SMTCoq

SMTCoq is a Coq tool that checks proof witnesses coming from external SAT and SMT solvers.

It relies on a certified checker for such witnesses. On top of it, vernacular commands and tactics to interface with the SAT solver zChaff and the SMT solver veriT are provided. It is designed in a modular way allowing to extend it easily to other solvers.

Since version 1.2, SMTCoq also provides the possibility to extract the checker to OCaml.

The current stable version is the version 1.2.

Installation

See the INSTALL.md file for instructions.

License

SMTCoq is released under the CeCILL-C license; see LICENSE for more details.

Use

Examples are given in the file examples/Example.v. They are meant to be easily re-usable for your own usage.

Overview

The SMTCoq module can be used in Coq files via the Require Import SMTCoq. command. For each supported solver, it provides:

a vernacular command to check answers: XXX_Checker "problem_file" "witness_file" returns true only if witness_file contains a zChaff proof of the unsatisfiability of the problem stated in problem_file;
a vernacular command to safely import theorems: XXX_Theorem theo "problem_file" "witness_file" produces a Coq term teo whose type is the theorem stated in problem_file if witness_file is a proof of the unsatisfiability of it, and fails otherwise.
a safe tactic to try to solve a Coq goal using the chosen solver.

The SMTCoq checker can also be extracted to OCaml and then used independently from Coq.

We now give more details for each solver, and explanations on extraction.

zChaff

Compile and install zChaff as explained in the installation instructions. In the following, we consider that the command zchaff is in your PATH variable environment.

Checking zChaff answers of unsatisfiability and importing theorems

To check the result given by zChaff on an unsatisfiable dimacs file file.cnf:

Produce a zChaff proof witness: zchaff file.cnf. This command produces a proof witness file named resolve_trace.
In a Coq file file.v, put:

Require Import SMTCoq.
Zchaff_Checker "file.cnf" "resolve_trace".

Compile file.v: coqc file.v. If it returns true then zChaff indeed proved that the problem was unsatisfiable.
You can also produce Coq theorems from zChaff proof witnesses: the commands

Require Import SMTCoq.
Zchaff_Theorem theo "file.cnf" "resolve_trace".

will produce a Coq term theo whose type is the theorem stated in file.cnf.

zChaff as a Coq decision procedure

The zchaff tactic can be used to solve any goal of the form:

forall l, b1 = b2

where l is a list of Booleans (that can be concrete terms).

veriT

Compile and install veriT as explained in the installation instructions. In the following, we consider that the command veriT is in your PATH variable environment.

Checking veriT answers of unsatisfiability and importing theorems

To check the result given by veriT on an unsatisfiable SMT-LIB2 file file.smt2:

Produce a veriT proof witness:

veriT --proof-prune --proof-merge --proof-with-sharing --cnf-definitional --disable-e --disable-ackermann --input=smtlib2 --proof=file.log file.smt2

This command produces a proof witness file named file.log.

In a Coq file file.v, put:

Require Import SMTCoq.
Section File.
  Verit_Checker "file.smt2" "file.log".
End File.

Compile file.v: coqc file.v. If it returns true then veriT indeed proved that the problem was unsatisfiable.
You can also produce Coq theorems from zChaff proof witnesses: the commands

Require Import SMTCoq.
Section File.
  Verit_Theorem theo "file.smt2" "file.log".
End File.

will produce a Coq term theo whose type is the theorem stated in file.smt2.

The theories that are currently supported are QF_UF, QF_LIA, QF_IDL and their combinations.

veriT as a Coq decision procedure

The verit tactic can be used to solve any goal of the form:

forall l, b1 = b2

where l is a list of Booleans. Those Booleans can be any concrete terms. The theories that are currently supported are QF_UF, QF_LIA, QF_IDL and their combinations.

Extraction

The src/extraction directory contains the OCaml extracted checker, as well as additional files to make use of it. You can compile it using the given Makefile (after compiling SMTCoq): it will produce an executable in the example directory for testing.

To use it, you can inspire from the file example/example.ml. Edit the first two lines of src/extraction/Makefile to compile your own files. Note that even the extracted version of SMTCoq requires both Coq and SMTCoq to be compiled (mainly since it relies on other Coq plugins).

wolvre/smtcoq