Diagrammatic confluence for Constraint Handling Rules

Abstract

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 non-terminating CHR programs. For this purpose, we derive from van Oostrom's decreasing diagrams method a novel criterion on CHR critical pairs that generalizes all preexisting criteria. We subsequently improve on a result on the modularity of CHR confluence, which permits modular combinations of possibly non-terminating confluent programs, without loss of confluence

On Termination, Confluence and Consistent CHR-based Type Inference

“…Hence, the result of Section 3 provides some general consistency criteria to ensure that type class programs are safe. Establishing confluence in the presence of non-termination is a notoriously difficult problem (Haemmerlé 2012). Our results in Section 4 advance the state of the art in this area by showing that existentially-terminating goals (to non-False states) are confluent for range-restricted, ground-terminating and locally confluent programs.…”

“…From the point of view of general CHR confluence state of art, we plan generalizing consistency of ground-confluent but non range-restricted program by using CLP projection (Haemmerlé et al 2011). It seems also worthwhile to prove ground-confluence of non ground-terminating programs using diagrammatic techniques (Haemmerlé 2012).…”

On Combining Backward and Forward Chaining in Constraint Logic Programming

“…Indeed, one can understand the CLP clauses as a set of backward rules and the constraint solver as an arbitrary confluent program, with both sets of rules using disjoint alphabets of predicate symbols for their heads. Thanks to the modularity of confluence [13,14] (i.e., the union of nonoverlapping confluent programs is confluent), the results presented here ensure the soundness and completeness of a general operational semantics for CLP, where the implementation of the solver would be made explicit.…”

“…This suggests that the confluence proof techniques for classical CHR-such as those based on local confluence [2], strong confluence [16], or decreasing diagrams [14]-can be extended to deal with the semantics presented here.…”

Confluence Modulo Equivalence in Constraint Handling Rules

“…Of other work concerned with confluence for CHR, we may mention [10,15] which considered confluence for non-terminating CHR programs. We may also refer to [18] that gives an overview of CHR related research until 2010, including confluence.…”