Higher-Order Equational Unification via Explicit Substitutions

Higher-Order Unification via Explicit Substitutions (Extended Abstract)

Higher-order uniication is equational uniication for-conversion. But it is not rst-order equational uniication, as substitution has to avoid capture. In this paper higher-order uniication is reduced to rst-order equational uniication in a suitable theory: the-calculus of explicit substitutions.

Higher Order Unification via Explicit Substitutions

Higher order uniication is equational uniication for-conversion. But it is not rst order equational uniication, as substitution has to avoid capture. Thus the methods for equational uniication (such as narrowing) built upon grafting (i.e. substitution without renaming), cannot be used for higher order uniication, which needs speciic algorithms. Our goal in this paper is to reduce higher order u...

Understanding Higher Order Unification via Explicit Substitutions and Patterns

Higher - Order Unification via Explicit Substitutions at a Distance

We adapted the unification procedure of Huet for a family of explicit substitutions (ES) calculi. The novelty of this adaptation is that it works for calculi with explicit substitutions that belong to the paradigm known as “at a distance”. In this kind of calculi, which have attracted quite some attention due to their simplicity and applicability, the substitution operation is not propagated ov...

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...