Scalable Fine-Grained Proofs for Formula Processing

Haniel Barbosa (1) , Jasmin Blanchette (2, 3, 1) , Mathias Fleury (2) , Pascal Fontaine (1, 4)

1 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
2 MPII - Max-Planck-Institut für Informatik
3 VU - Vrije Universiteit Amsterdam [Amsterdam]
4 MOSEL - Proof-oriented development of computer-based systems

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. To validate the framework, we implemented proof reconstruction in Isabelle/HOL.

Domaines: Logique en informatique [cs.LO]

Haniel Barbosa, Jasmin Blanchette, Mathias Fleury, Pascal Fontaine. Scalable Fine-Grained Proofs for Formula Processing. Journal of Automated Reasoning, 2020, 64 (3), pp.485-510. ⟨10.1007/s10817-018-09502-y⟩. ⟨hal-02515103⟩