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The long-range goal of this project is to develop an algorithm to decide whether two terms are unifiable over the theory of quandles. First, it is shown that the general E-unification reduces to the E-matching problem due to the right-cancellation axioms of quandles. The E-matching process takes the general narrowing approach to equational matching. However, a naive application of narrowing is, at best, recursively enumerable and hence will not terminate given terms that do not match. This modification of narrowing places a hard limit on the use of the delta rules of the term rewriting system for quandles to ensure termination. It is implemented in the SWI-Prolog logic programming language. The question remains open as to whether the imposed limits still allow the program to find a unifier for all matching pairs.
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Goldstein, Elliott N., "A Unification Algorithm For The First Order Theory of Quandles" (2021). Senior Projects Spring 2021. 152.
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