pySMT: a Python API for SMT

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 complaint solver,
• Dump your problems in the SMT-Lib format,
• and more...

Usage

>>> 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)
False

A More Complex Example

Is 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")

Check out more examples in the examples/ directory and the documentation on ReadTheDocs

Supported Theories and Solvers

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) 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.

pySMT works on both Python 3.5 and Python 2.7.

Installation

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. Once the installation is complete, you can use the option --env to obtain a string to update your PYTHONPATH:

$ pysmt-install --env
export PYTHONPATH="/home/pysmt/.smt_solvers/python-bindings-2.7:${PYTHONPATH}"

By default the solvers are installed in your home directory in the folder .smt_solvers. pysmt-install has many options to customize its behavior.

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

Solvers Support

The following table summarizes the features supported via pySMT for each of the available solvers.

Solver	pySMT name	Supported Theories	Quantifiers
MathSAT	msat	UF, LIA, LRA, BV, AX	No
Z3	z3	UF, LIA, LRA, BV, AX, NRA, NIA	Yes
CVC4	cvc4	UF, LIA, LRA, BV, AX	Yes
Yices	yices	UF, LIA, LRA, BV	No
SMT-Lib Interface	<custom>	UF, LIA, LRA, BV, AX	Yes
PicoSAT	picosat	[None]	No
Boolector	btor	UF, BV, AX	No
BDD (CUDD)	bdd	[None]	Yes

The following table summarizes the features supported via pySMT for each of the available quantifier eliminators

Quantifier Eliminator	pySMT name	Supported Logics
MathSAT FM	msat-fm	LRA
MathSAT LW	msat-lw	LRA, LIA
Z3	z3	LRA, LIA
BDD (CUDD)	bdd	BOOL

Unsat-Core extraction is currently supported on: MathSAT and Z3.

The following table summarizes the features supported via pySMT for each of the available Craig interpolators

Interpolator	pySMT name	Supported Logics
MathSAT	msat	QF_UFLIA, QF_UFLRA, QF_BV
Z3	z3	QF_UFLIA, QF_UFLRA

License

pySMT is release under the APACHE 2.0 License.

For further questions, feel free to open an issue, or write to [email protected] (Browse the Archive).