folds-0.6: src/Data/Fold/M.hs

{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE ExistentialQuantification #-}
-- |
-- Unlike 'Data.Fold.L' and 'Data.Fold.R' this 'Comonad'
-- is based on a @(->) r@ 'Comonad' for a 'Monoid' @r@ rather than
-- than on the @'Store' r@ 'Comonad'.
module Data.Fold.M
  ( M(..)
  ) where

import Control.Applicative
import Control.Comonad
import Control.Lens
import Control.Monad.Zip
import Data.Fold.Class
import Data.Fold.Internal
import Data.Foldable hiding (sum, product)
import Data.Functor.Extend
import Data.Functor.Bind
import Data.Profunctor.Unsafe
import Data.Proxy
import Data.Reflection
import Unsafe.Coerce
import Prelude hiding (sum, product, length)

-- | A 'foldMap' caught in amber. a.k.a. a monoidal reducer
data M a b = forall m. M (m -> b) (a -> m) (m -> m -> m) m

instance Scan M where
  run1 a (M k h _ _) = k (h a)
  prefix1 a (M k h m z) = case h a of
     x -> M (\y -> k (m x y)) h m z
  postfix1 (M k h m z) a = case h a of
     y -> M (\x -> k (m x y)) h m z
  interspersing a (M k h m z) = M (maybe' (k z) k) h' m' Nothing' where
    h' r  = Just' (h r)
    m' (Just' x) (Just' y) = Just' (x `m` h a `m` y)
    m' Nothing' my = my
    m' mx Nothing' = mx
  {-# INLINE run1 #-}
  {-# INLINE prefix1 #-}
  {-# INLINE postfix1 #-}
  {-# INLINE interspersing #-}

-- | efficient 'prefix', efficient 'postfix'
instance Folding M where
  run s (M k h m (z :: m)) = reify (m, z) $
    \ (_ :: Proxy s) -> k $ runN (foldMap (N #. h) s :: N m s)
  runOf l s (M k h m (z :: m)) = reify (m, z) $
    \ (_ :: Proxy s) -> k $ runN (foldMapOf l (N #. h) s :: N m s)
  prefix s (M k h m (z :: m)) = reify (m, z) $
    \ (_ :: Proxy s) -> case runN (foldMap (N #. h) s :: N m s) of
      x -> M (\y -> k (m x y)) h m z
  prefixOf l s (M k h m (z :: m)) = reify (m, z) $
    \ (_ :: Proxy s) -> case runN (foldMapOf l (N #. h) s :: N m s) of
      x -> M (\y -> k (m x y)) h m z
  postfix (M k h m (z :: m)) s = reify (m, z) $
    \ (_ :: Proxy s) -> case runN (foldMap (N #. h) s :: N m s) of
      y -> M (\x -> k (m x y)) h m z
  postfixOf l (M k h m (z :: m)) s = reify (m, z) $
    \ (_ :: Proxy s) -> case runN (foldMapOf l (N #. h) s :: N m s) of
      y -> M (\x -> k (m x y)) h m z
  filtering p (M k h m z) = M k (\a -> if p a then h a else z) m z
  {-# INLINE run #-}
  {-# INLINE runOf #-}
  {-# INLINE prefix #-}
  {-# INLINE prefixOf #-}
  {-# INLINE postfix #-}
  {-# INLINE postfixOf #-}
  {-# INLINE filtering #-}

instance Profunctor M where
  dimap f g (M k h m e) = M (g.k) (h.f) m e
  {-# INLINE dimap #-}
  rmap g (M k h m e) = M (g.k) h m e
  {-# INLINE rmap #-}
  lmap f (M k h m e) = M k (h.f) m e
  {-# INLINE lmap #-}
  (#.) _ = unsafeCoerce
  {-# INLINE (#.) #-}
  x .# _ = unsafeCoerce x
  {-# INLINE (.#) #-}

instance Choice M where
  left' (M k h m z) = M (_Left %~ k) (_Left %~ h) step (Left z) where
    step (Left x) (Left y) = Left (m x y)
    step (Right c) _ = Right c
    step _ (Right c) = Right c
  {-# INLINE left' #-}

  right' (M k h m z) = M (_Right %~ k) (_Right %~ h) step (Right z) where
    step (Right x) (Right y) = Right (m x y)
    step (Left c) _ = Left c
    step _ (Left c) = Left c
  {-# INLINE right' #-}

instance Functor (M a) where
  fmap f (M k h m z) = M (f.k) h m z
  {-# INLINE fmap #-}

  (<$) b = \_ -> pure b
  {-# INLINE (<$) #-}

instance Comonad (M a) where
  extract (M k _ _ z) = k z
  {-# INLINE extract #-}

  duplicate (M k h m z) = M (\n -> M (k . m n) h m z) h m z
  {-# INLINE duplicate #-}

instance Applicative (M a) where
  pure b = M (\() -> b) (\_ -> ()) (\() () -> ()) ()
  {-# INLINE pure #-}

  M xf bx xx xz <*> M ya by yy yz = M
    (\(Pair' x y) -> xf x $ ya y)
    (\b -> Pair' (bx b) (by b))
    (\(Pair' x1 y1) (Pair' x2 y2) -> Pair' (xx x1 x2) (yy y1 y2))
    (Pair' xz yz)
  {-# INLINE (<*>) #-}

  (<*) m = \_ -> m
  {-# INLINE (<*) #-}

  _ *> m = m
  {-# INLINE (*>) #-}

instance Bind (M a) where
  (>>-) = (>>=)
  {-# INLINE (>>-) #-}

instance Monad (M a) where
  return = pure
  {-# INLINE return #-}

  m >>= f = M (\xs a -> run xs (f a)) One Two Zero <*> m
  {-# INLINE (>>=) #-}

  _ >> n = n
  {-# INLINE (>>) #-}

instance MonadZip (M a) where
  mzipWith = liftA2
  {-# INLINE mzipWith #-}

instance Extend (M a) where
  extended = extend
  {-# INLINE extended #-}

  duplicated = duplicate
  {-# INLINE duplicated #-}

instance Apply (M a) where
  (<.>) = (<*>)
  {-# INLINE (<.>) #-}

  (<.) m = \_ -> m
  {-# INLINE (<.) #-}

  _ .> m = m
  {-# INLINE (.>) #-}

instance ComonadApply (M a) where
  (<@>) = (<*>)
  {-# INLINE (<@>) #-}

  (<@) m = \_ -> m
  {-# INLINE (<@) #-}

  _ @> m = m
  {-# INLINE (@>) #-}