Scalable Fine-Grained Proofs for Formula Processing

Haniel Barbosa 1, 2, 3 Jasmin Blanchette 3, 4 Pascal Fontaine 1, 3
1 UL - Université de Lorraine
2 UFRN - Universidade Federal do Rio Grande do Norte [Natal]
3 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
LORIA - FM - Department of Formal Methods , Inria Nancy - Grand Est, MPII - Max-Planck-Institut für Informatik
4 MPII - Max-Planck-Institut für Informatik
Abstract : 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.
Keywords : proof production proof checking satisfiability modulo theories automatic theorem proving
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Submitted on : Tuesday, May 23, 2017 - 3:42:40 PM
Last modification on : Tuesday, February 19, 2019 - 3:40:04 PM
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Haniel Barbosa, Jasmin Blanchette, Pascal Fontaine. Scalable Fine-Grained Proofs for Formula Processing. [Research Report] Universite de Lorraine, CNRS, Inria, LORIA, Nancy, France; Universidade Federal do Rio Grande do Norte, Natal, Brazil; Vrije Universiteit Amsterdam, Amsterdam, The Netherlands; Max-Planck-Institut für Informatik, Saarbrücken, Germany. 2017, pp.25. ⟨hal-01526841⟩

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