{-# LANGUAGE CPP                  #-}
{-# LANGUAGE DeriveFunctor        #-}
{-# LANGUAGE UndecidableInstances #-}

module Data.Algebra.Pointed
    ( Pointed (..)
    , PointedMonoid (..)
    ) where

#if __GLASGOW_HASKELL__ <= 802
import Data.Semigroup (Semigroup (..))
#endif

-- | Class of pointed sets
--
class Pointed p where
    point :: p

instance Pointed (Maybe a) where
    point :: Maybe a
point = Maybe a
forall a. Maybe a
Nothing

-- | @Monoid@ should be a subclass of @Pointed@.
--
newtype PointedMonoid m = PointedMonoid { forall m. PointedMonoid m -> m
runPointedMonoid :: m }
    deriving (Int -> PointedMonoid m -> ShowS
[PointedMonoid m] -> ShowS
PointedMonoid m -> String
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Functor)

instance Semigroup m => Semigroup (PointedMonoid m) where
    (PointedMonoid m
m) <> :: PointedMonoid m -> PointedMonoid m -> PointedMonoid m
<> (PointedMonoid m
n) = m -> PointedMonoid m
forall m. m -> PointedMonoid m
PointedMonoid (m
m m -> m -> m
forall a. Semigroup a => a -> a -> a
<> m
n)

instance Monoid m => Monoid (PointedMonoid m) where
    mempty :: PointedMonoid m
mempty = m -> PointedMonoid m
forall m. m -> PointedMonoid m
PointedMonoid m
forall a. Monoid a => a
mempty
#if __GLASGOW_HASKELL__ <= 802
    mappend (PointedMonoid m) (PointedMonoid n) = PointedMonoid $ mappend m n
#endif

instance Monoid m => Pointed (PointedMonoid m) where
    point :: PointedMonoid m
point = PointedMonoid m
forall a. Monoid a => a
mempty