Recursion Schemes, Collapsible Pushdown Automata and Higher-Order Model Checking

This paper is about two models of computation that underpin recent developments in the algorithmic verification of higher-order computation. Recursion schemes are in essence the simply-typed lambda calculus with recursion, generated from first-order symbols. Collapsible pushdown automata are a generalisation of pushdown automata to higher-order stacks — which are iterations of stack of stacks — that contain symbols equipped with links. We study and compare the expressive power of the two models and the algorithmic properties of infinite structures such as trees and graphs generated by them. We conclude with a brief overview of recent applications to the model checking of higher-order functional programs. A central theme of the work is the fruitful interplay of ideas between the neighbouring fields of semantics and algorithmic verification.

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