The unification of infinite sets of terms and its applications
In various fields using first order terms — like automated reasoning, logic programming or term rewriting — we encounter infinite sequences of structurally similar terms, leading to non-terminating or at least time and space consuming computations. As a remedy we introduce a meta-language consisting of recursive terms (R-terms), which are a finite representation of infinite sets of terms.
Given two R-terms r1 and r2 there may be infinitely many most general unifiers between those terms represented by r1 and those represented by r2. We present a unification algorithm for R-terms, which computes all first order unifiers simultaneously and yields a finite and complete representation for the potentially infinite set of first order unifiers.
We demonstrate the practicability of our approach by applying R-terms and meta-unification to automated theorem proving, logic programming and cycle unification.
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