Conditional rewrite rules are notorious for being difficult to implement in rewrite engines. This is because, like in the case of function calls in programming language implementations, rewrite engines need to ”freeze” the current rewriting environment and to create a new one in which the condition is reduced. Stacking these rewriting environments efficiently can easily become a nontrivial task...

The use of expansionary-rewrite rules in various typed-calculi has become increasingly common in recent years as their advantages over contractive-rewrite rules have become apparent. Not only does one obtain the decidability of-equality, but rewrite relations based on expansions give a natural interpretation of long-normal forms, generalise more easily to other type constructors, retain key pro...

This paper introduces several related graph rewrite systems derived from known identities on classical structures within a †-symmetric monoidal category. First, we develop a rewrite system based on a single classical structure, and use it to develop a proof of the so-called “spider-theorem,” where a connected graph containing a single classical structure can be uniquely determined by the number...

In 1978, Klop demonstrated that a rewrite system constructed by adding the untyped lambda calculus, which has the Church-Rosser property, to a Church-Rosser rst-order algebraic rewrite system may not be Church-Rosser. In contrast, Breazu-Tannen recently showed that augmenting any Church-Rosser rst-order algebraic rewrite system with the simply-typed lambda calculus results in a Church-Rosser re...

In this paper we consider  (extended) metaplectic representation of the  semidirect product  $G_{mathbb{J}}=mathbb{R}^{2d}timesmathbb{J}$  where $mathbb{J}$ is a closed subgroup of $Sp(d,mathbb{R})$, the symplectic group. We will investigate continuous representation frame on $G_{mathbb{J}}$. We also discuss the existence of duals for such frames and give several characterization for them. Fina...