    {-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-}

    {- |
        This module supplies a method for writing 'Uniplate' and 'Biplate' instances.
        This moulde gives the highest performance, but requires many instance definitions. The
        instances can be generated using Derive: <http://community.haskell.org/~ndm/derive/>.

        To take an example:

        > data Expr = Var Int | Pos Expr String | Neg Expr | Add Expr Expr
        > data Stmt = Seq [Stmt] | Sel [Expr] | Let String Expr
        >
        > instance Uniplate Expr where
        >     uniplate (Var x  ) = plate Var |- x
        >     uniplate (Pos x y) = plate Pos |* x |- y
        >     uniplate (Neg x  ) = plate Neg |* x
        >     uniplate (Add x y) = plate Add |* x |* y
        >
        > instance Biplate Expr Expr where
        >     biplate = plateSelf
        >
        > instance Uniplate Stmt where
        >     uniplate (Seq x  ) = plate Seq ||* x
        >     uniplate (Sel x  ) = plate Sel ||+ x
        >     uniplate (Let x y) = plate Let |-  x |- y
        >
        > instance Biplate Stmt Stmt where
        >     biplate = plateSelf
        >
        > instance Biplate Stmt Expr where
        >     biplate (Seq x  ) = plate Seq ||+ x
        >     biplate (Sel x  ) = plate Sel ||* x
        >     biplate (Let x y) = plate Let |-  x |* y

        To define instances for abstract data types, such as @Map@ or @Set@ from the @containers@ package,
        use 'plateProject'.

        This module provides a few monomorphic instances of 'Uniplate' / 'Biplate'
        for common types available in the base library, but does not provide any polymorphic
        instances. Given only monomorphic instances it is trivial to ensure that all instances
        are disjoint, making it easier to add your own instances.

        When defining polymorphic instances, be carefully to mention all potential children.
        Consider @Biplate Int (Int, a)@ - this instance cannot be correct because it will fail
        to return both @Int@ values on @(Int,Int)@. There are some legitimate polymorphic instances,
        such as @Biplate a [a]@ and @Biplate a a@, but take care to avoid overlapping instances.
    -}
    module Data.Generics.Uniplate.Direct(
        module Data.Generics.Uniplate.Operations,
        -- * The Combinators
        plate, plateSelf,
        (|+), (|-), (|*), (||+), (||*),
        plateProject
        ) where

    import Control.Arrow
    import Data.Generics.Uniplate.Operations
    import Data.Generics.Str
    import Data.Ratio

    type Type from to = (Str to, Str to -> from)

    -- | The main combinator used to start the chain.
    --
    -- The following rule can be used for optimisation:
    --
    -- > plate Ctor |- x == plate (Ctor x)
    {-# INLINE[1] plate #-}
    plate :: from -> Type from to
    plate f = (Zero, \_ -> f)

    {-# RULES
    "plate/-"    forall f x. plate f |- x = plate (f x)
    "plate/+"    forall f x. plate f |+ x = platePlus f x
    "plate/*"    forall f x. plate f |* x = plateStar f x #-}

    {-# INLINE plateStar #-}
    plateStar :: (to -> from) -> to -> Type from to
    plateStar f x = (One x, \(One x) -> f x)

    {-# INLINE platePlus #-}
    platePlus :: Biplate item to => (item -> from) -> item -> Type from to
    platePlus f x = case biplate x of
                            (ys,y_) -> (ys, \ys -> f $ y_ ys)

    -- | The field to the right is the target.
    {-# INLINE[1] (|*) #-}
    (|*) :: Type (to -> from) to -> to -> Type from to
    (|*) (xs,x_) y = (Two xs (One y),\(Two xs (One y)) -> x_ xs y)

    -- | The field to the right may contain the target.
    {-# INLINE[1] (|+) #-}
    (|+) :: Biplate item to => Type (item -> from) to -> item -> Type from to
    (|+) (xs,x_) y = case biplate y of
                          (ys,y_) -> (Two xs ys, \(Two xs ys) -> x_ xs (y_ ys))

    -- | The field to the right /does not/ contain the target.
    {-# INLINE[1] (|-) #-}
    (|-) :: Type (item -> from) to -> item -> Type from to
    (|-) (xs,x_) y = (xs,\xs -> x_ xs y)

    -- | The field to the right is a list of the type of the target
    {-# INLINE (||*) #-}
    (||*) :: Type ([to] -> from) to -> [to] -> Type from to
    (||*) (xs,x_) y = (Two xs (listStr y), \(Two xs ys) -> x_ xs (strList ys))

    -- | The field to the right is a list of types which may contain the target
    (||+) :: Biplate item to => Type ([item] -> from) to -> [item] -> Type from to
    (||+) (xs,x_) [] = (xs, \xs -> x_ xs []) -- can eliminate a Two _ Zero in the base case
    (||+) (xs,x_) (y:ys) = case plate (:) |+ y ||+ ys of
                           (ys,y_) -> (Two xs ys, \(Two xs ys) -> x_ xs (y_ ys))

    -- | Used for 'Biplate' definitions where both types are the same.
    plateSelf :: to -> Type to to
    plateSelf x = (One x, \(One x) -> x)

    -- | Write an instance in terms of a projection/injection pair. Usually used to define instances
    --   for abstract containers such as Map:
    --
    -- > instance Biplate (Map.Map [Char] Int) Char where
    -- >     biplate = plateProject Map.toList Map.fromList
    --
    --   If the types ensure that no operations will not change the keys
    --   we can use the 'fromDistictAscList' function to reconstruct the Map:
    --
    -- > instance Biplate (Map.Map [Char] Int) Int where
    -- >     biplate = plateProject Map.toAscList Map.fromDistinctAscList
    plateProject :: Biplate item to => (from -> item) -> (item -> from) -> from -> Type from to
    plateProject into outof = second (outof . ) . biplate . into

    instance Uniplate Int where uniplate x = plate x
    instance Uniplate Bool where uniplate x = plate x
    instance Uniplate Char where uniplate x = plate x
    instance Uniplate Integer where uniplate x = plate x
    instance Uniplate Double where uniplate x = plate x
    instance Uniplate Float where uniplate x = plate x
    instance Uniplate () where uniplate x = plate x

    instance Uniplate [Char] where
        uniplate (x:xs) = plate (x:) |* xs
        uniplate x = plate x

    instance Biplate [Char] Char where
        biplate (x:xs) = plate (:) |* x ||* xs
        biplate x = plate x

    instance Biplate [Char] [Char] where
        biplate = plateSelf

    instance Uniplate (Ratio Integer) where
        uniplate = plate

    instance Biplate (Ratio Integer) (Ratio Integer) where
        biplate = plateSelf

    instance Biplate (Ratio Integer) Integer where
        biplate x = (Two (One (numerator x)) (One (denominator x)), \(Two (One n) (One d)) -> n % d)