Normal higher-order termination

Abstract

We extend the termination proof methods based on reduction orderings to higher-order rewriting systems based on higher-order pattern matching. We accommodate, on the one hand, a weakly polymorphic, algebraic extension of Church's simply typed λ-calculus and, on the other hand, any use of eta, as a reduction, as an expansion, or as an equation. The user's rules may be of any type in this type system, either a base, functional, or weakly polymorphic type.