# pysmt/pysmt

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# 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), Strings (S) and their combinations. The following solvers are supported through native APIs:

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:

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

### 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