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
This program is distributed under the Apache Software License version
2.0. See the enclosed file LICENSE.
See https://gbury.github.io/mSAT/
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
You will need dune and iter. The command is:
$ make install
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.Ssignature) -
A theory (which implements the
Theory_intf.Ssignature) 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)
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 ...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 ...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
###################
...