Bounded Higher-order Unification using Regular Terms
نویسنده
چکیده
We present a procedure for the bounded unification of higher-order terms [24]. The procedure extends G. P. Huet’s pre-unification procedure [11] with rules for the generation and folding of regular terms. The concise form of the procedure allows the reuse of the pre-unification correctness proof. Furthermore, the regular terms can be restricted in order to get a decidable unifiability problem. Finally, the procedure avoids re-computation of terms in a non-deterministic search which leads to a better performance in practice when compared to other bounded unification algorithms.
منابع مشابه
Higher-Order Rigid E-Unification
Higher-order E-uniication, i.e. the problem of nding substitutions that make two simply typed-terms equal modulo or-equivalence and a given equational theory, is undecidable. We propose to rigidify it, to get a resource-bounded decidable uniication problem (with arbitrary high bounds), providing a complete higher-order E-uniication procedure. The techniques are inspired from Gallier's rigid E-u...
متن کاملRegular expression order-sorted unification and matching
We extend order-sorted unification by permitting regular expression sorts for variables and in the domains of function symbols. The obtained signature corresponds to a finite bottom-up unranked tree automaton. We prove that regular expression order-sorted (REOS) unification is of type infinitary and decidable. The unification problem presented by us generalizes some known problems, such as, e.g...
متن کاملBounded Second-Order Unification Is NP-Complete
Bounded Second-Order Unification is the problem of deciding, for a given second-order equation t ? = u and a positive integer m, whether there exists a unifier σ such that, for every second-order variable F , the terms instantiated for F have at most m occurrences of every bound variable. It is already known that Bounded Second-Order Unification is decidable and NP-hard, whereas general Second-...
متن کاملA Resolution Calculus for Second-order Logic with Eager Unification
The Effectiveness of the first-order resolution calculus is impaired when lifting it to higher-order logic. The main reason for that is the semi-decidability and infinitary nature of higher-order unification problems, which requires the integration of unification within the calculus and results in a non-effective search for refutations. We present a modification of the constrained resolution ca...
متن کاملOn the complexity of Bounded Second-Order Unification and Stratified Context Unification
Bounded Second-Order Unification is a decidable variant of undecidable Second-Order Unification. Stratified Context Unification is a decidable restriction of Context Unification, whose decidability is a long-standing open problem. This paper is a join of two separate previous, preliminary papers on NP-completeness of Bounded Second-Order Unification and Stratified Context Unification. It clarif...
متن کامل