from hypothesis import given

from rithm.integer import Int
from tests.utils import IntWithBuiltin, equivalence, implication

from . import strategies


@given(strategies.ints)
def test_reflexivity(int_: Int) -> None:
    assert int_ == int_


@given(strategies.ints, strategies.ints)
def test_symmetry(first: Int, second: Int) -> None:
    assert equivalence(first == second, second == first)


@given(strategies.ints, strategies.ints, strategies.ints)
def test_transitivity(first: Int, second: Int, third: Int) -> None:
    assert implication(first == second and second == third, first == third)


@given(strategies.ints, strategies.ints)
def test_alternatives(first: Int, second: Int) -> None:
    assert equivalence(first == second, first == second)
    assert equivalence(first == second, first >= second and first <= second)
    assert equivalence(first == second, first >= second >= first)
    assert equivalence(first == second, second <= first and second >= first)
    assert equivalence(first == second, second <= first <= second)


@given(strategies.ints, strategies.ints_with_builtins)
def test_polymorphism(first: Int, second_with_builtin: IntWithBuiltin) -> None:
    second, second_builtin = second_with_builtin

    assert equivalence(first == second, first == second_builtin)


@given(strategies.ints_with_builtins, strategies.ints_with_builtins)
def test_connection_with_builtin(
    first_with_builtin: IntWithBuiltin, second_with_builtin: IntWithBuiltin
) -> None:
    first, first_builtin = first_with_builtin
    second, second_builtin = second_with_builtin

    assert equivalence(first == second, first_builtin == second_builtin)