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.
See the INSTALL.md file for instructions.
SMTCoq is released under the CeCILL-C license; see LICENSE for more details.
Examples are given in the file examples/Example.v. They are meant to be easily re-usable for your own usage.
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"
returnstrue
only ifwitness_file
contains a zChaff proof of the unsatisfiability of the problem stated inproblem_file
; -
a vernacular command to safely import theorems:
XXX_Theorem theo "problem_file" "witness_file"
produces a Coq termteo
whose type is the theorem stated inproblem_file
ifwitness_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.
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.
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 namedresolve_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 returnstrue
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
.
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).
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.
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 returnstrue
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.
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.
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).