Predicate Abstraction and CEGAR for $$\nu \mathrm {HFL}_\mathbb {Z}$$ Validity Checking

An Overview of the HFL Model Checking Project

“…One approach [18] to proving the validity of a νHFL(Z) formula ϕ is to apply predicate abstraction to obtain a pure νHFL formula ϕ (i.e., a νHFL(Z) formula without integers) as an underapproximation of ϕ, and then apply an algorithm for pure HFL model checking [17] 2 (recall that pure HFL model checking is decidable; despite its high worst-case complexity, practical algorithms exist, which do not always suffer from the high complexity). This approach may be viewed as a generalization of the HORS model checking approach to (un)reachability verification [26] and non-termination verification [31].…”

“…As in standard approaches to combining predicate abstraction and model checking, predicates to be used for abstraction can be found in a counterexample-guided manner. More details can be found in [18].…”

Automatic HFL(Z) Validity Checking for Program Verification

“…The reduction provides a uniform approach to the temporal property verification of higher-order functional programs. Automatic validity checkers have been implemented for the first-order fragment of HFL(Z) [13] and νHFL(Z) [13,10,11], the fragment of HFL(Z) without least fixpoint operators. The former [13] enables automated verification of temporal properties of first-order programs, and the latter [13,10,11] enables automated verification of safety properties of higher-order programs.…”

“…Automatic validity checkers have been implemented for the first-order fragment of HFL(Z) [13] and νHFL(Z) [13,10,11], the fragment of HFL(Z) without least fixpoint operators. The former [13] enables automated verification of temporal properties of first-order programs, and the latter [13,10,11] enables automated verification of safety properties of higher-order programs. This line of work provides a streamlined, general approach to automated verification of temporal properties of programs.…”

“…Inspired by the approach of Kobayashi et al [13] for first-order HFL(Z), we approximate a given HFL(Z) formula with a formula of νHFL(Z), the fragment of HFL(Z) without the least-fixpoint operator. We can then use existing solvers [10,11] to prove the validity of the νHFL(Z) formula. The idea of removing the least-fixpoint operator is as follows.…”