We show that, unlike the case in finitary term rewriting, confluence is not a modular property of infinitary term rewriting systems, even when these are non-collapsing. We also give a positive result: two sufficient conditions for the modularity of confluence in the infinitary setting.

We assume that the Stefan problem with undercooling has a classical solution until the moment of contact of free boundaries and the free boundaries have continuous velocities until the moment of contact. Under these assumptions, we construct a smooth approximation of the global solution of the Stefan problem with undercooling, which, until the contact, gives the classical solution mentioned abo...

Nominal rewriting is a framework of higher-order rewriting introduced in (Fernández, Gabbay & Mackie, 2004; Fernández & Gabbay, 2007). Recently, (Suzuki et al., 2015) revisited confluence of nominal rewriting in the light of feasibility. We report on an implementation of a confluence tool for (non-closed) nominal rewriting, based on (Suzuki et al., 2015) and succeeding studies.

In this note we introduce critical-pair-closing systems which are aimed at analyzing confluence of term rewriting systems. Based on the notion two new confluence criteria are presented. One is a generalization of weak orthogonality based on relative termination, and another is a partial solution to the RTA Open Problem #13.

Terminating functional programs should be deterministic, i.e., should evaluate to a unique result, regardless of the evaluation order. For equational functional programs such determinism is exactly captured by the ground confluence property. For terminating equations this is equivalent to ground local confluence, which follows from local confluence. Checking local confluence by computing critic...

We show the existence of an infinitary confluent and normalising extension of the finite extensional lambda calculus with beta and eta. Besides infinite beta reductions also infinite eta reductions are possible in this extension, and terms without head normal form can be reduced to bottom. As corollaries we obtain a simple, syntax based construction of an extensional Böhm model of the finite la...

Confluence denotes the property of a state transition system that states can be rewritten in more than one way yielding the same result. Although it is a desirable property, confluence is often too strict in practical applications because it also considers states that can never be reached in practice. Additionally, sometimes states that have the same semantics in the practical context are consi...

-Properties of elastic solutions to interface crack problems are discussed in both the open formulation, in which the crack faces are assumed to be traction-free and interpenetration is permitted, and the unilateral formulation, where a contact zone is generally established adjacent to the crack tips. It is shown that if the contact zone is sufficiently small compared with the other dimensions ...

Confluence is a fundamental property of Constraint Handling Rules (CHR) since, as in other rewriting formalisms, it guarantees that the computations are not dependent on rule application order, and also because it implies the logical consistency of the program declarative view. In this paper we are concerned with proving the confluence of nonterminating CHR programs. For this purpose, we derive...