Extending SMTCoq, a Certified Checker for SMT (Extended Abstract)

Ekici, Burak; Katz, Guy; Keller, Chantal; Mebsout, Alain; Reynolds, Andrew; Tinelli, Cesare

doi:10.4204/eptcs.210.5

“…For integrating superposition provers with Coq, De Nivelle studied how to build efficient proof terms for clausification and skolemization [37]. For SMT, the main integrations with proof reconstruction are CVC Lite in HOL Light [31], haRVey (veriT's predecessor) in Isabelle/HOL [20], Z3 in HOL4 and Isabelle/ HOL [12,13], veriT in Coq [1], and CVC4 in Coq [19]. Some of these simulate the proofs in the proof assistant using dedicated tactics, in the style of our checker.…”

Section: Related Workmentioning

confidence: 99%

Scalable Fine-Grained Proofs for Formula Processing

Barbosa

¹

,

Blanchette

²

,

Fleury

³

et al. 2019

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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

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“…Reconstruction of proofs generated by external theorem provers has been implemented in various systems including CVC in HOL Light [13], Z3 in HOL4 and Isabelle/HOL [8], and SMTCoq reconstructs veriT [1] and CVC4 [12] proofs in Coq. None of the other solvers produce detailed proofs or information on Skolemization.…”

Section: Related Workmentioning

confidence: 99%

Reconstructing veriT Proofs in Isabelle/HOL

Fleury

¹

,

Schurr

²

2019

Electron. Proc. Theor. Comput. Sci.

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Automated theorem provers are now commonly used within interactive theorem provers to discharge an increasingly large number of proof obligations. To maintain the trustworthiness of a proof, the automatically found proof must be verified inside the proof assistant. We present here a reconstruction procedure in the proof assistant Isabelle/HOL for proofs generated by the satisfiability modulo theories solver veriT which is part of the smt tactic. We describe in detail the architecture of our improved reconstruction method and the challenges we faced in designing it. Our experiments show that the veriT-powered smt tactic is regularly suggested by Sledgehammer as the fastest method to automatically solve proof goals.

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“…For integrating superposition provers with Coq, De Nivelle studied how to build efficient proof terms for clausification and skolemization [32]. For SMT, the main integrations with proof reconstruction are CVC Lite in HOL Light [26], haRVey (veriT's predecessor) in Isabelle/HOL [16], Z3 in HOL4 and Isabelle/HOL [8,9], veriT in Coq [1], and CVC4 in Coq [15]. Some of these simulate the proofs in the proof assistant using dedicated tactics, in the style of our simple checker for Isabelle (Sect.…”

Section: Related Workmentioning

confidence: 99%

Scalable Fine-Grained Proofs for Formula Processing

Barbosa

¹

,

Blanchette

²

,

Fontaine

³

2017

Automated Deduction – CADE 26

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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, theory-specific 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.

show abstract

Extending SMTCoq, a Certified Checker for SMT (Extended Abstract)

Cited by 8 publications

References 19 publications

Scalable Fine-Grained Proofs for Formula Processing

Scalable Fine-Grained Proofs for Formula Processing

Reconstructing veriT Proofs in Isabelle/HOL

Scalable Fine-Grained Proofs for Formula Processing

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