Set.hs

module Pandora.Paradigm.Structure.Interface.Set where

import Pandora.Pattern.Category ((.), ($))
import Pandora.Pattern.Functor.Traversable (Traversable ((->>)))
import Pandora.Pattern.Object.Setoid (Setoid ((!=)))
import Pandora.Pattern.Object.Semigroup ((+))
import Pandora.Pattern.Object.Quasiring (one)
import Pandora.Paradigm.Primary.Functor.Function ((!), (!!), (%))
import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Nothing))
import Pandora.Paradigm.Primary.Functor.Predicate (equate)
import Pandora.Paradigm.Primary.Functor.Product (attached)
import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False))
import Pandora.Paradigm.Primary.Object.Numerator (Numerator (Zero))
import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce), find)
import Pandora.Paradigm.Inventory.State (State, modify)
import Pandora.Paradigm.Controlflow.Effect (run)

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

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

cardinality :: Traversable t => t a -> Numerator
cardinality s = attached . run @(State _) % Zero $ s ->> (modify @Numerator (+ one) !)