pySMT makes working with Satisfiability Modulo Theory simple.

Among others, you can:

• Define formulae in a solver independent way in a simple and inutitive way,
• Write ad-hoc simplifiers and operators,
• Dump your problems in the SMT-Lib format,
• Solve them using one of the native solvers, or by wrapping any SMT-Lib complaint solver.

pySMT provides methods to define a formula in Linear Real Arithmetic (LRA), Real Difference Logic (RDL), their combination (LIRA), Equalities and Uninterpreted Functions (EUF) and Bit-Vectors (BV). The following solvers are supported through native APIs:

• MathSAT (http://mathsat.fbk.eu/)
• Z3 (http://z3.codeplex.com/releases)
• 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/)

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. For Yices 2 we rely on pyices (https://github.com/cheshire/pyices). For CUDD we use repycudd (https://github.com/pysmt/repycudd).

pySMT works on both Python 2 and Python 3. Some solvers support both versions (e.g., MathSAT) but in general, many solvers still support only Python 2.

The following table summarizes the features supported via pySMT for each of the available solvers. (We indicate with square brackets the features that are supported by the solver itself by not by the current wrapper used within pySMT).

Solver	pySMT name	Supported Logics	Satisfiability	Model Construction	UNSAT-Core
MathSAT	msat	QF_UFLIRA, QF_BV	Yes	Yes	Yes
Z3	z3	UFLIRA, QF_BV	Yes	Yes	Yes
CVC4	cvc4	QF_UFLIRA, QF_BV	Yes	Yes	No
Yices	yices	QF_UFLIRA, QF_BV	Yes	Yes	No
SMT-Lib Interface	<custom>	UFLIRA, [QF_BV]	Yes	Yes	No [Yes]
PicoSAT	picosat	QF_BOOL	Yes	Yes	No [Yes]
BDD (CUDD)	bdd	BOOL	Yes	Yes	No

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
Z3	z3	LRA, LIA
BDD (CUDD)	bdd	BOOL

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

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. For instructions on how to install each solver refer to the section on solvers installation.

from pysmt.shortcuts import Symbol, And, Not, is_sat

varA = Symbol("A") # Default type is Boolean
varB = Symbol("B")
f = And([varA, Not(varB)])
g = f.substitute({varB:varA})

res = is_sat(f)
assert res # SAT
print("f := %s is SAT? %s" % (f, res))

res = is_sat(g)
print("g := %s is SAT? %s" % (g, res))
assert not res # UNSAT

A more complex example is the following:

Lets consider the letters composing the words HELLO and WORLD, with a possible integer value between 1 and 10 to each of them. Is there a value for each letter so that H+E+L+L+O = W+O+R+L+D = 25?

The following is the pySMT code for solving this problem:

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 of usage in the examples/ directory.

PySMT does not depend directly on any solver. If you want to perform solving, you need to have at least one solver installed, and then call it via pySMT either through 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. 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. Nevertheless, we try to keep pysmt/cmd/install.py as readable and documented as possible..

Finally, for CVC4 and picosat, we have patches that need to be applied. The patches are available in the repository 'pysmt/solvers_patches' and should be applied against the following versions of the solvers:

• CVC4: Git revision 68f22235a62f5276b206e9a6692a85001beb8d42
• pycudd: 2.0.2
• picosat 960

For instruction on how to use any SMT-LIB complaint solver with pySMT see examples/generic_smtlib.py