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

This extended abstract reports on current progress of SMTCoq, a communication tool between the Coq proof assistant and external SAT and SMT solvers. Based on a checker for generic first-order certificates implemented and proved correct in Coq, SMTCoq offers facilities both to check external SAT and SMT answers and to improve Coq's automation using such solvers, in a safe way. Currently supporting the SAT solver zChaff, and the SMT solver veriT for the combination of the theories of congruence closure and linear integer arithmetic, SMTCoq is meant to be extendable with a reasonable amount of effort: we present work in progress to support the SMT solver CVC4 and the theory of bit vectors.Comment: In Proceedings HaTT 2016, arXiv:1606.0542

A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014