sidekick/src/sat

MSAT

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
  
###################
...