pySMT makes working with Satisfiability Modulo Theory simple:
- Define formulae in a simple, intuitive, and solver independent way
- Solve your formulae using one of the native solvers, or by wrapping any SMT-Lib compliant solver,
- Dump your problems in the SMT-Lib format,
- and more...
>>> from pysmt.shortcuts import Symbol, And, Not, is_sat
>>>
>>> varA = Symbol("A") # Default type is Boolean
>>> varB = Symbol("B")
>>> f = And(varA, Not(varB))
>>> f
(A & (! B))
>>> is_sat(f)
True
>>> g = f.substitute({varB: varA})
>>> g
(A & (! A))
>>> is_sat(g)
FalseIs there a value for each letter (between 1 and 9) so that H+E+L+L+O = W+O+R+L+D = 25?
from pysmt.shortcuts import Symbol, And, GE, LT, Plus, Equals, Int, get_model
from pysmt.typing import INT
hello = [Symbol(s, INT) for s in "hello"]
world = [Symbol(s, INT) for s in "world"]
letters = set(hello+world)
domains = And([And(GE(l, Int(1)),
LT(l, Int(10))) for l in letters])
sum_hello = Plus(hello) # n-ary operators can take lists
sum_world = Plus(world) # as arguments
problem = And(Equals(sum_hello, sum_world),
Equals(sum_hello, Int(25)))
formula = And(domains, problem)
print("Serialization of the formula:")
print(formula)
model = get_model(formula)
if model:
print(model)
else:
print("No solution found")Portfolio solving consists of running multiple solvers in parallel. pySMT provides a simple interface to perform portfolio solving using multiple solvers and multiple solver configurations.
from pysmt.shortcuts import Portfolio, Symbol, Not
x, y = Symbol("x"), Symbol("y")
f = x.Implies(y)
with Portfolio(["cvc4",
"yices",
("msat", {"random_seed": 1}),
("msat", {"random_seed": 17}),
("msat", {"random_seed": 42})],
logic="QF_UFLIRA",
incremental=False,
generate_models=False) as s:
s.add_assertion(f)
s.push()
s.add_assertion(x)
res = s.solve()
v_y = s.get_value(y)
print(v_y) # TRUE
s.pop()
s.add_assertion(Not(y))
res = s.solve()
v_x = s.get_value(x)
print(v_x) # FALSEfrom pysmt.shortcuts import Symbol, get_env, Solver
from pysmt.logics import QF_UFLRA
name = "mathsat-smtlib" # Note: The API version is called 'msat'
# Path to the solver. The solver needs to take the smtlib file from
# stdin. This might require creating a tiny shell script to set the
# solver options.
path = ["/tmp/mathsat"]
logics = [QF_UFLRA,] # List of the supported logics
# Add the solver to the environment
env = get_env()
env.factory.add_generic_solver(name, path, logics)
# The solver name of the SMT-LIB solver can be now used anywhere
# where pySMT would accept an API solver name
with Solver(name=name, logic="QF_UFLRA") as s:
print(s.is_sat(Symbol("x"))) # TrueCheck out more examples in the examples/ directory and the documentation on ReadTheDocs
pySMT provides methods to define a formula in Linear Real Arithmetic (LRA), Real Difference Logic (RDL), Equalities and Uninterpreted Functions (EUF), Bit-Vectors (BV), Arrays (A), Strings (S) and their combinations. The following solvers are supported through native APIs:
- MathSAT (http://mathsat.fbk.eu/)
- Z3 (https://github.com/Z3Prover/z3/)
- CVC4 (http://cvc4.cs.nyu.edu/web/)
- Yices 2 (http://yices.csl.sri.com/)
- CUDD (http://vlsi.colorado.edu/~fabio/CUDD/)
- PicoSAT (http://fmv.jku.at/picosat/)
- Boolector (http://fmv.jku.at/boolector/)
Additionally, you can use any SMT-LIB 2 compliant solver.
PySMT assumes that the python bindings for the SMT Solver are
installed and accessible from your PYTHONPATH.
You can install the latest stable release of pySMT from PyPI:
# pip install pysmt
this will additionally install the pysmt-install command, that can be used to install the solvers: e.g.,
$ pysmt-install --check
will show you which solvers have been found in your PYTHONPATH.
PySMT does not depend directly on any solver, but if you want to
perform solving, you need to have at least one solver installed. This
can be used by pySMT via its native API, or passing through an SMT-LIB
file.
The script pysmt-install can be used to simplify the installation of the solvers:
$ pysmt-install --msat
will install MathSAT 5.
By default the solvers are downloaded, unpacked and built in your home directory
in the .smt_solvers folder. Compiled libraries and actual solver packages are
installed in the relevant site-packages directory (e.g. virtual environment's
packages root or local user-site). pysmt-install has many options to
customize its behavior. If you have multiple versions of python in your system,
we recommend the following syntax to run pysmt-install: python -m pysmt install.
Note: This script does not install required dependencies for building the solver (e.g., make or gcc) and has been tested mainly on Linux Debian/Ubuntu systems. We suggest that you refer to the documentation of each solver to understand how to install it with its python bindings.
For Yices, picosat, and CUDD, we use external wrappers:
- yicespy (https://github.com/pysmt/yicespy)
- repycudd (https://github.com/pysmt/repycudd)
- pyPicoSAT (https://github.com/pysmt/pyPicoSAT)
For instruction on how to use any SMT-LIB complaint solver with pySMT see examples/generic_smtlib.py
For more information, refer to online documentation on ReadTheDocs
The following table summarizes the features supported via pySMT for each of the available solvers.
Solver pySMT name Supported Theories Quantifiers Quantifier Elimination Unsat Core Interpolation MathSAT msat UF, LIA, LRA, BV, AX No msat-fm, msat-lw Yes Yes Z3 z3 UF, LIA, LRA, BV, AX, NRA, NIA z3 z3 Yes Yes CVC4 cvc4 UF, LIA, LRA, BV, AX, S Yes No No No Yices yices UF, LIA, LRA, BV No No No No Boolector btor UF, BV, AX No No No No SMT-Lib Interface <custom> UF, LIA, LRA, BV, AX Yes No No No PicoSAT picosat [None] No [No] No No BDD (CUDD) bdd [None] Yes bdd No No
pySMT is released under the APACHE 2.0 License.
For further questions, feel free to open an issue, or write to pysmt@googlegroups.com (Browse the Archive).
If you use pySMT in your work, please consider citing:
@inproceedings{pysmt2015,
title={PySMT: a solver-agnostic library for fast prototyping of SMT-based algorithms},
author={Gario, Marco and Micheli, Andrea},
booktitle={SMT Workshop 2015},
year={2015}
}