A type-directed abstraction refinement approach to higher-order model checking

Abstract

The trivial-automaton model checking problem for higher-order recursion schemes has become a widely studied object in connection with the automatic verification of higher-order programs. The problem is formidably hard 1 : despite considerable progress in recent years, no decision procedures have been demonstrated to scale robustly beyond recursion schemes that comprise more than a few hundred rewrite rules. We present a new, fixed-parameter polynomial time algorithm, based on a novel, type directed form of abstraction refinement in which behaviours of a scheme are distinguished by the abstraction according to the intersection types that they inhabit (the properties that they satisfy). Unlike other intersection type approaches, our algorithm reasons both about acceptance by the property automaton and acceptance by its dual, simultaneously, in order to minimize the amount of work done by converging on the solution to a problem instance from both sides. We have constructed PREFACE, a prototype implementation of the algorithm, and assembled an extensive body of evidence to demonstrate empirically that the algorithm readily scales to recursion schemes of several thousand rules, well beyond the capabilities of current stateof-the-art higher-order model checkers.

TravMC2: higher-order model checking for alternating parity tree automata

“…We have modified other examples, abstractions of real programs, from the literature [6,14] to check liveness properties. Typically this involved strengthening existing properties to ensure that finite behaviours are checked, where before they were not.…”

“…A wave of practically motivated results starting with TRECS [2,3,6,11,14] has attacked the problem of checking properties described by the class of (alternating) trivial tree automata. These Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.…”

“…To date, the most efficient safety higher-order model checker, PREFACE [14], readily scales to handle several thousand function definitions, but this is not yet the case for liveness properties. Currently there is only a single model checker for liveness properties in the literature, which extends the successful approach of TRECS to properties specified using alternating parity tree automata (APT) [5].…”

Compositional higher-order model checking via ω -regular games over Böhm trees

“…The introduction of negation to higher-order types could be of practical significance, since negative ground types have played a key rôle in PREFACE, a state-of-the-art model checker [18]. It would be interesting to understand the general semantic picture when E is a category, rather than a preorder.…”

“…Higher-order model checking (HOMC), or the model checking problem for trees generated by recursion schemes, is a widely studied problem in connection with the verification of higher-order programs [10,18]. With respect to monadic second-order (MSO) prop- * This work was partially supported by JSPS KAKENHI 23220001.…”