Confluence of CHR revisited: invariants and modulo equivalence

H. Christiansen, M. H. Kirkeby: “Confluence of CHR revisited: invariants and modulo equivalence”. In Logic-Based Program Synthesis and Transformation, 28th International Symposium, LOPSTR 2018, Frankfurt/Main, Germany, September 4-6, 2018, Revised Selected Papers. A part of Lecture Notes in Computer Science, Vol. 11408, pp. 83–99. DOI: 10.1007/978-3-030-13838-7_6

Abstract 

Abstract simulation of one transition system by another is introduced as a means to simulate a potentially infinite class of similar transition sequences within a single transition sequence. This is useful for proving confluence under invariants of a given system, as it may reduce the number of proof cases to consider from infinity to a finite number. The classical confluence results for Constraint Handling Rules (CHR) can be explained in this way, using CHR as a simulation of itself. Using an abstract simulation based on a ground representation, we extend these results to include confluence under invariant and modulo equivalence, which have not been done in a satisfactory way before.