{-
Copyright (c) Erik Hesselink & Sebastiaan Visser 2008

All rights reserved.

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modification, are permitted provided that the following conditions
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2. Redistributions in binary form must reproduce the above copyright
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   may be used to endorse or promote products derived from this software
   without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHORS OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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-}
{-# LANGUAGE
    TypeOperators
  , Arrows
  , TupleSections
  , FlexibleInstances
  , MultiParamTypeClasses
  #-}
module Data.Label.Abstract where

import Control.Arrow
import Prelude hiding ((.), id)
import Control.Applicative
import Control.Category

{-# INLINE _modify #-}
{-# INLINE lens    #-}
{-# INLINE get     #-}
{-# INLINE set     #-}
{-# INLINE modify  #-}
{-# INLINE bimap   #-}
{-# INLINE for     #-}
{-# INLINE liftBij #-}

-- | Abstract Point datatype. The getter and setter functions work in some
-- arrow.

data Point (~>) f i o = Point
  { _get :: f ~> o
  , _set :: (i, f) ~> f
  }

-- | Modification as a compositon of a getter and setter. Unfortunately,
-- `ArrowApply' is needed for this composition.

_modify :: ArrowApply (~>) => Point (~>) f i o -> (o ~> i, f) ~> f
_modify l = proc (m, f) -> do i <- m . _get l -<< f; _set l -< (i, f)

-- | Abstract Lens datatype. The getter and setter functions work in some
-- arrow. Arrows allow for effectful lenses, for example, lenses that might
-- fail or use state.

newtype Lens (~>) f a = Lens { unLens :: Point (~>) f a a }

-- | Create a lens out of a getter and setter.

lens :: (f ~> a) -> ((a, f) ~> f) -> Lens (~>) f a
lens g s = Lens (Point g s)

-- | Get the getter arrow from a lens.

get :: Arrow (~>) => Lens (~>) f a -> f ~> a
get = _get . unLens

-- | Get the setter arrow from a lens.

set :: Arrow (~>) => Lens (~>) f a -> (a, f) ~> f
set = _set . unLens

-- | Get the modifier arrow from a lens.

modify :: ArrowApply (~>) => Lens (~>) f o -> (o ~> o, f) ~> f
modify = _modify . unLens

instance ArrowApply (~>) => Category (Lens (~>)) where
  id = lens id (arr fst)
  Lens a . Lens b = lens (_get a . _get b) (_modify b . first (curryA (_set a)))
    where curryA f = arr (\i -> f . arr (i,))
  {-# INLINE id #-}
  {-# INLINE (.) #-}

instance Arrow (~>) => Functor (Point (~>) f i) where
  fmap f x = Point (arr f . _get x) (_set x)
  {-# INLINE fmap #-}

instance Arrow (~>) => Applicative (Point (~>) f i) where
  pure a  = Point (arr (const a)) (arr snd)
  a <*> b = Point (arr app . (_get a &&& _get b)) (_set b . (arr fst &&& _set a))
  {-# INLINE pure #-}
  {-# INLINE (<*>) #-}

-- | Make a 'Point' diverge in two directions.

bimap :: Arrow (~>) => (o' ~> o) -> (i ~> i') -> Point (~>) f i' o' -> Point (~>) f i o
bimap f g l = Point (f . _get l) (_set l . first g)

infix 8 `for`

for :: Arrow (~>) => (i ~> o) -> Lens (~>) f o -> Point (~>) f i o
for p = bimap id p . unLens

-- | The bijections datatype, an arrow that works in two directions. 

data Bijection (~>) a b = Bij { fw :: a ~> b, bw :: b ~> a }

-- | Bijections as categories.

instance Category (~>) => Category (Bijection (~>)) where
  id = Bij id id
  Bij a b . Bij c d = Bij (a . c) (d . b)
  {-# INLINE id #-}
  {-# INLINE (.) #-}

-- | Lifting 'Bijection's.

liftBij :: Functor f => Bijection (->) a b -> Bijection (->) (f a) (f b)
liftBij a = Bij (fmap (fw a)) (fmap (bw a))

-- | Apply Bijection to Lens

-- mapBij :: Bijection (->) b c -> Lens (->) a b -> Lens (->) a c
-- mapBij b l = lens g s where
--    g x = fw b (get l x)
--    s (a,x) = set l ((bw b a),x)

-- | The isomorphism type class is like a `Functor' but works in two directions.

infixr 8 `iso`

class Iso (~>) f where
  iso :: Bijection (~>) a b -> f a ~> f b

-- | We can diverge 'Lens'es using an isomorphism.

instance Arrow (~>) => Iso (~>) (Lens (~>) f) where
  iso bi = arr ((\a -> lens (fw bi . _get a) (_set a . first (bw bi))) . unLens)
  {-# INLINE iso #-}

-- | We can diverge 'Bijection's using an isomorphism.

instance Arrow (~>) => Iso (~>) (Bijection (~>) a) where
  iso = arr . (.)
  {-# INLINE iso #-}