Automata-Based Abstraction for Automated Verification of Higher-Order Tree-Processing Programs

Verifying Higher-Order Functions with Tree Automata

“…We have verified a selection of examples coming from [26] and observed that we can verify the same regular properties as they can.…”

“…Despite the evident scalability issues of this simple version of the verification algorithm, we have been able to verify a series of properties of several classical higher-order functions: map, filter , exists, forall , foldRight, foldLeft as well as higher-order sorting functions parameterised by an ordering function. Most examples are taken from or inspired by [26,28] and have corresponding TRSs in the K set defined above. The property ϕ consists in checking that a finite set of forbidden terms is not reachable (Patterns section of Timbuk specifications).…”

“…Kobayashi et al developed a tree automata-based technique [26] (but not relying on TRS and completion), able to verify regular properties (including safety properties on Example 1). We have verified a selection of examples coming from [26] and observed that we can verify the same regular properties as they can.…”

“…The flow analysis of higher-order functions was studied by Jones [21] who proposed to model higher-order functions as term rewriting systems and use regular grammars to approximate the result. More recently, the breakthrough results of Ong [29] and Kobayashi [23,24,26] show that combining abstraction with model checking techniques can be used with success to analyse higher-order functions automatically. Their approach relies on abstraction for computing over-approximations of the set of reachable states, on which safety properties can then be verified.…”

Extending Timbuk to Verify Functional Programs

“…From a theoretical perspective, Tree Automata Completion can be seen as an alternative to well-established higher-order model-checking techniques like PMRS [21] or HORS [19] to verify higher-order functional programs. Timbuk implements Tree Automata Completion but was missing several features for those theoretical results to be usable in practice.…”