CPMpy z3 interface (cpmpy.solvers.z3)

Interface to Z3’s Python API.

Z3 is a highly versatile and effective theorem prover from Microsoft. Underneath, it is an SMT solver with a wide scala of theory solvers. We will interface to the finite-domain integer related parts of the API. (see https://github.com/Z3Prover/z3)

Warning

For incrementally solving an optimisation function, instantiate the solver object with a model that has an objective function, e.g. s = cp.SolverLookup.get("z3", Model(maximize=1)).

Always use cp.SolverLookup.get("z3") to instantiate the solver object.

Installation

Requires that the ‘z3-solver’ python package is installed:

$ pip install z3-solver

See detailed installation instructions at: https://github.com/Z3Prover/z3#python

The rest of this documentation is for advanced users.

List of classes

CPM_z3

Interface to Z3's Python API.

Module details

class cpmpy.solvers.z3.CPM_z3(cpm_model=None, subsolver='sat')[source]

Interface to Z3’s Python API.

Creates the following attributes (see parent constructor for more):

  • z3_solver: object, z3’s Solver() object

The DirectConstraint, when used, calls a function in the z3 namespace and z3_solver.add()’s the result.

Documentation of the solver’s own Python API: https://z3prover.github.io/api/html/namespacez3py.html

Note

Terminology note: a ‘model’ for z3 is a solution!

add(cpm_expr)[source]

Z3 supports nested expressions so translate expression tree and post to solver API directly

Any CPMpy expression given is immediately transformed (through transform()) and then posted to the solver in this function.

This can raise ‘NotImplementedError’ for any constraint not supported after transformation

The variables used in expressions given to add are stored as ‘user variables’. Those are the only ones the user knows and cares about (and will be populated with a value after solve). All other variables are auxiliary variables created by transformations.

Parameters:

cpm_expr (Expression or list of Expression) – CPMpy expression, or list thereof

Returns:

self

get_core()[source]

For use with s.solve(assumptions=[...]). Only meaningful if the solver returned UNSAT. In that case, get_core() returns a small subset of assumption variables that are unsat together.

CPMpy will return only those variables that are False (in the UNSAT core)

Note that there is no guarantee that the core is minimal, though this interface does upon up the possibility to add more advanced Minimal Unsatisfiabile Subset algorithms on top. All contributions welcome!

has_objective()[source]

Returns whether the solver has an objective function or not.

maximize(expr)

Post the given expression to the solver as objective to maximize

maximize() can be called multiple times, only the last one is stored

minimize(expr)

Post the given expression to the solver as objective to minimize

minimize() can be called multiple times, only the last one is stored

property native_model

Returns the solver’s underlying native model (for direct solver access).

objective(expr, minimize=True)[source]

Post the given expression to the solver as objective to minimize/maximize

objective() can be called multiple times, only the last one is stored

Note

technical side note: any constraints created during conversion of the objective are premanently posted to the solver

objective_value()

Returns the value of the objective function of the latest solver run on this model

Returns:

an integer or ‘None’ if it is not run, or a satisfaction problem

solution_hint(cpm_vars, vals)

For warmstarting the solver with a variable assignment

Typically implemented in SAT-based solvers

Parameters:

  • cpm_vars – list of CPMpy variables

  • vals – list of (corresponding) values for the variables

solve(time_limit=None, assumptions=[], **kwargs)[source]

Call the z3 solver

Parameters:

  • time_limit (float, optional) – maximum solve time in seconds

  • assumptions – list of CPMpy Boolean variables (or their negation) that are assumed to be true. For repeated solving, and/or for use with s.get_core(): if the model is UNSAT, get_core() returns a small subset of assumption variables that are unsat together.

  • **kwargs – any keyword argument, sets parameters of solver object

Arguments that correspond to solver parameters:

  • … (no common examples yet)

The full list doesn’t seem to be documented online, you have to run its help() function:

import z3
z3.Solver().help()

Warning

Warning! Some parameternames in z3 have a ‘.’ in their name, such as (arbitrarily chosen): sat.lookahead_simplify You have to construct a dictionary of keyword arguments upfront:

params = {"sat.lookahead_simplify": True}
s.solve(**params)
solveAll(display=None, time_limit=None, solution_limit=None, call_from_model=False, **kwargs)

Compute all solutions and optionally display the solutions.

This is the generic implementation, solvers can overwrite this with a more efficient native implementation

Parameters:

  • display (-) – either a list of CPMpy expressions, OR a callback function, called with the variables after value-mapping default/None: nothing displayed

  • time_limit (-) – stop after this many seconds (default: None)

  • solution_limit (-) – stop after this many solutions (default: None)

  • call_from_model (-) – whether the method is called from a CPMpy Model instance or not

  • argument (- any other keyword) –

Returns:

number of solutions found

solver_var(cpm_var)[source]

Creates solver variable for cpmpy variable or returns from cache if previously created

solver_vars(cpm_vars)

Like solver_var() but for arbitrary shaped lists/tensors

status()
static supported()[source]

Check for support in current system setup. Return True if the system has package installed or supports solver, else returns False.

Returns:

Solver support by current system setup.

Return type:

[bool]

transform(cpm_expr)[source]

Transform arbitrary CPMpy expressions to constraints the solver supports

Implemented through chaining multiple solver-independent transformation functions from the cpmpy/transformations/ directory.

See the Adding a new solver docs on readthedocs for more information.

Parameters:

cpm_expr (Expression or list of Expression) – CPMpy expression, or list thereof

Returns:

list of Expression