module Pandora.Paradigm.Structure.Interface.Set where

import Pandora.Core.Morphism ((!), (%))
import Pandora.Pattern.Category ((.))
import Pandora.Pattern.Functor.Traversable (Traversable ((->>)))
import Pandora.Pattern.Object.Setoid (Setoid ((/=)))
import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Nothing), maybe)
import Pandora.Paradigm.Primary.Functor.Predicate (equate)
import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False))
import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic, find)

member :: (Setoid a, Monotonic e a) => a -> e -> Boolean
member x = maybe False (True !) . find (equate x)

subset :: (Monotonic (t a) a, Traversable t, Setoid a, Setoid (t a)) => t a -> t a -> Boolean
subset ss s = Nothing /= (ss ->> find % s . equate)