The notion of skew confluence was introduced to characterize non-confluent term rewriting systems that had unique infinite normal forms or Böhm like trees. This notion however is not expressive enough to deal with all possible sources of non-confluence in the context of infinite terms or terms extended with letrec. To that end, we present a new notion called ω-skew confluence. We show that ω-sk...

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.

The Beganchik locality is a stratigraphic sequence of loessic deposits, pedogenic horizons and Paleolithic occupations located at the Kama-Volga confluence. exposed on bluff formed west side an erosional remnant between Kuybyshev Reservoir former channel Aktay River. Although site known for its Terminal Paleolithic-Mesolithic Pleistocene-Holocene transition, evidence older remains fauna has bee...

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...

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...