fCube: An Efficient Prover for Intuitionistic Propositional Logic

Ferrari, Mauro; Fiorentini, Camillo; Fiorino, Guido

doi:10.1007/978-3-642-16242-8_21

Cited by 20 publications

(17 citation statements)

References 10 publications

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“…We also observed that, even for checking existence of terms InSynth outperforms recent propositional intuitionistic provers [9,19] on our benchmarks. Our overall experience suggests that InSynth is effective in providing help to developers.…”

Section: Introductionsupporting

confidence: 51%

“…The distribution of the execution time between prover and the reconstruction is shown in columns Prove and Recon, respectively. The last column group gives execution times of two state-of-the-art intuitionistic theorem provers (Imogen [19] and fCube [9]) employed for checking provability of inhabitation problems for the benchmarks. Table 2 shows the differences in both effectiveness and execution time between the variants of the algorithm.…”

Section: Measuring Overall Effectivenessmentioning

confidence: 99%

“…Among recent modern provers are Imogen [19] and fCube [9]. These tools can reason about more expressive fragments of logic: they support not only implication but also intuitionistic counterparts for other propositional operators such as ∨, ⇒, ⇔, and Imogen also supports first-order and not only propositional fragment.…”

Section: Related Workmentioning

confidence: 99%

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Complete completion using types and weights

GveroTihomir¹,

KuncakViktor²,

KurajIvan³

et al. 2013

SIGPLAN Not.

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Developing modern software typically involves composing functionality from existing libraries. This task is difficult because libraries may expose many methods to the developer. To help developers in such scenarios, we present a technique that synthesizes and suggests valid expressions of a given type at a given program point. As the basis of our technique we use type inhabitation for lambda calculus terms in long normal form. We introduce a succinct representation for type judgements that merges types into equivalence classes to reduce the search space, then reconstructs any desired number of solutions on demand. Furthermore, we introduce a method to rank solutions based on weights derived from a corpus of code. We implemented the algorithm and deployed it as a plugin for the Eclipse IDE for Scala. We show that the techniques we incorporated greatly increase the effectiveness of the approach. Our evaluation benchmarks are code examples from programming practice; we make them available for future comparisons.

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Section: Introductionsupporting

confidence: 51%

Section: Measuring Overall Effectivenessmentioning

confidence: 99%

See 1 more Smart Citation

Complete completion using types and weights

GveroTihomir¹,

KuncakViktor²,

KurajIvan³

et al. 2013

SIGPLAN Not.

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“…where a local formula [Ferrari et al 2010] is a formula L of L defined according to the following grammar:…”

Section: A Concrete Evaluationmentioning

confidence: 99%

An Evaluation-Driven Decision Procedure for G3i

Ferrari

Fiorentini

Fiorino

2015

ACM Trans. Comput. Logic

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It is well known that G3i, the sequent calculus for intuitionistic propositional logic where weakening and contraction are absorbed into the rules, is not terminating. Indeed, due to the contraction in the rule for left implication, the naïve goal-oriented proof-search strategy, consisting in applying the rules of the calculus bottom up until possible, can generate branches of infinite length. The usual solution to this problem is to support the proof-search procedure with a loop checking mechanism that prevents the generation of infinite branches by storing and analyzing some information regarding the branch under development.In this article, we propose a new technique based on evaluation functions. An evaluation function is a lightweight computational mechanism that, analyzing only the current goal of the proof search, allows one to drive the application of rules to guarantee termination and to avoid useless backtracking. We describe an evaluation-driven proof-search procedure that given a sequent σ returns either a G3i-derivation of σ or a countermodel for σ . We prove that such a procedure is terminating and correct, and that the depth of the G3i-trees generated during proof search is quadratic in the size of σ . Finally, we discuss the overhead time introduced by evaluation functions in the proof-search procedure.

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“…-EPPI+ extends EPPI with context rules of Section 6. An implementation of EPPI+ is presented in Ferrari et al [2010], where the proof-search strategy is described in full details. -EPPI++ extends EPPI+ with the rule pruning of Section 7.…”

Section: Empirical Evaluationmentioning

confidence: 99%

Simplification Rules for Intuitionistic Propositional Tableaux

Ferrari

Fiorentini

Fiorino

2012

ACM Trans. Comput. Logic

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The implementation of a logic requires, besides the definition of a calculus and a decision procedure, the development of techniques to reduce the search space. In this paper we introduce some simplification rules for Intuitionistic propositional logic that try to replace a formula with an equi-satisfiable ``simpler'' one with the aim to reduce the search space. Our results are proved via semantical techniques based on Kripke models. We also provide an empirical evaluation of their impact on implementations

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fCube: An Efficient Prover for Intuitionistic Propositional Logic

Cited by 20 publications

References 10 publications

Complete completion using types and weights

Complete completion using types and weights

An Evaluation-Driven Decision Procedure for G3i

Simplification Rules for Intuitionistic Propositional Tableaux

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