Termination of Constraint Contextual Rewriting

The effective integration of decision procedures in formula simplification is a fundamental problem in mechanical verification. The main source of difficulty occurs when the decision procedure is asked to solve goals containing symbols which are interpreted for the prover but uninterpreted for the decision procedure. To cope with the problem, Boyer & Moore proposed a technique, called augmentation , which extends the information available to the decision procedure with suitably selected facts. Constraint Contextual Rewriting (CCR, for short) is an extended form of contextual rewriting which generalizes the Boyer & Moore integration schema. In this paper we give a detailed account of the control issues related to the termination of CCR. These are particularly subtle and complicated since augmentation is mutually dependent from rewriting and it must be prevented from indefinitely extending the set of facts available to the decision procedure. A proof of termination of CCR is given.

[1]  Fausto Giunchiglia,et al.  Reasoning Theories: Towards an Architecture for Open Mechanized Reasoning Systems , 1994, FroCoS.

[2]  Robert E. Shostak,et al.  Deciding Combinations of Theories , 1982, JACM.

[3]  M. A. McRobbie,et al.  Automated Deduction — Cade-13 , 1996, Lecture Notes in Computer Science.

[4]  Jan Willem Klop,et al.  Term Rewriting Systems: From Church-Rosser to Knuth-Bendix and Beyond , 1990, ICALP.

[5]  Greg Nelson,et al.  Simplification by Cooperating Decision Procedures , 1979, TOPL.

[6]  Edward Y. Chang,et al.  STeP: The Stanford Temporal Prover , 1995, TAPSOFT.

[7]  William McCune,et al.  Automated Deduction—CADE-14 , 1997, Lecture Notes in Computer Science.

[8]  Natarajan Shankar,et al.  On Shostak's Decision Procedure for Combinations of Theories , 1996, CADE.

[9]  Deepak Kapur,et al.  An Overview of the Tecton Proof System , 1994, Theor. Comput. Sci..

[10]  Joxan Jaffar,et al.  Constraint logic programming , 1987, POPL '87.

[11]  Greg Nelson,et al.  Fast Decision Procedures Based on Congruence Closure , 1980, JACM.

[12]  J. Strother Moore,et al.  An Industrial Strength Theorem Prover for a Logic Based on Common Lisp , 1997, IEEE Trans. Software Eng..

[13]  Jean-Pierre Jouannaud,et al.  Rewrite Systems , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[14]  Jaime G. Carbonell,et al.  Automated Deduction — CADE-16 , 2002, Lecture Notes in Computer Science.

[15]  Hantao Zhang,et al.  Contextual Rewriting , 1985, RTA.

[16]  Alan Bundy,et al.  A Framework for the Flexible Integration of a Class of Decision Procedures into Theorem Provers , 1999, CADE.

[17]  Robert S. Boyer,et al.  Integrating decision procedures into heuristic theorem provers: a case study of linear arithmetic , 1988 .

[18]  Hantao Zhang,et al.  Contextual Rewriting in Automated Reasoning , 1995, Fundam. Informaticae.

[19]  Z. Manna,et al.  Integrating decision procedures for temporal verification , 1998 .

[20]  Nikolaj Bjørner,et al.  A Practical Integration of First-Order Reasoning and Decision Procedures , 1997, CADE.