#### msat-bin

MSAT is an OCaml library that features a modular SAT-solver and some

extensions (including SMT), derived from Alt-Ergo Zero.

It was presented at ICFP 2017,

using a poster

### COPYRIGHT

This program is distributed under the Apache Software License version

2.0. See the enclosed file `LICENSE`

.

### Documentation

See https://gbury.github.io/mSAT/

### INSTALLATION

#### Via opam

Once the package is on opam, just `opam install msat`

.

For the development version, use:

```
opam pin add msat https://github.com/Gbury/mSAT.git
```

#### Manual installation

You will need `dune`

and `iter`

. The command is:

```
$ make install
```

### USAGE

#### Generic SAT/SMT Solver

A modular implementation of the SMT algorithm can be found in the `Msat.Solver`

module,

as a functor which takes two modules :

A representation of formulas (which implements the

`Formula_intf.S`

signature)A theory (which implements the

`Theory_intf.S`

signature) to check consistence of assertions.A dummy empty module to ensure generativity of the solver (solver modules heavily relies on

side effects to their internal state)

#### Sat Solver

A ready-to-use SAT solver is available in the `Msat_sat`

module

using the `msat.sat`

library. It can be loaded

as shown in the following code :

```
# #require "msat";;
# #require "msat.sat";;
# #print_depth 0;; (* do not print details *)
```

Then we can create a solver and create some boolean variables:

```
module Sat = Msat_sat
module E = Sat.Int_lit (* expressions *)
let solver = Sat.create()
(* We create here two distinct atoms *)
let a = E.fresh () (* A 'new_atom' is always distinct from any other atom *)
let b = E.make 1 (* Atoms can be created from integers *)
```

We can try and check the satisfiability of some clauses — here, the clause `a or b`

.`Sat.assume`

adds a list of clauses to the solver. Calling `Sat.solve`

will check the satisfiability of the current set of clauses, here "Sat".

```
# a <> b;;
- : bool = true
# Sat.assume solver [[a; b]] ();;
- : unit = ()
# let res = Sat.solve solver;;
val res : Sat.res = Sat.Sat ...
```

The Sat solver has an incremental mutable state, so we still have

the clause `a or b`

in our assumptions.

We add `not a`

and `not b`

to the state, and get "Unsat".

```
# Sat.assume solver [[E.neg a]; [E.neg b]] () ;;
- : unit = ()
# let res = Sat.solve solver ;;
val res : Sat.res = Sat.Unsat ...
```

##### Formulas API

Writing clauses by hand can be tedious and error-prone.

The functor `Msat_tseitin.Make`

in the library `msat.tseitin`

proposes a formula AST (parametrized by

atoms) and a function to convert these formulas into clauses:

```
# #require "msat.tseitin";;
```

```
(* Module initialization *)
module F = Msat_tseitin.Make(E)
let solver = Sat.create ()
(* We create here two distinct atoms *)
let a = E.fresh () (* A fresh atom is always distinct from any other atom *)
let b = E.make 1 (* Atoms can be created from integers *)
(* Let's create some formulas *)
let p = F.make_atom a
let q = F.make_atom b
let r = F.make_and [p; q]
let s = F.make_or [F.make_not p; F.make_not q]
```

We can try and check the satisfiability of the given formulas, by turning

it into clauses using `make_cnf`

:

```
# Sat.assume solver (F.make_cnf r) ();;
- : unit = ()
# Sat.solve solver;;
- : Sat.res = Sat.Sat ...
```

```
# Sat.assume solver (F.make_cnf s) ();;
- : unit = ()
# Sat.solve solver ;;
- : Sat.res = Sat.Unsat ...
```

#### CDCL(T): a Sudoku solver as an example

The directory `src/sudoku/`

contains a simple Sudoku solver that

uses the interface `Msat.Make_cdcl_t`

.

In essence, it implements the logical theory `CDCL(Sudoku)`

.

The script `sudoku_solve.sh`

compiles and runs the solver,

as does `dune exec src/sudoku/sudoku_solve.exe`

.

It's able to parse sudoku grids denoted as 81 integers

(see `tests/sudoku/sudoku.txt`

for example).

Here is a sample grid and the output from the solver (in roughly .5s):

```
$ echo '..............3.85..1.2.......5.7.....4...1...9.......5......73..2.1........4...9' > sudoku.txt
$ dune exec src/sudoku/sudoku_solve.exe -- sudoku.txt
...
#########################
solve grid:
.........
.....3.85
..1.2....
...5.7...
..4...1..
.9.......
5......73
..2.1....
....4...9
...
987654321
246173985
351928746
128537694
634892157
795461832
519286473
472319568
863745219
###################
...
```

md5=ba623630b0b8e0edc016079dd214c80b

sha512=51c133cefe8550125e7b1db18549e893bac15663fdd7a9fac87235c07de755f39eab9fc3cfdf6571612fd79b3d5b22f49f459581b480c7349bacddf2618c8a99