A Clausal Normal Form Translation for FOOL

Kotelnikov, Evgenii; Kovács, Laura; Suda, Martin; Воронков, Андрей

doi:10.29007/ltkk

Cited by 10 publications

(16 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Two chapters in the Handbook of Automated Reasoning [2,39] are dedicated to aspects of formula preprocessing. Reger et al [42] describe a one-pass algorithm implemented in the Vampire prover, together with an extension [29] to unfold 'let' expressions and "first-class" Boolean constructs. The focus is on producing small formulas, quickly.…”

Section: Related Workmentioning

confidence: 99%

Scalable Fine-Grained Proofs for Formula Processing

et al. 2019

View full text Add to dashboard Cite

We present a framework for processing formulas in automatic theorem provers, with generation of detailed proofs. The main components are a generic contextual recursion algorithm and an extensible set of inference rules. Clausification, skolemization, theoryspecific simplifications, and expansion of 'let' expressions are instances of this framework. With suitable data structures, proof generation adds only a linear-time overhead, and proofs can be checked in linear time. We implemented the approach in the SMT solver veriT. This allowed us to dramatically simplify the code base while increasing the number of problems for which detailed proofs can be produced, which is important for independent checking and reconstruction in proof assistants. To validate the framework, we implemented proof reconstruction in Isabelle/HOL. 1 Introduction An increasing number of automatic theorem provers can generate certificates, or proofs, that justify the formulas they derive. These proofs can be checked by other programs and shared across reasoning systems. It might also happen that a human user would want to inspect

show abstract

Section: Related Workmentioning

confidence: 99%

Scalable Fine-Grained Proofs for Formula Processing

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Vampire reads formulas written in the TPTP language [16]. The TFX subset 5 Vampire translates let-in with tuple definitions to clausal normal form of first-order logic using the VCNF clausification algorithm [7].…”

Section: Polymorphic Theory Of First Class Tuplesmentioning

confidence: 99%

“…Our previous work introduced FOOL [8], its implementation in Vampire [6], and an efficient clausification algorithm for FOOL formulas [7].…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

A FOOLish Encoding of the Next State Relations of Imperative Programs

Kotelnikov¹,

Kovács²,

Воронков³

2018

EasyChair Preprints

Self Cite

View full text Add to dashboard Cite

Abstract. Automated theorem provers are routinely used in program analysis and verification for checking program properties. These properties are translated from program fragments to formulas expressed in the logic supported by the theorem prover. Such translations can be complex and require deep knowledge of how theorem provers work in order for the prover to succeed on the translated formulas. Our previous work introduced FOOL, a modification of first-order logic that extends it with syntactical constructs resembling features of programming languages. One can express program properties directly in FOOL and leave translations to plain first-order logic to the theorem prover. In this paper we present a FOOL encoding of the next state relations of imperative programs. Based on this encoding we implement a translation of imperative programs annotated with their pre-and post-conditions to partial correctness properties of these programs. We present experimental results that demonstrate that program properties translated using our method can be efficiently checked by the first-order theorem prover Vampire.

show abstract

“…Kotelnikov et al [11,38] investigate the encoding of a number of constructs which typically occur in specification constructs of language semantics directly within the Vampire theorem prover. Concretely, they adapt the internal input language and calculi of Vampire to support first-class Boolean sorts, let-bindings, and if-then-else expressions.…”

Section: Related Workmentioning

confidence: 99%

Exploration of language specifications by compilation to first-order logic

Grewe

Erdweg

Pacak

et al. 2018

Science of Computer Programming

View full text Add to dashboard Cite

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.

show abstract

A Clausal Normal Form Translation for FOOL

Cited by 10 publications

References 14 publications

Scalable Fine-Grained Proofs for Formula Processing

Scalable Fine-Grained Proofs for Formula Processing

A FOOLish Encoding of the Next State Relations of Imperative Programs

Exploration of language specifications by compilation to first-order logic

Contact Info

Product

Resources

About