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.

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 --msat

this will download and install Mathsat 5. You will need to set your PYTHONPATH as suggested by the installer to make the python bindings visible. To verify that a solver has been installed run

$ pysmt-install --check

Note pysmt-install is provided to simplify the installation of solvers. However, each solver has its own dependencies, license and restrictions on use that you need to take into account.

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

• MathSAT (http://mathsat.fbk.eu/) >= 5
• Z3 (http://z3.codeplex.com/releases) >= 4
• CVC4 (http://cvc4.cs.nyu.edu/web/)
• Yices 2 (http://yices.csl.sri.com/)
• pyCUDD (http://bears.ece.ucsb.edu/pycudd.html)
• PicoSAT (http://fmv.jku.at/picosat/)

The library assumes that the python binding for the SMT Solver are installed and accessible from your PYTHONPATH. For Yices 2 we rely on pyices (https://github.com/cheshire/pyices).

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.

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")