A recursive program is determined, up to bisimilarity, by the operation of the recursion body on arbitrary processes, of which it is a fixpoint. The traditional proof of this fact uses Howe’s method, but that does not tell us how the fixpoint is obtained. In this paper, we show that the fixpoint may be obtained by a least fixpoint procedure iterated through the hierarchy of countable ordinals, ...

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 v...

We show that the modal μ-calculus over GL collapses to the modal fragment by showing that the fixpoint formula is reached after two iterations and answer to a question posed by van Benthem in [vBe06]. Further, we introduce the modal μ∼-calculus by allowing fixpoint constructors for any formula where the fixpoint variable appears guarded but not necessarily positive and show that this calculus o...