Computing Tiny Clause Normal Forms

Azmy, Noran; Weidenbach, Christoph

doi:10.1007/978-3-642-38574-2_7

Cited by 6 publications

(11 citation statements)

References 6 publications

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“…Internally, ATPs heuristically apply variable elimination as well as subformula naming strategies [14,15], which are supposed to generate the optimal internal representation. However, even despite this fact, we observed in our initial experiments that the encoding of variables can have a huge impact on the performance of provers.…”

Section: Encoding Of Variablesmentioning

confidence: 99%

Exploration of language specifications by compilation to first-order logic

Grewe

Erdweg

Pacak

et al. 2018

Science of Computer Programming

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Exploration of language specifications helps to discover errors and inconsistencies early during the development of a programming language. We propose exploration of language specifications via application of existing automated first-order theorem provers (ATPs). To this end, we translate language specifications and exploration tasks to first-order logic, which many ATPs accept as input. However, there are several different strategies for compiling a language specification to first-order logic, and even small variations in the translation may have a large impact on the time it takes ATPs to find proofs. In this paper, we first present a systematic empirical study on how to best compile language specifications to first-order logic such that existing ATPs can solve typical exploration tasks efficiently. We have developed a compiler product line that implements 36 different compilation strategies and used it to feed language specifications to 4 existing first-order theorem provers. As benchmarks, we developed language specifications for typed SQL and for a Questionnaire Language (QL), with 50 exploration goals each. Our study empirically confirms that the choice of a compilation strategy greatly influences prover performance in general and shows which strategies are advantageous for prover performance. Second, we extend our empirical study with 4 domain-specific strategies for axiom selection and find that axiom selection does not influence prover performance in our benchmark specifications.

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Section: Encoding Of Variablesmentioning

confidence: 99%

Exploration of language specifications by compilation to first-order logic

Grewe

Erdweg

Pacak

et al. 2018

Science of Computer Programming

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“…Positive skolemization suffers from a technical limitation connected to polymorphism: Lemmas containing polymorphic skolemizable variables cannot be reconstructed, because the variables introduced by obtain must have a ground type. 4 An easy workaround would be to relaunch Sledgehammer with a monomorphizing type encoding [13, Section 3] to obtain a more suitable ATP proof, in which all types are ground. A more challenging alternative would involve detecting which monomorphic instances of the problematic lemmas are needed and re-engineer the proof accordingly.…”

Section: The Positive Casementioning

confidence: 99%

“…The unskolemization algorithm is not perfect. We believe it is complete for what one could call naive skolemization, but the algorithm implemented by FLOTTER is anything but naive [4]. Furthermore, it is possible to construct examples where clauses are derived from both the negated conjecture and from other facts, leading to confusion in the redirection algorithm.…”

Section: Spassmentioning

confidence: 99%

“…Sledgehammer historically performed clausification itself, using the neg_clausify tactic, which implemented a naive exponential application of distributive laws. This was changed to use the ATPs' native clausifiers, since they normally generate a polynomial number of clauses and include other optimizations [4]. However, skolemization transforms a formula into an equisatisfiable, but not equivalent, formula; as a result, it must be treated specially when reconstructing the proof (Section 5).…”

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confidence: 99%

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Semi-intelligible Isar Proofs from Machine-Generated Proofs

et al. 2015

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Sledgehammer is a component of the Isabelle/HOL proof assistant that integrates external automatic theorem provers (ATPs) to discharge interactive proof obligations. As a safeguard against bugs, the proofs found by the external provers are reconstructed in Isabelle. Reconstructing complex arguments involves translating them to Isabelle's Isar format, supplying suitable justifications for each step. Sledgehammer transforms the proofs by contradiction into direct proofs; it iteratively tests and compresses the output, resulting in simpler and faster proofs; and it supports a wide range of ATPs, including E, LEO-II, Satallax, SPASS, Vampire, veriT, Waldmeister, and Z3. Keywords Automatic theorem provers • Proof assistants • Natural deduction 1 Introduction Sledgehammer [12,62] is a proof tool that connects the Isabelle/HOL proof assistant [53,54] with external automatic theorem provers (ATPs), including first-order superposition provers, higher-order provers, and solvers based on satisfiability modulo theories (SMT). Given an interactive proof goal, it heuristically selects hundreds of facts (lemmas, definitions, and axioms) from Isabelle's vast libraries, translates them to the external provers' logics, and invokes the provers in parallel (Section 2).

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“…the number of function and predicate symbols. Implementors of CNF translations commonly employ formula simplification [12], (generalised) formula naming [12,1], and other clausification techniques, aimed to make the CNF smaller.…”

Section: Introductionmentioning

confidence: 99%

A Clausal Normal Form Translation for FOOL

Kotelnikov¹,

Kovács²,

Suda³

et al.

EPiC Series in Computing

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Automated theorem provers for first-order logic usually operate on sets of first-order clauses. It is well-known that the translation of a formula in full first-order logic to a clausal normal form (CNF) can crucially affect performance of a theorem prover. In our recent work we introduced a modification of first-order logic extended by the first class boolean sort and syntactical constructs that mirror features of programming languages. We called this logic FOOL. Formulas in FOOL can be translated to ordinary first-order formulas and checked by first-order theorem provers. While this translation is straightforward, it does not result in a CNF that can be efficiently handled by state-of-the-art theorem provers which use superposition calculus. In this paper we present a new CNF translation algorithm for FOOL that is friendly and efficient for superposition-based first-order provers. We implemented the algorithm in the Vampire theorem prover and evaluated it on a large number of problems coming from formalisation of mathematics and program analysis. Our experimental results show an increase of performance of the prover with our CNF translation compared to the naive translation.

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Computing Tiny Clause Normal Forms

Cited by 6 publications

References 6 publications

Exploration of language specifications by compilation to first-order logic

Exploration of language specifications by compilation to first-order logic

Semi-intelligible Isar Proofs from Machine-Generated Proofs

A Clausal Normal Form Translation for FOOL

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