Resolving inductive definitions with binders in higher-order typed functional programming

Abstract

This paper studies inductive definitions involving binders, in which aliasing between free and bound names is permitted. Such aliasing occurs in informal specifications of operational semantics, butis excluded by the common representation of binding as meta-level ?-abstraction. Drawing upon ideas from functional logic programming, were present such definitions with aliasing as recursively defined functions in a higher-order typed functional programming language that extend score ML with types for name-binding, a type of "semi-decidable propositions" and existential quantification for types with decidable equality. We show that the representation is sound and complete with respect to the language's operational semantics, which combines the use of evaluation contexts with constraint programming. We also give a new and simple proof that the associated constraint problem is NP-complete.