content: {-# LANGUAGE CPP #-}
  -----------------------------------------------------------------------------
  -- |
  -- Module      :  Data.Foldable
  -- Copyright   :  Ross Paterson 2005
  -- License     :  BSD-style (see the LICENSE file in the distribution)
  --
  -- Maintainer  :  ross@soi.city.ac.uk
  -- Stability   :  experimental
  -- Portability :  portable
  --
  -- Class of data structures that can be folded to a summary value.
  --
  -- Many of these functions generalize "Prelude", "Control.Monad" and
  -- "Data.List" functions of the same names from lists to any 'Foldable'
  -- functor.  To avoid ambiguity, either import those modules hiding
  -- these names or qualify uses of these function names with an alias
  -- for this module.
  
  module Data.Foldable (
          -- * Folds
          Foldable(..),
          -- ** Special biased folds
          foldr',
          foldl',
          foldrM,
          foldlM,
          -- ** Folding actions
          -- *** Applicative actions
          traverse_,
          for_,
          sequenceA_,
          asum,
          -- *** Monadic actions
          mapM_,
          forM_,
          sequence_,
          msum,
          -- ** Specialized folds
          toList,
          concat,
          concatMap,
          and,
          or,
          any,
          all,
          sum,
          product,
          maximum,
          maximumBy,
          minimum,
          minimumBy,
          -- ** Searches
          elem,
          notElem,
          find
          ) where
  
  import Prelude hiding (foldl, foldr, foldl1, foldr1, mapM_, sequence_,
                  elem, notElem, concat, concatMap, and, or, any, all,
                  sum, product, maximum, minimum)
  import qualified Prelude (foldl, foldr, foldl1, foldr1)
  import Control.Applicative
  import Control.Monad (MonadPlus(..))
  import Data.Maybe (fromMaybe, listToMaybe)
  import Data.Monoid
  
  #ifdef __NHC__
  import Control.Arrow (ArrowZero(..)) -- work around nhc98 typechecker problem
  #endif
  
  #ifdef __GLASGOW_HASKELL__
  import GHC.Exts (build)
  #endif
  
  -- | Data structures that can be folded.
  --
  -- Minimal complete definition: 'foldMap' or 'foldr'.
  --
  -- For example, given a data type
  --
  -- > data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
  --
  -- a suitable instance would be
  --
  -- > instance Foldable Tree
  -- >    foldMap f Empty = mempty
  -- >    foldMap f (Leaf x) = f x
  -- >    foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
  --
  -- This is suitable even for abstract types, as the monoid is assumed
  -- to satisfy the monoid laws.
  --
  class Foldable t where
          -- | Combine the elements of a structure using a monoid.
          fold :: Monoid m => t m -> m
          fold = foldMap id
  
          -- | Map each element of the structure to a monoid,
          -- and combine the results.
          foldMap :: Monoid m => (a -> m) -> t a -> m
          foldMap f = foldr (mappend . f) mempty
  
          -- | Right-associative fold of a structure.
          --
          -- @'foldr' f z = 'Prelude.foldr' f z . 'toList'@
          foldr :: (a -> b -> b) -> b -> t a -> b
          foldr f z t = appEndo (foldMap (Endo . f) t) z
  
          -- | Left-associative fold of a structure.
          --
          -- @'foldl' f z = 'Prelude.foldl' f z . 'toList'@
          foldl :: (a -> b -> a) -> a -> t b -> a
          foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
  
          -- | A variant of 'foldr' that has no base case,
          -- and thus may only be applied to non-empty structures.
          --
          -- @'foldr1' f = 'Prelude.foldr1' f . 'toList'@
          foldr1 :: (a -> a -> a) -> t a -> a
          foldr1 f xs = fromMaybe (error "foldr1: empty structure")
                          (foldr mf Nothing xs)
            where mf x Nothing = Just x
                  mf x (Just y) = Just (f x y)
  
          -- | A variant of 'foldl' that has no base case,
          -- and thus may only be applied to non-empty structures.
          --
          -- @'foldl1' f = 'Prelude.foldl1' f . 'toList'@
          foldl1 :: (a -> a -> a) -> t a -> a
          foldl1 f xs = fromMaybe (error "foldl1: empty structure")
                          (foldl mf Nothing xs)
            where mf Nothing y = Just y
                  mf (Just x) y = Just (f x y)
  
  -- instances for Prelude types
  
  instance Foldable Maybe where
          foldr f z Nothing = z
          foldr f z (Just x) = f x z
  
          foldl f z Nothing = z
          foldl f z (Just x) = f z x
  
  instance Foldable [] where
          foldr = Prelude.foldr
          foldl = Prelude.foldl
          foldr1 = Prelude.foldr1
          foldl1 = Prelude.foldl1
  
  -- | Fold over the elements of a structure,
  -- associating to the right, but strictly.
  foldr' :: Foldable t => (a -> b -> b) -> b -> t a -> b
  foldr' f z xs = foldl f' id xs z
    where f' k x z = k $! f x z
  
  -- | Monadic fold over the elements of a structure,
  -- associating to the right, i.e. from right to left.
  foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b
  foldrM f z xs = foldl f' return xs z
    where f' k x z = f x z >>= k
  
  -- | Fold over the elements of a structure,
  -- associating to the left, but strictly.
  foldl' :: Foldable t => (a -> b -> a) -> a -> t b -> a
  foldl' f z xs = foldr f' id xs z
    where f' x k z = k $! f z x
  
  -- | Monadic fold over the elements of a structure,
  -- associating to the left, i.e. from left to right.
  foldlM :: (Foldable t, Monad m) => (a -> b -> m a) -> a -> t b -> m a
  foldlM f z xs = foldr f' return xs z
    where f' x k z = f z x >>= k
  
  -- | Map each element of a structure to an action, evaluate
  -- these actions from left to right, and ignore the results.
  traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()
  traverse_ f = foldr ((*>) . f) (pure ())
  
  -- | 'for_' is 'traverse_' with its arguments flipped.
  for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()
  {-# INLINE for_ #-}
  for_ = flip traverse_
  
  -- | Map each element of a structure to a monadic action, evaluate
  -- these actions from left to right, and ignore the results.
  mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
  mapM_ f = foldr ((>>) . f) (return ())
  
  -- | 'forM_' is 'mapM_' with its arguments flipped.
  forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m ()
  {-# INLINE forM_ #-}
  forM_ = flip mapM_
  
  -- | Evaluate each action in the structure from left to right,
  -- and ignore the results.
  sequenceA_ :: (Foldable t, Applicative f) => t (f a) -> f ()
  sequenceA_ = foldr (*>) (pure ())
  
  -- | Evaluate each monadic action in the structure from left to right,
  -- and ignore the results.
  sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
  sequence_ = foldr (>>) (return ())
  
  -- | The sum of a collection of actions, generalizing 'concat'.
  asum :: (Foldable t, Alternative f) => t (f a) -> f a
  {-# INLINE asum #-}
  asum = foldr (<|>) empty
  
  -- | The sum of a collection of actions, generalizing 'concat'.
  msum :: (Foldable t, MonadPlus m) => t (m a) -> m a
  {-# INLINE msum #-}
  msum = foldr mplus mzero
  
  -- These use foldr rather than foldMap to avoid repeated concatenation.
  
  -- | List of elements of a structure.
  toList :: Foldable t => t a -> [a]
  #ifdef __GLASGOW_HASKELL__
  toList t = build (\ c n -> foldr c n t)
  #else
  toList = foldr (:) []
  #endif
  
  -- | The concatenation of all the elements of a container of lists.
  concat :: Foldable t => t [a] -> [a]
  concat = fold
  
  -- | Map a function over all the elements of a container and concatenate
  -- the resulting lists.
  concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
  concatMap = foldMap
  
  -- | 'and' returns the conjunction of a container of Bools.  For the
  -- result to be 'True', the container must be finite; 'False', however,
  -- results from a 'False' value finitely far from the left end.
  and :: Foldable t => t Bool -> Bool
  and = getAll . foldMap All
  
  -- | 'or' returns the disjunction of a container of Bools.  For the
  -- result to be 'False', the container must be finite; 'True', however,
  -- results from a 'True' value finitely far from the left end.
  or :: Foldable t => t Bool -> Bool
  or = getAny . foldMap Any
  
  -- | Determines whether any element of the structure satisfies the predicate.
  any :: Foldable t => (a -> Bool) -> t a -> Bool
  any p = getAny . foldMap (Any . p)
  
  -- | Determines whether all elements of the structure satisfy the predicate.
  all :: Foldable t => (a -> Bool) -> t a -> Bool
  all p = getAll . foldMap (All . p)
  
  -- | The 'sum' function computes the sum of the numbers of a structure.
  sum :: (Foldable t, Num a) => t a -> a
  sum = getSum . foldMap Sum
  
  -- | The 'product' function computes the product of the numbers of a structure.
  product :: (Foldable t, Num a) => t a -> a
  product = getProduct . foldMap Product
  
  -- | The largest element of a non-empty structure.
  maximum :: (Foldable t, Ord a) => t a -> a
  maximum = foldr1 max
  
  -- | The largest element of a non-empty structure with respect to the
  -- given comparison function.
  maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
  maximumBy cmp = foldr1 max'
    where max' x y = case cmp x y of
                          GT -> x
                          _  -> y
  
  -- | The least element of a non-empty structure.
  minimum :: (Foldable t, Ord a) => t a -> a
  minimum = foldr1 min
  
  -- | The least element of a non-empty structure with respect to the
  -- given comparison function.
  minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
  minimumBy cmp = foldr1 min'
    where min' x y = case cmp x y of
                          GT -> y
                          _  -> x
  
  -- | Does the element occur in the structure?
  elem :: (Foldable t, Eq a) => a -> t a -> Bool
  elem = any . (==)
  
  -- | 'notElem' is the negation of 'elem'.
  notElem :: (Foldable t, Eq a) => a -> t a -> Bool
  notElem x = not . elem x
  
  -- | The 'find' function takes a predicate and a structure and returns
  -- the leftmost element of the structure matching the predicate, or
  -- 'Nothing' if there is no such element.
  find :: Foldable t => (a -> Bool) -> t a -> Maybe a
  find p = listToMaybe . concatMap (\ x -> if p x then [x] else [])
  