Exact bounds for acyclic higher-order recursion schemes

Semantics of Higher-Order Recursion Schemes

Higher-order recursion schemes are recursive equations defining new operations from given ones called “terminals”. Every such recursion scheme is proved to have a least interpreted semantics in every Scott’s model of λ-calculus in which the terminals are interpreted as continuous operations. For the uninterpreted semantics based on infinite λ-terms we follow the idea of Fiore, Plotkin and Turi ...

Types and Recursion Schemes for Higher-Order Program Verification

Saturation-Based Model Checking of Higher-Order Recursion Schemes

Model checking of higher-order recursion schemes (HORS) has recently been studied extensively and applied to higher-order program verification. Despite recent efforts, obtaining a scalable model checker for HORS remains a big challenge. We propose a new model checking algorithm for HORS, which combines two previous, independent approaches to higher-order model checking. Like previous type-based...

IO vs OI in Higher-Order Recursion Schemes

We propose a study of the modes of derivation of higher-order recursion schemes, proving that value trees obtained from schemes using innermost-outermost derivations (IO) are the same as those obtained using unrestricted derivations. Given that higher-order recursion schemes can be used as a model of functional programs, innermost-outermost derivations policy represents a theoretical view point...

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 —...