Local higher-order fixpoint iteration

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