Haskell Monoid

haskell-monoid.hs

-- | Instance Array
-- | String is in fact an Array of Char
instance Semigroup [a] where
  (<>) = (++)
instance Monoid [a] where
  mempty = []
  
-- | Instance Num under addition
newtype Sum n = Sum n
instance Num n => Semigroup (Sum n) where
  (<>) = (+)
instance Monoid (Sum n) where
  mempty = 0

-- | Instance Num under multiplication
newtype Prod n = Prod n
instance Num n => Semigroup (Prod n) where
  (<>) = (*)
instance Monoid (Prod n) where
  mempty = 1
  
-- | Instance CSS Color
newtype Color = Color String
instance Semigroup Color where
  a <> (Color "transparent") = a
  (Color "transparent") <> b = b
  a <> b = ... -- implementation
instance Monoid Color where
  mempty = "transparent"
  
-- | Instance Function
instance Semigroup b => Semigroup (a -> b) where
  f <> g = \x -> f x <> g x
instance Monoid b => Monoid (a -> b) where
  mempty _ = mempty