cp4py 0.1.1

Constraint Programming language and translator for Python

cp4py

Constraint Programming language and translator for Python.

Overview

cp4py provides a unified DSL (Domain Specific Language) for constraint programming that can be translated to multiple backend solvers.

Installation

pip install cp4py

# With specific solver backends
pip install cp4py[ortools]
pip install cp4py[z3]
pip install cp4py[scip]
pip install cp4py[cvc5]
pip install cp4py[gurobi]
pip install cp4py[cplex]
pip install cp4py[cpoptimizer]

Supported Solvers

Solver	Variable Types	License
OR-Tools	int	Free
Z3	int, real	Free
SCIP	int, real	Free
CVC5	int, real	Free
Gurobi	int, real	Commercial
CPLEX	int, real	Commercial
CP Optimizer	int	Commercial

Language Syntax

cp4py uses prefix notation with Python lists:

Variable Declaration

["int", "x", 1, 9]        # Integer variable x in [1, 9]
["real", "x", 0.0, 1.0]   # Real variable x in [0.0, 1.0]

Comparison Operators

["<=", "x", 5]    # x <= 5
["<", "x", 5]     # x < 5
[">=", "x", 5]    # x >= 5
[">", "x", 5]     # x > 5
["==", "x", 5]    # x == 5
["!=", "x", 5]    # x != 5

Arithmetic

["+", "x", "y", "z"]              # x + y + z
["sum", "x", "y", "z"]            # x + y + z (same as +)
["sum", [2, "x"], [3, "y"], "z"]  # 2*x + 3*y + z

Logical Operators

["or", ["<=", "x", 5], [">=", "x", 10]]   # x <= 5 OR x >= 10
["and", [">=", "x", 0], ["<=", "x", 10]]  # x >= 0 AND x <= 10

Global Constraints

["alldifferent", "x", "y", "z"]  # x, y, z are all different

Objective Functions

["minimize", "x"]                      # Minimize x
["maximize", ["sum", [2, "x"], "y"]]   # Maximize 2*x + y

Usage

Basic Example: Magic Square

from cp4py import Var
from cp4py.translators.ortools import ORToolsTranslator

def magic_square_3x3():
    x = Var("x")

    def model():
        # Variables: 9 cells with values 1-9
        for i in range(3):
            for j in range(3):
                yield ["int", x(i, j), 1, 9]

        # All different
        yield ["alldifferent"] + [x(i, j) for i in range(3) for j in range(3)]

        # Row sums = 15
        for i in range(3):
            yield ["==", ["+", x(i, 0), x(i, 1), x(i, 2)], 15]

        # Column sums = 15
        for j in range(3):
            yield ["==", ["+", x(0, j), x(1, j), x(2, j)], 15]

        # Diagonal sums = 15
        yield ["==", ["+", x(0, 0), x(1, 1), x(2, 2)], 15]
        yield ["==", ["+", x(0, 2), x(1, 1), x(2, 0)], 15]

    translator = ORToolsTranslator()
    translator.translate(model())
    return translator.solve()

result = magic_square_3x3()

Knapsack Problem

from cp4py import Var
from cp4py.translators.ortools import ORToolsTranslator

def knapsack(weights, values, capacity):
    n = len(weights)
    x = Var("x")

    def model():
        for i in range(n):
            yield ["int", x(i), 0, 1]

        # Weight constraint
        yield ["<=", ["sum"] + [[weights[i], x(i)] for i in range(n)], capacity]

        # Maximize value
        yield ["maximize", ["sum"] + [[values[i], x(i)] for i in range(n)]]

    translator = ORToolsTranslator()
    translator.translate(model())
    return translator.solve()

weights = [2, 3, 4, 5, 9]
values = [3, 4, 5, 8, 10]
result = knapsack(weights, values, capacity=10)

Switching Solvers

from cp4py.translators.ortools import ORToolsTranslator
from cp4py.translators.z3 import Z3Translator
from cp4py.translators.scip import SCIPTranslator
from cp4py.translators.cvc5 import CVC5Translator
from cp4py.translators.gurobi import GurobiTranslator
from cp4py.translators.cplex import CPLEXTranslator
from cp4py.translators.cpoptimizer import CPOptimizerTranslator

# Use any translator
translator = Z3Translator()
translator.translate(model())
result = translator.solve()

Var Helper Class

The Var class helps generate indexed variable names:

from cp4py import Var

x = Var("x")
x()        # "x"
x(0)       # "x_0"
x(0, 1)    # "x_0_1"
x(2, 3, 4) # "x_2_3_4"

# With bounds (optional)
y = Var("y", lb=0, ub=100)
y.lb  # 0
y.ub  # 100

Examples

See the examples/ directory:

python examples/knapsack.py -ortools
python examples/knapsack.py -z3
python examples/knapsack.py -scip
python examples/knapsack.py -cvc5
python examples/knapsack.py -gurobi
python examples/knapsack.py -cplex
python examples/knapsack.py -cpoptimizer

License

MIT