Pumping by Typing

Naoki Kobayashi

Abstract: Higher-order recursion schemes (HORS), which are higher-order grammars for generating infinite trees, have recently been studied extensively in the context of model checking and its applications to higher-order program verification. We develop a pumping lemma for HORS by using a novel but simple intersection type system for reasoning about reductions of λ-terms. Our proof is arguably much simpler than the proof of Kartzow and Parys' pumping lemma for collapsible pushdown automata. As an application, we give an alternative proof of Kartzow and Parys' result about the strictness of the hierarchy of trees generated by HORS.