Homer: A Higher-Order Observational Equivalence Model checkER

Hopkins, David; Ong, C.-H. Luke

doi:10.1007/978-3-642-02658-4_51

Cited by 12 publications

(6 citation statements)

References 6 publications

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“…Similarly Jhala et al use refinement types to analyse OCaml programs by reducing the problem to first-order model-checking, which is thus incomplete [19]. Finally, Hopkins et al have produced tools for equivalence checking fragments of ML and Idealized Algol up to order-3 [17,18].…”

Section: Related Workmentioning

confidence: 99%

C-SHORe

et al. 2013

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Higher-order recursion schemes (HORS) have recently received much attention as a useful abstraction of higher-order functional programs with a number of new verification techniques employing HORS model-checking as their centrepiece. This paper contributes to the ongoing quest for a truly scalable model-checker for HORS by offering a different, automata theoretic perspective. We introduce the first practical model-checking algorithm that acts on a generalisation of pushdown automata equi-expressive with HORS called collapsible pushdown systems (CPDS). At its core is a substantial modification of a recently studied saturation algorithm for CPDS. In particular it is able to use information gathered from an approximate forward reachability analysis to guide its backward search. Moreover, we introduce an algorithm that prunes the CPDS prior to model-checking and a method for extracting counter-examples in negative instances. We compare our tool with the state-of-the-art verification tools for HORS and obtain encouraging results. In contrast to some of the main competition tackling the same problem, our algorithm is fixed-parameter tractable, and we also offer significantly improved performance over the only previously published tool of which we are aware that also enjoys this property. The tool and additional material are available from

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Section: Related Workmentioning

confidence: 99%

C-SHORe

et al. 2013

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“…Where applicable we also compare its performance against HOMER, a game semantics based equivalence checker [8] for the 3rd-order fragment of Idealized Algol (IA). The main difference between RML and IA is that IA uses call-by-name evaluation (and blockallocated variables), which lead to game models that differ significantly [1].…”

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

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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.

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“…Another direction we intend to pursue is to implement the model checking algorithm described, building upon the infrastructure of the call-by-name tool Homer [8].…”

Section: Complexitymentioning

confidence: 99%

A Fragment of ML Decidable by Visibly Pushdown Automata

Hopkins

Murawski

Ong

2011

Automata, Languages and Programming

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Abstract. The simply-typed, call-by-value language, RML, may be viewed as a canonical restriction of Standard ML to ground-type references, augmented by a "bad variable" construct in the sense of Reynolds. By a short type, we mean a type of order at most 2 and arity at most 1. We consider the O-strict fragment of (finitary) RML, RML O-Str , consisting of terms-in-context x1 : θ1, · · · , xn : θn M : θ such that θ is short, and every argument type of every θi is short. RML O-Str is surprisingly expressive; it includes several instances of (in)equivalence in the literature that are challenging to prove using methods based on (state-based) logical relations. We show that it is decidable whether a given pair of RML O-Str terms-in-context is observationally equivalent. Using the fully abstract game semantics of RML, our algorithm reduces the problem to the language equivalence of visibly pushdown automata. When restricted to terms in canonical form, the problem is EXPTIME-complete.

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Homer: A Higher-Order Observational Equivalence Model checkER

Cited by 12 publications

References 6 publications

C-SHORe

C-SHORe

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

A Fragment of ML Decidable by Visibly Pushdown Automata

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