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#!/usr/bin/env python
###############################################################################
# Top contributors (to current version):
# Yoni Zohar
#
# This file is part of the cvc5 project.
#
# Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
# in the top-level source directory and their institutional affiliations.
# All rights reserved. See the file COPYING in the top-level source
# directory for licensing information.
# #############################################################################
#
# A simple demonstration of the api capabilities of cvc5, adapted from quickstart.cpp
##
import pycvc5
from pycvc5 import kinds
if __name__ == "__main__":
# Create a solver
solver = pycvc5.Solver()
# We will ask the solver to produce models and unsat cores,
# hence these options should be turned on.
solver.setOption("produce-models", "true");
solver.setOption("produce-unsat-cores", "true");
# The simplest way to set a logic for the solver is to choose "ALL".
# This enables all logics in the solver.
# Alternatively, "QF_ALL" enables all logics without quantifiers.
# To optimize the solver's behavior for a more specific logic,
# use the logic name, e.g. "QF_BV" or "QF_AUFBV".
# Set the logic
solver.setLogic("ALL");
# In this example, we will define constraints over reals and integers.
# Hence, we first obtain the corresponding sorts.
realSort = solver.getRealSort();
intSort = solver.getIntegerSort();
# x and y will be real variables, while a and b will be integer variables.
# Formally, their python type is Term,
# and they are called "constants" in SMT jargon:
x = solver.mkConst(realSort, "x");
y = solver.mkConst(realSort, "y");
a = solver.mkConst(intSort, "a");
b = solver.mkConst(intSort, "b");
# Our constraints regarding x and y will be:
#
# (1) 0 < x
# (2) 0 < y
# (3) x + y < 1
# (4) x <= y
#
# Formally, constraints are also terms. Their sort is Boolean.
# We will construct these constraints gradually,
# by defining each of their components.
# We start with the constant numerals 0 and 1:
zero = solver.mkReal(0);
one = solver.mkReal(1);
# Next, we construct the term x + y
xPlusY = solver.mkTerm(kinds.Plus, x, y);
# Now we can define the constraints.
# They use the operators +, <=, and <.
# In the API, these are denoted by Plus, Leq, and Lt.
constraint1 = solver.mkTerm(kinds.Lt, zero, x);
constraint2 = solver.mkTerm(kinds.Lt, zero, y);
constraint3 = solver.mkTerm(kinds.Lt, xPlusY, one);
constraint4 = solver.mkTerm(kinds.Leq, x, y);
# Now we assert the constraints to the solver.
solver.assertFormula(constraint1);
solver.assertFormula(constraint2);
solver.assertFormula(constraint3);
solver.assertFormula(constraint4);
# Check if the formula is satisfiable, that is,
# are there real values for x and y that satisfy all the constraints?
r1 = solver.checkSat();
# The result is either SAT, UNSAT, or UNKNOWN.
# In this case, it is SAT.
print("expected: sat")
print("result: ", r1)
# We can get the values for x and y that satisfy the constraints.
xVal = solver.getValue(x);
yVal = solver.getValue(y);
# It is also possible to get values for compound terms,
# even if those did not appear in the original formula.
xMinusY = solver.mkTerm(kinds.Minus, x, y);
xMinusYVal = solver.getValue(xMinusY);
# We can now obtain the values as python values
xPy = xVal.getRealValue();
yPy = yVal.getRealValue();
xMinusYPy = xMinusYVal.getRealValue();
print("value for x: ", xPy)
print("value for y: ", yPy)
print("value for x - y: ", xMinusYPy)
# Another way to independently compute the value of x - y would be
# to use the python minus operator instead of asking the solver.
# However, for more complex terms,
# it is easier to let the solver do the evaluation.
xMinusYComputed = xPy - yPy;
if xMinusYComputed == xMinusYPy:
print("computed correctly")
else:
print("computed incorrectly")
# Further, we can convert the values to strings
xStr = str(xPy);
yStr = str(yPy);
xMinusYStr = str(xMinusYPy);
# Next, we will check satisfiability of the same formula,
# only this time over integer variables a and b.
# We start by resetting assertions added to the solver.
solver.resetAssertions();
# Next, we assert the same assertions above with integers.
# This time, we inline the construction of terms
# to the assertion command.
solver.assertFormula(solver.mkTerm(kinds.Lt, solver.mkInteger(0), a));
solver.assertFormula(solver.mkTerm(kinds.Lt, solver.mkInteger(0), b));
solver.assertFormula(
solver.mkTerm(kinds.Lt, solver.mkTerm(kinds.Plus, a, b), solver.mkInteger(1)));
solver.assertFormula(solver.mkTerm(kinds.Leq, a, b));
# We check whether the revised assertion is satisfiable.
r2 = solver.checkSat();
# This time the formula is unsatisfiable
print("expected: unsat")
print("result:", r2)
# We can query the solver for an unsatisfiable core, i.e., a subset
# of the assertions that is already unsatisfiable.
unsatCore = solver.getUnsatCore();
print("unsat core size:", len(unsatCore))
print("unsat core:", unsatCore)
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