Local Higher-Order Fixpoint Iteration

TL;DR

This paper extends local fixpoint iteration techniques to higher-order functions, providing a new algorithm for efficient fixpoint evaluation in complex applications like program verification.

Contribution

It introduces a novel algorithm for local fixpoint iteration in higher-order functions and proves its correctness, expanding the applicability of fixpoint techniques.

Findings

Algorithm successfully implements local fixpoint iteration for higher-order fixpoints

Proven correctness of the proposed algorithm

Potential for optimization in applications like program verification

Abstract

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.