63,197 research outputs found
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
CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates
Termination is an important property of programs; notably required for
programs formulated in proof assistants. It is a very active subject of
research in the Turing-complete formalism of term rewriting systems, where many
methods and tools have been developed over the years to address this problem.
Ensuring reliability of those tools is therefore an important issue. In this
paper we present a library formalizing important results of the theory of
well-founded (rewrite) relations in the proof assistant Coq. We also present
its application to the automated verification of termination certificates, as
produced by termination tools
A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4
Being able to soundly estimate roundoff errors of finite-precision
computations is important for many applications in embedded systems and
scientific computing. Due to the discrepancy between continuous reals and
discrete finite-precision values, automated static analysis tools are highly
valuable to estimate roundoff errors. The results, however, are only as correct
as the implementations of the static analysis tools. This paper presents a
formally verified and modular tool which fully automatically checks the
correctness of finite-precision roundoff error bounds encoded in a certificate.
We present implementations of certificate generation and checking for both Coq
and HOL4 and evaluate it on a number of examples from the literature. The
experiments use both in-logic evaluation of Coq and HOL4, and execution of
extracted code outside of the logics: we benchmark Coq extracted unverified
OCaml code and a CakeML-generated verified binary
A formally verified compiler back-end
This article describes the development and formal verification (proof of
semantic preservation) of a compiler back-end from Cminor (a simple imperative
intermediate language) to PowerPC assembly code, using the Coq proof assistant
both for programming the compiler and for proving its correctness. Such a
verified compiler is useful in the context of formal methods applied to the
certification of critical software: the verification of the compiler guarantees
that the safety properties proved on the source code hold for the executable
compiled code as well
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