A Note on the Relation between Inflationary Fixpoints and Least Fixpoints of Higher-Order

Least fixpoints of monotone functions are an important concept in computer science which can be generalised to inflationary fixpoints of arbitrary functions. This raises questions after the expressive power of these two concepts, in particular whether the latter can be expressed as the former in certain circumstances. We show that the inflationary fixpoint of an arbitrary function on a lattice of finite height can be expressed as the least fixpoint of a monotone function on an associated function lattice