The undecidability of simultaneous rigid E-unification
Theoretical Computer Science
Communications of the ACM
Communications of the ACM
Maple's evaluation process as constraint contextual rewriting
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
An Order Theory Resolution Calculus
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Termination of Constraint Contextual Rewriting
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
Uniform Derivation of Decision Procedures by Superposition
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
System Description: RDL : Rewrite and Decision Procedure Laboratory
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Integrating decision procedures for temporal verification
Integrating decision procedures for temporal verification
Formal proof of a program: Find
Science of Computer Programming
Contextual Rewriting In Automated Reasoning
Fundamenta Informaticae
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The most effective theorem proving systems (such as PVS, Acl2, and HOL) provide a kind of two-level reasoning, where the knowledge of a given domain is treated by a special purpose reasoner and a generic reasoning module is used for the actual problem specification. To obtain an effective integration between these two levels of reasoning is far from being a trivial task. In this paper, we propose a combination of Window Reasoning and Constraint Contextual Rewriting to achieve an effective integration of such levels. The former supports hierarchical reasoning for arbitrarily complex expressions. The latter provides the necessary theorem proving support for domain specific reasoning. The two levels of reasoning cooperate by building and exploiting a context, i.e. a set of facts which can be assumed true while transforming a given subexpression. We also argue that the proposed combination schema can be useful for building sound simplifiers to be used in computer algebra systems.