Zenon: An Extensible Automated Theorem Prover Producing Checkable Proofs

Bonichon, Richard; Delahaye, David; Doligez, Damien

doi:10.1007/978-3-540-75560-9_13

Cited by 72 publications

(79 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This mainly consists in extending the usual rules of Zenon [4] by allowing them to work modulo a congruence relation over propositions induced by a set of rewrite rules over propositions and a set of equational axioms and rewrite rules over terms (this extension is partially inspired by the presentation of tableaux modulo presented in [3]). …”

Section: Deduction Modulo Rules For Zenonmentioning

confidence: 99%

“…The proof is presented using the rules of Sec. 3, even though these rules are more used for proof search rather than for proof presentation (for that purpose, Zenon actually uses an intermediate format, which is described in detail in [4]). Moreover, to make the presentation more compact, one proof step may consist of several rules.…”

Section: A Nontrivial Example From the Tptp Librarymentioning

confidence: 99%

See 1 more Smart Citation

Zenon Modulo: When Achilles Outruns the Tortoise Using Deduction Modulo

Delahaye

Doligez

Gilbert

et al. 2013

Logic for Programming, Artificial Intelligence, and Reasoning

Self Cite

View full text Add to dashboard Cite

Abstract. We propose an extension of the tableau-based first order automated theorem prover Zenon to deduction modulo. The theory of deduction modulo is an extension of predicate calculus, which allows us to rewrite terms as well as propositions, and which is well suited for proof search in axiomatic theories, as it turns axioms into rewrite rules. We also present a heuristic to perform this latter step automatically, and assess our approach by providing some experimental results obtained on the benchmarks provided by the TPTP library, where this heuristic is able to prove difficult problems in set theory in particular. Finally, we describe an additional backend for Zenon that outputs proof certificates for Dedukti, which is a proof checker based on the λΠ-calculus modulo.

show abstract

Section: Deduction Modulo Rules For Zenonmentioning

confidence: 99%

Section: A Nontrivial Example From the Tptp Librarymentioning

confidence: 99%

Zenon Modulo: When Achilles Outruns the Tortoise Using Deduction Modulo

Delahaye

Doligez

Gilbert

et al. 2013

Logic for Programming, Artificial Intelligence, and Reasoning

Self Cite

View full text Add to dashboard Cite

show abstract

“…In these expressions, x is a constant, variable or operator, and e is an expression whose type can already be inferred. 4 These typing hypotheses are obtained by decomposing the assumptions present in a proof obligation by elementary heuristics. In our example, we have the typing hypotheses x ∈ S and S ⊆ Nat, and the previously inferred types for x and S will be refined to Nat and P Nat.…”

Section: The Operator [[·]]mentioning

confidence: 99%

“…The two main backends of the current version of tlaps are Zenon [4], a tableau prover for first-order logic and set theory, and Isabelle/TLA + , a faithful encoding of TLA + in the Isabelle [13] proof assistant, which provides automated proof methods based on first-order reasoning and rewriting. The backends available prior to the work presented here also included a generic translation to the input language of SMT solvers that focused on quantifier-free formulas of linear arithmetic (not shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

Automatic Verification of TLA + Proof Obligations with SMT Solvers

Merz

Vanzetto

2012

Logic for Programming, Artificial Intelligence, and Reasoning

View full text Add to dashboard Cite

Abstract. TLA + is a formal specification language that is based on ZF set theory and the Temporal Logic of Actions TLA. The TLA + proof system tlaps assists users in deductively verifying safety properties of TLA + specifications. tlaps is built around a proof manager, which interprets the TLA + proof language, generates corresponding proof obligations, and passes them to backend verifiers. In this paper we present a new backend for use with SMT solvers that supports elementary set theory, functions, arithmetic, tuples, and records. Type information required by the solvers is provided by a typing discipline for TLA + proof obligations, which helps us disambiguate the translation of expressions of (untyped) TLA + , while ensuring its soundness. Preliminary results show that the backend can help to significantly increase the degree of automation of certain interactive proofs.

show abstract

“…One can distinguish between general-purpose and special-purpose ones. General-purpose tactics are, for example, tauto, first-order, and zenon [5] in Coq and blast [16] in Isabelle. A strong point of these tactics is their smooth integration in the proof assistant.…”

Section: Related Work and Future Researchmentioning

confidence: 99%

On the Mechanization of the Proof of Hessenberg’s Theorem in Coherent Logic

Bezem

Hendriks

2007

J Autom Reasoning

View full text Add to dashboard Cite

We propose to combine interactive proof construction with proof automation for a fragment of first-order logic called Coherent Logic (CL). CL allows enough existential quantification to make Skolemization unnecessary. Moreover, CL has a constructive proof system based on forward reasoning, which is easy to automate and where standardized proof objects can easily be obtained. We have implemented in Prolog a CL prover which generates Coq proof scripts. We test our approach with a case study: Hessenberg's theorem, which states that in elementary projective plane geometry Pappus' axiom implies Desargues' axiom. Our CL prover makes it possible to automate large parts of the proof, in particular taking care of the large number of degenerate cases.

show abstract

Zenon: An Extensible Automated Theorem Prover Producing Checkable Proofs

Cited by 72 publications

References 8 publications

Zenon Modulo: When Achilles Outruns the Tortoise Using Deduction Modulo

Zenon Modulo: When Achilles Outruns the Tortoise Using Deduction Modulo

Automatic Verification of TLA + Proof Obligations with SMT Solvers

On the Mechanization of the Proof of Hessenberg’s Theorem in Coherent Logic

Contact Info

Product

Resources

About