definition module Data.Monoid

from StdOverloaded import class +, class *, class zero, class one
from Data.Maybe import :: Maybe
from Data.Void import :: Void

class Semigroup a where
  mappend :: a a -> a

class Monoid a | Semigroup a where
  mempty :: a

mconcat         :: .[a] -> a | Monoid a
(<++>) infixr 6 :: a a -> a | Semigroup a

instance Semigroup [a]
instance Semigroup (a -> b) | Semigroup b
instance Semigroup ()
instance Semigroup Void
instance Semigroup (a, b) | Semigroup a & Semigroup b
instance Semigroup (a, b, c) | Semigroup a & Semigroup b & Semigroup c
instance Semigroup (a, b, c, d) | Semigroup a & Semigroup b & Semigroup c & Semigroup d
instance Semigroup (a, b, c, d, e) | Semigroup a & Semigroup b & Semigroup c & Semigroup d & Semigroup e
instance Semigroup (Maybe a) | Semigroup a

instance Monoid [a]
instance Monoid (a -> b) | Monoid b
instance Monoid ()
instance Monoid Void
instance Monoid (a, b) | Monoid a & Monoid b
instance Monoid (a, b, c) | Monoid a & Monoid b & Monoid c
instance Monoid (a, b, c, d) | Monoid a & Monoid b & Monoid c & Monoid d
instance Monoid (a, b, c, d, e) | Monoid a & Monoid b & Monoid c & Monoid d & Monoid e
instance Monoid (Maybe a)

:: Dual a = Dual a

:: Endo a = Endo (a -> a)

:: All = All Bool

:: Any = Any Bool

:: Sum a = Sum a

:: Product a = Product a

:: First a = First (Maybe a)

:: Last a = Last (Maybe a)

instance Semigroup (Dual a) | Semigroup a
instance Semigroup (Endo a)
instance Semigroup All
instance Semigroup Any
instance Semigroup (Sum a) | + a & zero a
instance Semigroup (Product a) | * a & one a
instance Semigroup (First a)
instance Semigroup (Last a)

instance Monoid (Dual a) | Monoid a
instance Monoid (Endo a)
instance Monoid All
instance Monoid Any
instance Monoid (Sum a) | + a & zero a
instance Monoid (Product a) | * a & one a
instance Monoid (First a)
instance Monoid (Last a)

getDual :: (Dual a) -> a

appEndo :: (Endo a) -> (a -> a)

getAll :: All -> Bool

getAny :: Any -> Bool

getSum :: (Sum a) -> a

getProduct :: (Product a) -> a

getFirst :: (First a) -> Maybe a

getLast :: (Last a) -> Maybe a