Infinite normal forms for non-linear term rewriting systems

Infinite Normal Forms for Non-Linear Term Rewritting Systems

Nonterminating rewrite relations have recently been studied in order to set a framework within which infinite terms can be seen as limits of infinite converging derivations. Results about the existence of infinite normal forms have been given only for orthogonal term rewriting systems, namely left-linear and nonoverlapping systems. In this paper we show that some of those results can be extende...

Two Normal Forms for Rewriting P Systems

Lifting Infinite Normal Form Definitions From Term Rewriting to Term Graph Rewriting

Infinite normal forms are a way of giving semantics to non-terminating rewrite systems. The notion is a generalization of the Böhm tree in the lambda calculus. It was first introduced in [AB97] to provide semantics for a lambda calculus on terms with letrec. In that paper infinite normal forms were defined directly on the graph rewrite system. In [Blo01] the framework was improved by defining t...

Uniqueness of Normal Forms and Modularity of Confluence for Term Rewriting Systems

Programming language interpreters, proving theorems of the form A = B, abstract data types and program optimization can all be represented by a finite set of rules called a rewrite system. In this paper, we study two fundamental concepts, uniqueness of normal forms and confluence, for nonlinear systems in the absence of termination. This is a difficult topic with only a few results so far. Thro...

Unique Normal Forms in Infinitary Weakly Orthogonal Term Rewriting

We present some contributions to the theory of infinitary rewriting for weakly orthogonal term rewrite systems, in which critical pairs may occur provided they are trivial. We show that the infinitary unique normal form property (UN∞) fails by a simple example of a weakly orthogonal TRS with two collapsing rules. By translating this example, we show that UN∞ also fails for the infinitary λβη-ca...