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_antisymmetry(first: Int, second: Int) -> None:
    assert equivalence(first <= second <= first, first == second)


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


@given(strategies.ints, strategies.ints)
def test_alternatives(first: Int, second: Int) -> None:
    assert equivalence(first <= second, first < second or first == second)
    assert equivalence(first <= second, second > first or first == second)
    assert equivalence(first <= second, first < second or not first != second)
    assert equivalence(first <= second, second > first or not first != second)
    assert equivalence(first <= second, second >= first)
    assert equivalence(first <= second, not second < first)
    assert equivalence(first <= second, not 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)
