Reduction from branching-time property verification of higher-order programs to HFL validity checking

An Overview of the HFL Model Checking Project

“…We have so far discussed automated methods for HFL(Z) validity checking. As the HFL(Z) formula obtained from a program verification problem can be considered a kind of "verification condition," 3 it is also natural to prove the validity of the formula semi-automatically, possibly using a proof assistant such as Coq, as exploited in our recent work [29,44]. Integration with the automated methods is left for future work.…”

“…In the reductions from program verification problems to HFL(Z) validity checking [25,27,44], liveness and safety properties are respectively turned into µ-and ν-formulas. Thus, following the techniques for liveness property verification [8,14,32,33,37], it is natural to first remove µ-formulas by using analogous techniques.…”

Temporal Refinements for Guarded Recursive Types

“…Automatic verification of higher-order programs with infinite data-types (integers) has been explored for safety [40], termination [46], and more generally ω-regular [51] properties. In presence of infinite datatypes, semi-automatic extensions of HOMC have recently been proposed [69]. In contrast with this paper, most HOMC approaches do not consider input-output behaviors on coalgebraic data.…”

Fold/Unfold Transformations for Fixpoint Logic

“…As mentioned in Section 1, fixpoint logic-based approaches to program verification (including CHC-based ones) have been drawing attention. Kobayashi et al [22,23,35] have shown that temporal property verification of (higher-order) programs can be reduced to the validity checking of (higher-order) fixpoint logic formulas. They proposed a concrete method for checking validity of first-order fixpoint formulas and implemented a validity checking tool Mu2CHC.…”