-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Collection of functor utilities, providing handy operators, like generalization of (.).
--   
--   Collection of functor utilities, providing handy operators, like
--   generalization of (.).
@package functor-utils
@version 1.17.2

module Data.Functor.Utils
type family Applicatives lst :: Constraint
type family Functors lst :: Constraint
fmap0 :: (a -> b) -> a -> b
fmap1 :: Functor f => (a -> b) -> f a -> f b
fmap2 :: Functors '[f1, f2] => (a -> b) -> f2 (f1 a) -> f2 (f1 b)
fmap3 :: Functors '[f1, f2, f3] => (a -> b) -> f3 (f2 (f1 a)) -> f3 (f2 (f1 b))
fmap4 :: Functors '[f1, f2, f3, f4] => (a -> b) -> f4 (f3 (f2 (f1 a))) -> f4 (f3 (f2 (f1 b)))
fmap5 :: Functors '[f1, f2, f3, f4, f5] => (a -> b) -> f5 (f4 (f3 (f2 (f1 a)))) -> f5 (f4 (f3 (f2 (f1 b))))
(.) :: Functor f1 => (a -> b) -> f1 a -> f1 b
infixr 9 .
(.:) :: Functors '[f1, f2] => (a -> b) -> f2 (f1 a) -> f2 (f1 b)
infixr 8 .:
(.:.) :: Functors '[f1, f2, f3] => (a -> b) -> f3 (f2 (f1 a)) -> f3 (f2 (f1 b))
infixr 8 .:.
(.::) :: Functors '[f1, f2, f3, f4] => (a -> b) -> f4 (f3 (f2 (f1 a))) -> f4 (f3 (f2 (f1 b)))
infixr 8 .::
(.::.) :: Functors '[f1, f2, f3, f4, f5] => (a -> b) -> f5 (f4 (f3 (f2 (f1 a)))) -> f5 (f4 (f3 (f2 (f1 b))))
infixr 8 .::.
(∘) :: Functor f1 => (a -> b) -> f1 a -> f1 b
infixr 9 ∘
(∘∘) :: Functors '[f1, f2] => (a -> b) -> f2 (f1 a) -> f2 (f1 b)
infixr 8 ∘∘
(∘∘∘) :: Functors '[f1, f2, f3] => (a -> b) -> f3 (f2 (f1 a)) -> f3 (f2 (f1 b))
infixr 8 ∘∘∘
(∘∘∘∘) :: Functors '[f1, f2, f3, f4] => (a -> b) -> f4 (f3 (f2 (f1 a))) -> f4 (f3 (f2 (f1 b)))
infixr 8 ∘∘∘∘
(∘∘∘∘∘) :: Functors '[f1, f2, f3, f4, f5] => (a -> b) -> f5 (f4 (f3 (f2 (f1 a)))) -> f5 (f4 (f3 (f2 (f1 b))))
infixr 8 ∘∘∘∘∘
(<<$>>) :: Functors '[f1, f2] => (a -> b) -> f2 (f1 a) -> f2 (f1 b)
infixl 4 <<$>>
(<<<$>>>) :: Functors '[f1, f2, f3] => (a -> b) -> f3 (f2 (f1 a)) -> f3 (f2 (f1 b))
infixl 4 <<<$>>>
(<<<<$>>>>) :: Functors '[f1, f2, f3, f4] => (a -> b) -> f4 (f3 (f2 (f1 a))) -> f4 (f3 (f2 (f1 b)))
infixl 4 <<<<$>>>>
(<<<<<$>>>>>) :: Functors '[f1, f2, f3, f4, f5] => (a -> b) -> f5 (f4 (f3 (f2 (f1 a)))) -> f5 (f4 (f3 (f2 (f1 b))))
infixl 4 <<<<<$>>>>>
(<<*>>) :: Applicatives '[f1, f2] => f2 (f1 (a -> b)) -> f2 (f1 a) -> f2 (f1 b)
infixl 4 <<*>>
(<<<*>>>) :: Applicatives '[f1, f2, f3] => f3 (f2 (f1 (a -> b))) -> f3 (f2 (f1 a)) -> f3 (f2 (f1 b))
infixl 4 <<<*>>>
(<<<<*>>>>) :: Applicatives '[f1, f2, f3, f4] => f4 (f3 (f2 (f1 (a -> b)))) -> f4 (f3 (f2 (f1 a))) -> f4 (f3 (f2 (f1 b)))
infixl 4 <<<<*>>>>
(<<<<<*>>>>>) :: Applicatives '[f1, f2, f3, f4, f5] => f5 (f4 (f3 (f2 (f1 (a -> b))))) -> f5 (f4 (f3 (f2 (f1 a)))) -> f5 (f4 (f3 (f2 (f1 b))))
infixl 4 <<<<<*>>>>>
(|$) :: (a -> b) -> a -> (a, b)
infixl 4 |$
($|) :: (a -> b) -> a -> (b, a)
infixl 4 $|
(<|$>) :: Functor f => (a -> b) -> f a -> f (a, b)
infixl 4 <|$>
(<$|>) :: Functor f => (a -> b) -> f a -> f (b, a)
infixl 4 <$|>
composed :: Iso' (f (g a)) (Compose f g a)

-- | following functions are usefull when operating on nested structures
--   with lenses, for example | given function foo :: a -&gt; m (n a) and a
--   lens l :: Lens' x a, we can use | nested l foo to get signature of x
--   -&gt; m (n x)
nested :: (Functor f1, Functor f2) => (f2 (Compose f3 g1 a1) -> f1 (Compose f4 g2 a2)) -> f2 (f3 (g1 a1)) -> f1 (f4 (g2 a2))

-- | Right-to-left composition of functors. The composition of applicative
--   functors is always applicative, but the composition of monads is not
--   always a monad.
newtype Compose (f :: k -> Type) (g :: k1 -> k) (a :: k1) :: forall k k1. () => k -> Type -> k1 -> k -> k1 -> Type
Compose :: f (g a) -> Compose
[getCompose] :: Compose -> f (g a)
infixr 9 `Compose`
infixr 9 `Compose`