Nitpick: A Counterexample Generator for Higher-Order Logic Based on a Relational Model Finder

Blanchette, Jasmin Christian; Nipkow, Tobias

doi:10.1007/978-3-642-14052-5_11

Cited by 189 publications

(153 citation statements)

References 11 publications

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“…In our computer-formalization and assessment of Fitting's textbook [17], we provide further evidence that our embedded logic works as intended by verifying the book's theorems and examples. 10 We utilize here (counter-)model finder Nitpick [12] for the first time. For the conjectured lemma, Nitpick finds a countermodel (not shown here), i.e.…”

Section: Verifying the Embeddingmentioning

confidence: 99%

Automating Emendations of the Ontological Argument in Intensional Higher-Order Modal Logic

Fuenmayor

Benzmüller

2017

KI 2017: Advances in Artificial Intelligence

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Abstract. A shallow semantic embedding of an intensional higher-order modal logic (IHOML) in Isabelle/HOL is presented. IHOML draws on Montague/Gallin intensional logics and has been introduced by Melvin Fitting in his textbook Types, Tableaus and Gödel's God in order to discuss his emendation of Gödel's ontological argument for the existence of God. Utilizing IHOML, the most interesting parts of Fitting's textbook are formalized, automated and verified in the Isabelle/HOL proof assistant. A particular focus thereby is on three variants of the ontological argument which avoid the modal collapse, which is a strongly criticized side-e↵ect in Gödel's resp. Scott's original work.

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Section: Verifying the Embeddingmentioning

confidence: 99%

Automating Emendations of the Ontological Argument in Intensional Higher-Order Modal Logic

Fuenmayor

Benzmüller

2017

KI 2017: Advances in Artificial Intelligence

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“…Our experience suggests that Leon is more scalable than the alternative systems that can deal with this expressive properties. Counterexample generation has been introduced into Isabelle through tools like Nitpick [6]. Further experimental comparisons would be desirable, but these techniques do not use theory solvers and appear slower than Leon on complex functional programs.…”

Section: Related Workmentioning

confidence: 99%

Satisfiability Modulo Recursive Programs

2011

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Abstract. We present a semi-decision procedure for checking satisfiability of expressive correctness properties of recursive first-order functional programs. In our approach, both properties and programs are expressed in the same language, a subset of Scala. We implemented our procedure and integrated it with the Z3 SMT solver and the Scala compiler. Our procedure is sound for counterexamples and for proofs of terminating functions. It is terminating and thus complete for many important classes of specifications, including all satisfiable formulas and all formulas where recursive functions satisfy certain syntactic restrictions. Using our system, Leon, we verified detailed correctness properties for functional data structure implementations, as well as syntax tree manipulations. We have found our system to be fast for both finding counterexamples and finding correctness proofs, and to scale to larger programs than alternative techniques.

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“…First, this operation creates a binary relation via comprehension which relates each element of the source collection to the evaluation result of the respective body expression. For instance, the OCL expression Set{1,2,3}->collect(i|i*i) would yield the intermediate relation [ [1,1], [2,4], [3,9]]. The transformation respects the fact that the result of collect must be flattened.…”

Section: From Ocl Constraints To Relational Constraintsmentioning

confidence: 99%

“…Kodkod has been successfully applied in different fields, e. g., for executing declarative specifications in case of runtime exceptions in Java programs [25], reasoning about memory models [29], or generating counterexamples for Isabelle/HOL a proof assistant for higher-order logic (Nitpick) [3].…”

Section: Related Workmentioning

confidence: 99%

From UML and OCL to Relational Logic and Back

Kuhlmann

Gogolla

2012

Lecture Notes in Computer Science

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Abstract. Languages like UML and OCL are used to precisely model systems. Complex UML and OCL models therefore represent a crucial part of model-driven development, as they formally specify the main system properties. Consequently, creating complete and correct models is a critical concern. For this purpose, we provide a lightweight model validation method based on efficient SAT solving techniques. In this paper, we present a transformation from UML class diagram and OCL concepts into relational logic. Relational logic in turn represents the source for advanced SAT-based model instance finders like Kodkod. This paper focuses on a natural transformation approach which aims to exploit the features of relational logic as directly as possible through straitening the handling of main UML and OCL features. This approach allows us to explicitly benefit from the efficient handling of relational logic in Kodkod and to interpret found results backwards in terms of UML and OCL.

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Nitpick: A Counterexample Generator for Higher-Order Logic Based on a Relational Model Finder

Cited by 189 publications

References 11 publications

Automating Emendations of the Ontological Argument in Intensional Higher-Order Modal Logic

Automating Emendations of the Ontological Argument in Intensional Higher-Order Modal Logic

Satisfiability Modulo Recursive Programs

From UML and OCL to Relational Logic and Back

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