Polymorphic higher-order recursive path orderings

This paper extends the termination proof techniques based on reduction orderings to a higher-order setting, by defining a family of recursive path orderings for terms of a typed lambda-calculus generated by a signature of polymorphic higher-order function symbols. These relations can be generated from two given well-founded orderings, on the function symbols and on the type constructors. The obtained orderings on terms are well-founded, monotonic, stable under substitution and include β-reductions. They can be used to prove the strong normalization property of higher-order calculi in which constants can be defined by higher-order rewrite rules using first-order pattern matching. For example, the polymorphic version of G¨odel’s recursor for the natural numbers is easily oriented. And indeed, our ordering is polymorphic, in the sense that a single comparison allows to prove the termination property of all monomorphic instances of a polymorphic rewrite rule. Many non-trivial examp...

• Type: Journal
• Year: 2007
• Where: JACM
• Authors: Jean-Pierre Jouannaud, Albert Rubio
• Keywords: Function Symbols, JACM 2007, Recursive Path, Rewrite Rule