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{-# LANGUAGE DeriveTraversable #-}
module Data.Bag where
-- | An ordered sequence that can be folded over.
data Bag a = BZero | BOne a | BTwo (Bag a) (Bag a) | BList [Bag a]
deriving (Functor, Foldable, Traversable)
-- Really only here for 'pure'
instance Applicative Bag where
pure = BOne
BZero <*> _ = BZero
BOne f <*> t = f <$> t
BTwo f1 f2 <*> t = BTwo (f1 <*> t) (f2 <*> t)
BList fs <*> t = BList [f <*> t | f <- fs]
instance Semigroup (Bag a) where (<>) = BTwo
instance Monoid (Bag a) where mempty = BZero
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