Model-checking higher-order functions

Abstract. We present HECTOR, an observational equivalence checker for a higherorder fragment of ML. The input language is RML, the canonical restriction of standard ML to ground-type references. HECTOR accepts programs from a decidable fragment of RML identified by us at ICALP'11, which comprises programs of short-type (order at most 2 and arity at most 1) that may contain free variables whose arguments are also of short-type. This is an expressive fragment that contains complex higher-order types, and includes many examples from the literature which have proven challenging to verify using other methods. To our knowledge, HECTOR is the first fully-automated equivalence checker for higherorder, call-by-value programs. Both sound and complete, the tool relies on the fully abstract game semantics of RML to construct, on-the-fly, visibly pushdown automata which precisely capture program behaviour. These automata are then checked for language equivalence, and if they are inequivalent a counterexample (in the form of a separating context) is constructed.

show abstract

“…MAGE can only check reachability. Other tools, notably TRECS [10] and HMC [9], can verify safety properties of ML programs, but not equivalence.…”

Section: Examples and Experimentsmentioning

confidence: 99%

Hector: An Equivalence Checker for a Higher-Order Fragment of ML

Hopkins

Murawski

Ong

2012

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…Kobayashi and Ong [7,9] have proposed a type system for recursion schemes that is equivalent to the modal µ-calculus model-checking of recursion schemes (the decidability of the model-checking problem has been proved by Ong [17]). These type systems have been applied to verification of higher-order programs [7,11,10], and practically effective typability checkers have been developed [6,8]. The present work extends type systems to deal with infinite state systems, namely deterministic pushdown automata.…”

Section: Related Workmentioning

confidence: 99%

An Intersection Type System for Deterministic Pushdown Automata

Tsukada

Kobayashi

2012

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract. We propose a generic method for deciding the language inclusion problem between context-free languages and deterministic contextfree languages. Our method extends a given decision procedure for a subclass to another decision procedure for a more general subclass called a refinement of the former. To decide L0 ⊆ L1, we take two additional arguments: a language L2 of which L1 is a refinement, and a proof of L0 ⊆ L2. Our technique then refines the proof of L0 ⊆ L2 to a proof or a refutation of L0 ⊆ L1. Although the refinement procedure may not terminate in general, we give a sufficient condition for the termination. We employ a type-based approach to formalize the idea, inspired from Kobayashi's intersection type system for model-checking recursion schemes. To demonstrate the usefulness, we apply this method to obtain simpler proofs of the previous results of Minamide and Tozawa on the inclusion between context-free languages and regular hedge languages, and of Greibach and Friedman on the inclusion between context-free languages and superdeterministic languages.

show abstract

“…Just as software model checkers for procedural languages like BLAST [4] and SLAM [3] have been constructed based on finite-state and pushdown model checking, one may hope to construct software model checkers for higher-order functional languages based on higher-order model checking. Some evidence for such a possibility has been provided recently [12,10,17,16,20].…”

Section: Introductionmentioning

confidence: 96%

“…The model checking of higher-order recursion schemes [9,19] (higher-order model checking, for short) has been studied extensively, and recently applied to higherorder program verification [12,10,17,16,20]. A higher-order recursion scheme [9,19] is a grammar for describing a possibly infinite tree, and the higher-order model checking is concerned about whether the tree described by a given higherorder recursion scheme satisfies a given property (typically expressed by the modal μ-calculus or tree automata).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Practical Linear Time Algorithm for Trivial Automata Model Checking of Higher-Order Recursion Schemes

Kobayashi

2011

Foundations of Software Science and Computational Structures

Self Cite

View full text Add to dashboard Cite

Abstract. The model checking of higher-order recursion schemes has been actively studied and is now becoming a basis of higher-order program verification. We propose a new algorithm for trivial automata model checking of higher-order recursion schemes. To our knowledge, this is the first practical model checking algorithm for recursion schemes that runs in time linear in the size of the higher-order recursion scheme, under the assumption that the size of trivial automata and the largest order and arity of functions are fixed. The previous linear time algorithm was impractical due to a huge constant factor, and the only practical previous algorithm suffers from the hyper-exponential worst-case time complexity, under the same assumption. The new algorithm is remarkably simple, consisting of just two fixed-point computations. We have implemented the algorithm and confirmed that it outperforms Kobayashi's previous algorithm in a certain case.

show abstract

Model-checking higher-order functions

Cited by 65 publications

References 31 publications

Hector: An Equivalence Checker for a Higher-Order Fragment of ML

Hector: An Equivalence Checker for a Higher-Order Fragment of ML

An Intersection Type System for Deterministic Pushdown Automata

A Practical Linear Time Algorithm for Trivial Automata Model Checking of Higher-Order Recursion Schemes

Contact Info

Product

Resources

About