Local Higher-Order Fixpoint Iteration

Florian Bruse
(University of Kassel)
Jörg Kreiker
(University of Applied Sciences, Fulda)
Martin Lange
(University of Kassel)
Marco Sälzer
(University of Kassel)

Local fixpoint iteration describes a technique that restricts fixpoint iteration in function spaces to needed arguments only. It has been studied well for first-order functions in abstract interpretation and also in model checking. Here we consider the problem for least and greatest fixpoints of arbitrary type order. We define an abstract algebra of simply typed higher-order functions with fixpoints that can express fixpoint evaluation problems as they occur routinely in various applications, including program verification. We present an algorithm that realises local fixpoint iteration for such higher-order fixpoints, prove its correctness and study its optimisation potential in the context of several applications.

In Jean-Francois Raskin and Davide Bresolin: Proceedings 11th International Symposium on Games, Automata, Logics, and Formal Verification (GandALF 2020), Brussels, Belgium, September 21-22, 2020, Electronic Proceedings in Theoretical Computer Science 326, pp. 97–113.
Published: 20th September 2020.

ArXived at: http://dx.doi.org/10.4204/EPTCS.326.7 bibtex PDF
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