Confluence of CHR Revisited: Invariants and Modulo Equivalence

Henning Christiansen; Maja Hanne Kirkeby

doi:10.1007/978-3-030-13838-7_6

Confluence of CHR Revisited: Invariants and Modulo Equivalence

Henning Christiansen, Maja Hanne Kirkeby

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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.

Original language	English
Title of host publication	Logic-Based Program Synthesis and Transformation : 28th International.Symposium, LOPSTR 2018, Frankfurt/Main, Germany, September 4-6, 2018, Revised Selected Papers
Editors	Fred Mesnard, Peter J. Stuckey
Volume	11408
Place of Publication	Cham
Publisher	Springer
Publication date	2019
Pages	94-111
ISBN (Print)	978-3-030-13837-0
ISBN (Electronic)	978-3-030-13838-7
DOIs	https://doi.org/10.1007/978-3-030-13838-7_6
Publication status	Published - 2019
Event	LOPSTR 2018 -28th International Symposium on Logic-Based Program Synthesis and Transformation - Göthe-University Frankfurt am Main, Frankfurt am Main, Germany Duration: 4 Sep 2018 → 6 Sep 2018 Conference number: 28 http://ppdp-lopstr-18.cs.uni-frankfurt.de/lopstr18.html

Conference

Conference	LOPSTR 2018 -28th International Symposium on Logic-Based Program Synthesis and Transformation
Number	28
Location	Göthe-University Frankfurt am Main
Country/Territory	Germany
City	Frankfurt am Main
Period	04/09/2018 → 06/09/2018
Internet address	http://ppdp-lopstr-18.cs.uni-frankfurt.de/lopstr18.html

Series	Lecture Notes in Computer Science
Volume	11408
ISSN	0302-9743

Series	Theoretical Computer Science and General Issues
Volume	11408

Keywords

Constraint Handling Rules
Confluence
Confluence modulo equivalence
Invariants
Observable confluence

Link to document

10.1007/978-3-030-13838-7_6

ComgXHR-RevisitedAccepted author manuscript, 387 KB

Cite this

Christiansen, H., & Kirkeby, M. H. (2019). Confluence of CHR Revisited: Invariants and Modulo Equivalence. In F. Mesnard, & P. J. Stuckey (Eds.), Logic-Based Program Synthesis and Transformation: 28th International.Symposium, LOPSTR 2018, Frankfurt/Main, Germany, September 4-6, 2018, Revised Selected Papers (Vol. 11408, pp. 94-111). Springer. Lecture Notes in Computer Science Vol. 11408 Theoretical Computer Science and General Issues Vol. 11408 https://doi.org/10.1007/978-3-030-13838-7_6

Christiansen, Henning ; Kirkeby, Maja Hanne. / Confluence of CHR Revisited : Invariants and Modulo Equivalence. Logic-Based Program Synthesis and Transformation: 28th International.Symposium, LOPSTR 2018, Frankfurt/Main, Germany, September 4-6, 2018, Revised Selected Papers. editor / Fred Mesnard ; Peter J. Stuckey. Vol. 11408 Cham : Springer, 2019. pp. 94-111 (Lecture Notes in Computer Science, Vol. 11408). (Theoretical Computer Science and General Issues, Vol. 11408).

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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.",

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Christiansen, H & Kirkeby, MH 2019, Confluence of CHR Revisited: Invariants and Modulo Equivalence. in F Mesnard & PJ Stuckey (eds), Logic-Based Program Synthesis and Transformation: 28th International.Symposium, LOPSTR 2018, Frankfurt/Main, Germany, September 4-6, 2018, Revised Selected Papers. vol. 11408, Springer, Cham, Lecture Notes in Computer Science, vol. 11408, Theoretical Computer Science and General Issues, vol. 11408, pp. 94-111, LOPSTR 2018 -28th International Symposium on Logic-Based Program Synthesis and Transformation, Frankfurt am Main, Germany, 04/09/2018. https://doi.org/10.1007/978-3-030-13838-7_6

Confluence of CHR Revisited : Invariants and Modulo Equivalence. / Christiansen, Henning ; Kirkeby, Maja Hanne.

Logic-Based Program Synthesis and Transformation: 28th International.Symposium, LOPSTR 2018, Frankfurt/Main, Germany, September 4-6, 2018, Revised Selected Papers. ed. / Fred Mesnard; Peter J. Stuckey. Vol. 11408 Cham : Springer, 2019. p. 94-111 (Lecture Notes in Computer Science, Vol. 11408). (Theoretical Computer Science and General Issues, Vol. 11408).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Christiansen H , Kirkeby MH. Confluence of CHR Revisited: Invariants and Modulo Equivalence. In Mesnard F, Stuckey PJ, editors, Logic-Based Program Synthesis and Transformation: 28th International.Symposium, LOPSTR 2018, Frankfurt/Main, Germany, September 4-6, 2018, Revised Selected Papers. Vol. 11408. Cham: Springer. 2019. p. 94-111. (Lecture Notes in Computer Science, Vol. 11408). (Theoretical Computer Science and General Issues, Vol. 11408). doi: 10.1007/978-3-030-13838-7_6