Unification in the union of disjoint equational theories: combining decision procedures
Journal of Symbolic Computation
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Variations on the Common Subexpression Problem
Journal of the ACM (JACM)
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
An algorithm for reasoning about equality
Communications of the ACM
Validity Checking for Combinations of Theories with Equality
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
Using Decision Procedures with a Higher-Order Logic
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
A Generalization of Shostak's Method for Combining Decision Procedures
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
Shostak's Congruence Closure as Completion
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
ICS: Integrated Canonizer and Solver
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
Formal Verification of a Combination Decision Procedure
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
On Shostak's Decision Procedure for Combinations of Theories
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Complexity of finitely presented algebras
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Integrating decision procedures for temporal verification
Integrating decision procedures for temporal verification
Decision procedures in automated deduction
Decision procedures in automated deduction
Journal of Automated Reasoning
FME '02 Proceedings of the International Symposium of Formal Methods Europe on Formal Methods - Getting IT Right
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
Canonization for disjoint unions of theories
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Strategies for combining decision procedures
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2003)
Efficient theory combination via boolean search
Information and Computation - Special issue: Combining logical systems
Programmed Strategies for Program Verification
Electronic Notes in Theoretical Computer Science (ENTCS)
Generalizing DPLL and satisfiability for equalities
Information and Computation
Enforcing resource bounds via static verification of dynamic checks
ACM Transactions on Programming Languages and Systems (TOPLAS) - Special Issue ESOP'05
Trust and Automation in Verification Tools
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Automated deduction for verification
ACM Computing Surveys (CSUR)
User control and direction of a more efficient simplifier in ACL2
Proceedings of the Eighth International Workshop on the ACL2 Theorem Prover and its Applications
Annals of Mathematics and Artificial Intelligence
Combination of convex theories: Modularity, deduction completeness, and explanation
Journal of Symbolic Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
Canonization for disjoint unions of theories
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Strategies for combining decision procedures
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
Theory-specific automated reasoning
A 25-year perspective on logic programming
Rewriting, inference, and proof
WRLA'10 Proceedings of the 8th international conference on Rewriting logic and its applications
The reduced product of abstract domains and the combination of decision procedures
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Nelson-Oppen, shostak and the extended canonizer: a family picture with a newborn
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
Decision procedures for the formal analysis of software
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
Efficient satisfiability modulo theories via delayed theory combination
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Building efficient decision procedures on top of SAT solvers
SFM'06 Proceedings of the 6th international conference on Formal Methods for the Design of Computer, Communication, and Software Systems
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Ground decision procedures for combinations of theories are used in many systems for automated deduction. There are two basic paradigms for combining decision procedures. The Nelson-Oppen method combines decision procedures for disjoint theories by exchanging equality information on the shared variables. In Shostak's method, the combination of the theory of pure equality with canonizable and solvable theories is decided through an extension of congruence closure that yields a canonizer for the combined theory. Shostak's original presentation, and others that followed it, contained serious errors which were corrected for the basic procedure by the present authors. Shostak also claimed that it was possible to combine canonizers and solvers for disjoint theories. This claim is easily verifiable for canonizers, but is unsubstantiated for the case of solvers. We show how our earlier procedure can be extended to combine multiple disjoint canonizable, solvable theories within the Shostak framework.