Journal of Symbolic Computation
Minimal and complete word unification
Journal of the ACM (JACM)
Communications of the ACM
The MVL theorem proving system
ACM SIGART Bulletin - Special issue on implemented knowledge representation and reasoning systems
Programming in Mathematica (2nd ed.)
Programming in Mathematica (2nd ed.)
Word unification and transformation of generalized equations
Journal of Automated Reasoning
Symbolic mathematics system evaluators (extended abstract)
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Solvability of context equations with two context variable is decidable
Journal of Symbolic Computation
The Mathematica Book
Theorem Proving with Sequence Variables and Flexible Arity Symbols
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
E-Unification for Subsystems of S4
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Context Sequence Matching for XML
Electronic Notes in Theoretical Computer Science (ENTCS)
The meaning of infinity in calculus and computer algebra systems
Journal of Symbolic Computation
VeriFLog: a constraint logic programming approach to verification of website content
APWeb'06 Proceedings of the 2006 international conference on Advanced Web and Network Technologies, and Applications
Reasoning support for expressive ontology languages using a theorem prover
FoIKS'06 Proceedings of the 4th international conference on Foundations of Information and Knowledge Systems
Anti-patterns for rule-based languages
Journal of Symbolic Computation
Anti-unification for Unranked Terms and Hedges
Journal of Automated Reasoning
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We study matching in flat theories both from theoretical and practical points of view. A flat theory is defined by the axiom f(x@?,f(y@?),z@?)@?f(x@?,y@?,z@?) that indicates that nested occurrences of the function symbol f can be flattened out. From the theoretical side, we design a procedure to solve a system of flat matching equations and prove its soundness, completeness, and minimality. The minimal complete set of matchers for such a system can be infinite. The procedure enumerates this set and stops if it is finite. We identify a class of problems on which the procedure stops. From the practical point of view, we look into restrictions of the procedure that give an incomplete terminating algorithm. From this perspective, we give a set of rules that, in our opinion, describes the precise semantics for the flat matching algorithm implemented in the Mathematica system.