Reviving Basic Narrowing Modulo
We define an inference rule called the Parallel rule. Given a rewrite system R and an equational theory E, where R is E-convergent modulo, we show that if R is saturated under the Parallel rule then Basic Narrowing modulo E is complete for R. If R is finitely saturated under both Parallel and Forward Overlap then Basic Narrowing, with right hand side abstracted, is complete and terminates, and thus it is a decision procedure for unification modulo \(R \cup E\). We give examples, such as the theory of XOR, the theory of abelian groups and Associativity with a unit element. We also show that R has the finite variant property modulo E if and only if R can be finitely saturated under Parallel and Forward Overlap, provided that E unification is finitary.
KeywordsBasic Narrowing E-unification Finite Variant Property
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