Local Higher-Order Fixpoint Iteration

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 higherorder fixpoints, prove its correctness and study its optimisation potential in the context of several applications.

The tail-recursive fragment of timed recursive CTL

“…e.g. [13,9]. For this, it is crucial that the interplay between the fixpoints and the recursive definitions is not too complex.…”

“…The first aspect concerns trTRCTL in particular, as the restriction to tail recursive definitions opens up techniques like local model checking, cf. [9]. The second aspect may include making even more aspects of clock values visible to the logic, for example via so-called diagonal constraints.…”