package msatbin
Install
Dune Dependency
Authors
Maintainers
Sources
md5=ba623630b0b8e0edc016079dd214c80b
sha512=51c133cefe8550125e7b1db18549e893bac15663fdd7a9fac87235c07de755f39eab9fc3cfdf6571612fd79b3d5b22f49f459581b480c7349bacddf2618c8a99
Description
README
MSAT
MSAT is an OCaml library that features a modular SATsolver and some extensions (including SMT), derived from AltErgo 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 readytouse 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 errorprone. 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
###################
...
Dependencies (5)
 camlzip

containers
>= "2.8.1" & < "4.0"

msat
= version

dune
>= "1.1"

ocaml
>= "4.03"
Dev Dependencies
None
Used by
None
Conflicts
None