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(Co-)Inductive semantics for Constraint Handling Rules



In this paper, we address the problem of defining a fixpoint semantics for Constraint Handling Rules (CHR) that captures the behavior of both simplification and propagation rules in a sound and complete way with respect to their declarative semantics. Firstly, we show that the logical reading of states with respect to a set of simplification rules can be characterized by a least fixpoint over the transition system generated by the abstract operational semantics of CHR. Similarly, we demonstrate that the logical reading of states with respect to a set of propagation rules can be characterized by the greatest fixpoint. Then, in order to take advantage of both types of rules without losing fixpoint characterization, we present a new operational semantics with persistent constraints.

We finally establish that this semantics can be characterized by two nested fixpoints, and we show that the resulting language is an elegant framework to program using coinductive reasoning.



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Abdennadher, S. 1997. Operational semantics and confluence of Constraint Propagation Rules. In Third International Conference on Principles and Practice of Constraint Programming (CP), LNCS, vol. 1330. Springer, Berlin, 252266.
Abdennadher, S., Frühwirth, T. and Meuss, H. 1999. Confluence and semantics of Constraint Simplification Rules. Constraints 4, 2, 133165.
Barwise, J. and Moss, L. 1996. Vicious Circles. CSLI, Stanford, CA.
Betz, H., Raiser, F. and Frühwirth, T. 2010. A complete and terminating execution model for Constraint Handling Rules. Theory and Practice of Logic Programming 10, special issues 4–6 (ICLP), 597610.
Bezem, M. and Coquand, T. 2005. Automating coherent logic. In International Conferences on Logic for Programming, Artificial Intelligence and Reasoning (LPAR), LNCS, vol. 3835. Springer, Berlin, 246260.
Clarke, E. M., Grumberg, O. and Peled, D. A. 2000. Model Checking. MIT Press, Cambridge, MA.
de Koninck, L., Schrijvers, T. and Demoen, B. 2007. User-definable rule priorities for CHR. In 9th International Conference on Principles and Practice of Declarative Programming, July 14–16, Wroclaw, Poland(PPDP). ACM, New York, 2536.
Frühwirth, T. 1998. Theory and practice of Constraint Handling Rules. Journal of Logic Programming 37, 1–3, 95138.
Frühwirth, T. 2009. Constraint Handling Rules. Cambridge University Press, Cambridge, UK.
Gabbrielli, M. and Meo, M. 2009. A compositional semantics for CHR. ACM Transactions Computer Logic 10, 2.
Gabbrielli, M., Meo, M. and Tacchella, P. 2008. A compositional semantics for CHR with propagation rules. In Constraint Handling Rules: Current Research Topics. LNAI, vol. 5388. Springer, Berlin, 119160.
Goguen, J. A., Lin, K. and Rosu, G. 2000. Circular coinductive rewriting. In Proceedings of the 15th IEEE International Conference on Automated Software Engineering. ASE, Washington, DC, 123132.
Haemmerlé, R. 2011. Toward Logically Complete Fixpoint Semantics for Constraint Hangling Rules. Technical Report CLIP3/2011, Technical University of Madrid, Madrid, Spain.
Haemmerlé, R. and Fages, F. 2007. Abstract critical pairs and confluence of arbitrary binary relations. In Conference on Rewriting Techniques and Applications, LNCS, vol. 4533. Springer, New York, 214228.
Haemmerlé, R., Lopez-Garcia, P. and Hemenegildo, M. V. To appear. CLP projection for constraint handling rules. In Conference on Principles and Practice of Declarative Programming (PPDP). ACM, New York.
Jaffar, J. and Lassez, J.-L. 1987. Constraint logic programming. In Symposium on Principles of Programming Languages (POPL). ACM, New York, 111119.
Lloyd, J. 1987. Foundations of Logic Programming. Springer, Berlin.
Raiser, F., Betz, H. and Frühwirth, T. 2009. Equivalence of CHR States Revisited. CHR Report CW 555. Katholieke University, Leuven, Belgium, 34–48.
Rutten, J. 1998. Automata and coinduction (an exercise in coalgebra). In Proceedings of the Ninth International Conference on Concurrency Theory (CONCUR), LNCS, vol. 1466. Springer, New York, 194218.
Saraswat, V. A., Rinard, M. C. and Panangaden, P. 1991. Semantic foundations of concurrent constraint programming. In Proceedings of Principles of Programming Languages (POPL). ACM, New York, 333352.
Simon, L., Mallya, A., Bansal, A. and Gupta, G. 2006. Coinductive logic programming. In International Conference on Logic Programming (ICLP), LNCS, vol. 4079. Springer, Berlin, 330345.
Tarski, A. 1955. A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics 5 (2), 285309.
Terese, . 2003. Term Rewriting Systems, Vol. 55. Cambridge University Press, Cambridge, UK.


(Co-)Inductive semantics for Constraint Handling Rules



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