Higher-Order Substitutions

Higher-Order Equational Unification via Explicit Substitutions

We show how to reduce the uniication problem modulo-conversion and a rst-order equational theory E, into a rst-order uni-cation problem in a union of two non-disjoint equational theories including E and a calculus of explicit substitutions. A rule-based uniica-tion procedure in this combined theory is described and may be viewed as an extension of the one initially designed by G. Dowek, T. Hard...

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...

Functional Programming With Higher-order Abstract Syntax and Explicit Substitutions

This paper sketches a foundation for programming with higher-order abstract syntax and explicit substitutions based on contextual modal type theory [NPP05]. Contextual modal types not only allows us to cleanly separate the representation of data objects from computation, but allow us to recurse over data objects with free variables. In this paper, we extend these ideas even further by adding fi...

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...