# 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).