-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Nested composition of functors with a type index tracking nesting.
--
@package NestedFunctor
@version 0.2.0.2
-- | This module implements something akin to Compose, but with a
-- type index that tracks the order in which things are nested. This
-- makes it possible to write code using polymorphic recursion over the
-- levels of the structure contained in a Nested value.
module Data.Functor.Nested
-- | Flat x is the type index used for the base case of a
-- Nested value. Thus, a (Nested (Flat []) Int is
-- isomorphic to a [Int].
data Flat (x :: * -> *)
-- | Nest o i is the type index used for the recursive case of a
-- Nested value: the o parameter is the type constructors
-- corresponding to the outside levels, and the i
-- parameter is the single type constructor corresponding to the
-- inner-most level. Thus, a (Nested (Nest (Flat Maybe) [])
-- Int) is isomorphic to a (Maybe [Int]).
data Nest (o :: *) (i :: * -> *)
-- | A Nested fs a is the composition of all the layers mentioned
-- in fs, applied to an a. Specifically, the
-- fs parameter is a sort of snoc-list holding type constructors
-- of kind (* -> *). The outermost layer appears as the
-- parameter to Flat; the innermost layer appears as the
-- rightmost argument to the outermost Nest. For instance:
--
--
-- [Just ['a']] :: [Maybe [Char]]
-- Flat [Just ['a']] :: Nested (Flat []) (Maybe [Char])
-- Nest (Flat [Just ['a']]) :: Nested (Nest (Flat []) Maybe) [Char]
-- Nest (Nest (Flat [Just ['a']])) :: Nested (Nest (Nest (Flat []) Maybe) []) Char
--
data Nested fs a
Flat :: f a -> Nested (Flat f) a
Nest :: Nested fs (f a) -> Nested (Nest fs f) a
-- | The UnNest type family describes what happens when you peel
-- off one Nested constructor from a Nested value.
-- | Removes one Nested constructor (either Nest or
-- Flat) from a Nested value.
--
--
-- unNest . Nest == id
-- unNest . Flat == id
--
--
--
-- unNest (Nest (Flat [['x']])) == Flat [['x']]
-- unNest (Flat (Just 'x')) == Just 'x'
--
unNest :: Nested fs a -> UnNest (Nested fs a)
class NestedAs x y
asNestedAs :: NestedAs x y => x -> y -> x `AsNestedAs` y
-- | This type family calculates the result type of applying the
-- Nested constructors to its first argument a number of times
-- equal to the depth of nesting in its second argument.
-- | This type family calculates the type of a Nested value if one
-- more Nest constructor is applied to it.
instance (AsNestedAs (f a) (UnNest (Nested (Nest g h) b)) ~ Nested fs (f' a'), AddNest (Nested fs (f' a')) ~ Nested (Nest fs f') a', NestedAs (f a) (UnNest (Nested (Nest g h) b))) => NestedAs (f a) (Nested (Nest g h) b)
instance AsNestedAs (f a) (Nested (Flat g) b) ~ Nested (Flat f) a => NestedAs (f a) (Nested (Flat g) b)
instance (Distributive f, Distributive (Nested fs)) => Distributive (Nested (Nest fs f))
instance Distributive f => Distributive (Nested (Flat f))
instance (Applicative f, Alternative (Nested fs)) => Alternative (Nested (Nest fs f))
instance Alternative f => Alternative (Nested (Flat f))
instance (Traversable f, Traversable (Nested fs)) => Traversable (Nested (Nest fs f))
instance Traversable f => Traversable (Nested (Flat f))
instance (Foldable f, Foldable (Nested fs)) => Foldable (Nested (Nest fs f))
instance Foldable f => Foldable (Nested (Flat f))
instance (Comonad f, Comonad (Nested fs), Distributive f, Functor (Nested (Nest fs f))) => Comonad (Nested (Nest fs f))
instance Comonad f => Comonad (Nested (Flat f))
instance (ComonadApply f, Distributive f, ComonadApply (Nested fs)) => ComonadApply (Nested (Nest fs f))
instance ComonadApply f => ComonadApply (Nested (Flat f))
instance (Applicative f, Applicative (Nested fs)) => Applicative (Nested (Nest fs f))
instance Applicative f => Applicative (Nested (Flat f))
instance (Functor f, Functor (Nested fs)) => Functor (Nested (Nest fs f))
instance Functor f => Functor (Nested (Flat f))
instance Show (Nested fs (f a)) => Show (Nested (Nest fs f) a)
instance Show (f a) => Show (Nested (Flat f) a)