between these two worlds. As an example, we show how the soundness of term graph rewriting w.r.t. term rewriting can be extended to the infinitary setting.