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Variadic equational matching in associative and commutative theories
Journal of Symbolic Computation ( IF 0.7 ) Pub Date : 2021-01-19 , DOI: 10.1016/j.jsc.2021.01.001
Besik Dundua , Temur Kutsia , Mircea Marin

In this paper we study matching in equational theories that specify counterparts of associativity and commutativity for variadic function symbols. We design a procedure to solve a system of matching equations and prove its termination, soundness, completeness, and minimality. The minimal complete set of matchers for such a system can be infinite, but our algorithm computes its finite representation in the form of solved set. From the practical side, we identify two finitary cases and impose restrictions on the procedure to get an incomplete algorithm, which, based on our experiments, describes the input-output behavior and properties of Mathematica's flat and orderless pattern matching.



中文翻译:

关联和交换理论中的方差方程匹配

在本文中,我们研究方程式理论中的匹配,该方程式指定可变参数符号的关联性和可交换性。我们设计了一个过程来求解匹配方程组,并证明其终止,稳健性,完整性和最小性。这样的系统的匹配器的最小完整集可以是无限的,但是我们的算法以求解集的形式计算其有限表示。从实践的角度,我们确定了两种最终情况,并对程序施加了限制,以获得一个不完整的算法,该算法根据我们的实验描述了Mathematica的平面和无序模式匹配的输入输出行为和属性。

更新日期:2021-01-22
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