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pySMT: A library for SMT formulae manipulation and solving

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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 compliant 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")```

### Portfolio

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(["cvc5",
"yices",
("msat", {"random_seed": 1}),
("msat", {"random_seed": 17}),
("msat", {"random_seed": 42})],
logic="QF_UFLIRA",
incremental=False,
generate_models=False) as s:
s.push()
res = s.solve()
v_y = s.get_value(y)
print(v_y) # TRUE

s.pop()
res = s.solve()
v_x = s.get_value(x)
print(v_x) # FALSE```

### Using other SMT-LIB Solvers

```from 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()

# 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"))) # True```

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`.

## 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.

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:

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 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 Yes z3 Yes No
cvc5 cvc5 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).

```@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}
}
```

pySMT: A library for SMT formulae manipulation and solving

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