Cyclic lambda graph rewriting

Studies cyclic λ-graphs. The starting point is to treat a λ-graph as a system of recursion equations involving λ-terms, and to manipulate such systems in an unrestricted manner, using equational logic, just as is possible for first-order term rewriting. Surprisingly, now the confluence property breaks down in an essential way. Confluence can be restored by introducing a restraining mechanism on the `copying´ operation. This leads to a family of λ-graph calculi, which are inspired by the family of λσ-calculi (λ-calculi with explicit substitution). However, these concern acyclic expressions only. In this paper we are not concerned with optimality questions for acyclic λ-reduction. We also indicate how Wadsworth´s (1978) interpreter can be simulated in the λ-graph rewrite rules that we propose