simetrica :: Eq a => Rel a -> Bool

   simetrica (R ([1,3],[(1,1),(1,3),(3,1)]))  ==  True
   simetrica (R ([1,3],[(1,1),(1,3),(3,2)]))  ==  False
   simetrica (R ([1,3],[]))                   ==  True

import Relaciones_binarias (Rel(R))
import Test.QuickCheck

-- 1ª solución
-- ===========

simetrica :: Eq a => Rel a -> Bool
simetrica (R (_,g)) = and [(y,x) `elem` g | (x,y) <- g]

-- 2ª solución
-- ===========

simetrica2 :: Eq a => Rel a -> Bool
simetrica2 (R (_,g)) = all (\(x,y) -> (y,x) `elem` g) g

-- 3ª solución
-- ===========

simetrica3 :: Eq a => Rel a -> Bool
simetrica3 (R (_,g)) = aux g
  where aux [] = True
        aux ((x,y):ps) = (y,x) `elem` g && aux ps

-- Comprobación de equivalencia
-- ============================

-- La propiedad es
prop_simetrica :: Rel Int -> Bool
prop_simetrica r =
  all (== simetrica r)
      [simetrica2 r,
       simetrica3 r]

-- La comprobación es
--    λ> quickCheck prop_simetrica
--    +++ OK, passed 100 tests.

from typing import TypeVar

from hypothesis import given
from hypothesis import strategies as st

from src.Relaciones_binarias import Rel, relacionArbitraria

A = TypeVar('A')

# 1ª solución
# ===========

def simetrica(r: Rel[A]) -> bool:
    (_, g) = r
    return all(((y, x) in g for (x, y) in g))

# 2ª solución
# ===========

def simetrica2(r: Rel[A]) -> bool:
    (_, g) = r
    def aux(ps: list[tuple[A, A]]) -> bool:
        if not ps:
            return True
        (x, y) = ps[0]
        return (y, x) in g and aux(ps[1:])

    return aux(g)

# 3ª solución
# ===========

def simetrica3(r: Rel[A]) -> bool:
    (_, g) = r
    for (x, y) in g:
        if (y, x) not in g:
            return False
    return True

# Comprobación de equivalencia
# ============================

# La propiedad es
@given(st.integers(min_value=0, max_value=10))
def test_simetrica(n: int) -> None:
    r = relacionArbitraria(n)
    res = simetrica(r)
    assert simetrica2(r) == res
    assert simetrica3(r) == res

# La comprobación es
#    > poetry run pytest -q Relaciones_simetricas.py
#    1 passed in 0.11s