On the relationship between higher-order recursion schemes and higher-order fixpoint logic

Abstract

We study the relationship between two kinds of higher-order extensions of model checking: HORS model checking, where models are extended to higher-order recursion schemes, and HFL model checking, where the logic is extended to higher-order modal fixpoint logic. These extensions have been independently studied until recently, and the former has been applied to higher-order program verification, while the latter has been applied to assume-guarantee reasoning and process equivalence checking. We show that there exist (arguably) natural reductions between the two problems. To prove the correctness of the translation from HORS to HFL model checking, we establish a type-based characterization of HFL model checking, which should be of independent interest. The results reveal a close relationship between the two problems, enabling cross-fertilization of the two research threads. Categories and Subject Descriptors F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic Keywords higher-order recursion schemes, higher-order modal fixpoint logic, model checking By the condition βj > 0 and Lemma 20, T IsZero k (β j #) is accepted from q0. Thus, we have the required result.

Local Higher-Order Fixpoint Iteration

“…Denotational semantics is perhaps the application domain which is most easily seen to need lattices of functions, possibly of higher order, in order to explain the meaning of, for example, functional programs of higher order. Certain infinite-state model checking problems, in particular so-called higher-order model checking [29] are tightly linked to the evaluation of fixpoints in functions spaces as well [22].…”