{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE Trustworthy #-} -- can't use Safe due to IsList instance
{-# LANGUAGE TypeFamilies #-}

-----------------------------------------------------------------------------
-- |
-- Module      :  Data.List.NonEmpty
-- Copyright   :  (C) 2011-2015 Edward Kmett,
--                (C) 2010 Tony Morris, Oliver Taylor, Eelis van der Weegen
-- License     :  BSD-style (see the file LICENSE)
--
-- Maintainer  :  [email protected]
-- Stability   :  provisional
-- Portability :  portable
--
-- A 'NonEmpty' list is one which always has at least one element, but
-- is otherwise identical to the traditional list type in complexity
-- and in terms of API. You will almost certainly want to import this
-- module @[email protected]
--
-- @since 4.9.0.0
----------------------------------------------------------------------------

module Data.List.NonEmpty (
   -- * The type of non-empty streams
     NonEmpty(..)

   -- * Non-empty stream transformations
   , map         -- :: (a -> b) -> NonEmpty a -> NonEmpty b
   , intersperse -- :: a -> NonEmpty a -> NonEmpty a
   , scanl       -- :: Foldable f => (b -> a -> b) -> b -> f a -> NonEmpty b
   , scanr       -- :: Foldable f => (a -> b -> b) -> b -> f a -> NonEmpty b
   , scanl1      -- :: (a -> a -> a) -> NonEmpty a -> NonEmpty a
   , scanr1      -- :: (a -> a -> a) -> NonEmpty a -> NonEmpty a
   , transpose   -- :: NonEmpty (NonEmpty a) -> NonEmpty (NonEmpty a)
   , sortBy      -- :: (a -> a -> Ordering) -> NonEmpty a -> NonEmpty a
   , sortWith      -- :: Ord o => (a -> o) -> NonEmpty a -> NonEmpty a
   -- * Basic functions
   , length      -- :: NonEmpty a -> Int
   , head        -- :: NonEmpty a -> a
   , tail        -- :: NonEmpty a -> [a]
   , last        -- :: NonEmpty a -> a
   , init        -- :: NonEmpty a -> [a]
   , (<|), cons  -- :: a -> NonEmpty a -> NonEmpty a
   , uncons      -- :: NonEmpty a -> (a, Maybe (NonEmpty a))
   , unfoldr     -- :: (a -> (b, Maybe a)) -> a -> NonEmpty b
   , sort        -- :: NonEmpty a -> NonEmpty a
   , reverse     -- :: NonEmpty a -> NonEmpty a
   , inits       -- :: Foldable f => f a -> NonEmpty a
   , tails       -- :: Foldable f => f a -> NonEmpty a
   -- * Building streams
   , iterate     -- :: (a -> a) -> a -> NonEmpty a
   , repeat      -- :: a -> NonEmpty a
   , cycle       -- :: NonEmpty a -> NonEmpty a
   , unfold      -- :: (a -> (b, Maybe a) -> a -> NonEmpty b
   , insert      -- :: (Foldable f, Ord a) => a -> f a -> NonEmpty a
   , some1       -- :: Alternative f => f a -> f (NonEmpty a)
   -- * Extracting sublists
   , take        -- :: Int -> NonEmpty a -> [a]
   , drop        -- :: Int -> NonEmpty a -> [a]
   , splitAt     -- :: Int -> NonEmpty a -> ([a], [a])
   , takeWhile   -- :: Int -> NonEmpty a -> [a]
   , dropWhile   -- :: Int -> NonEmpty a -> [a]
   , span        -- :: Int -> NonEmpty a -> ([a],[a])
   , break       -- :: Int -> NonEmpty a -> ([a],[a])
   , filter      -- :: (a -> Bool) -> NonEmpty a -> [a]
   , partition   -- :: (a -> Bool) -> NonEmpty a -> ([a],[a])
   , group       -- :: Foldable f => Eq a => f a -> [NonEmpty a]
   , groupBy     -- :: Foldable f => (a -> a -> Bool) -> f a -> [NonEmpty a]
   , groupWith     -- :: (Foldable f, Eq b) => (a -> b) -> f a -> [NonEmpty a]
   , groupAllWith  -- :: (Foldable f, Ord b) => (a -> b) -> f a -> [NonEmpty a]
   , group1      -- :: Eq a => NonEmpty a -> NonEmpty (NonEmpty a)
   , groupBy1    -- :: (a -> a -> Bool) -> NonEmpty a -> NonEmpty (NonEmpty a)
   , groupWith1     -- :: (Foldable f, Eq b) => (a -> b) -> f a -> NonEmpty (NonEmpty a)
   , groupAllWith1  -- :: (Foldable f, Ord b) => (a -> b) -> f a -> NonEmpty (NonEmpty a)
   -- * Sublist predicates
   , isPrefixOf  -- :: Foldable f => f a -> NonEmpty a -> Bool
   -- * \"Set\" operations
   , nub         -- :: Eq a => NonEmpty a -> NonEmpty a
   , nubBy       -- :: (a -> a -> Bool) -> NonEmpty a -> NonEmpty a
   -- * Indexing streams
   , (!!)        -- :: NonEmpty a -> Int -> a
   -- * Zipping and unzipping streams
   , zip         -- :: NonEmpty a -> NonEmpty b -> NonEmpty (a,b)
   , zipWith     -- :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c
   , unzip       -- :: NonEmpty (a, b) -> (NonEmpty a, NonEmpty b)
   -- * Converting to and from a list
   , fromList    -- :: [a] -> NonEmpty a
   , toList      -- :: NonEmpty a -> [a]
   , nonEmpty    -- :: [a] -> Maybe (NonEmpty a)
   , xor         -- :: NonEmpty a -> Bool
   ) where


import           Prelude             hiding (break, cycle, drop, dropWhile,
                                      filter, foldl, foldr, head, init, iterate,
                                      last, length, map, repeat, reverse,
                                      scanl, scanl1, scanr, scanr1, span,
                                      splitAt, tail, take, takeWhile,
                                      unzip, zip, zipWith, (!!))
import qualified Prelude

import           Control.Applicative (Applicative (..), Alternative (many))
import           Data.Foldable       hiding (length, toList)
import qualified Data.Foldable       as Foldable
import           Data.Function       (on)
import qualified Data.List           as List
import           Data.Ord            (comparing)
import           GHC.Base            (NonEmpty(..))

infixr 5 <|

-- | Number of elements in 'NonEmpty' list.
length :: NonEmpty a -> Int
length (_ :| xs) = 1 + Prelude.length xs

-- | Compute n-ary logic exclusive OR operation on 'NonEmpty' list.
xor :: NonEmpty Bool -> Bool
xor (x :| xs)   = foldr xor' x xs
  where xor' True y  = not y
        xor' False y = y

-- | 'unfold' produces a new stream by repeatedly applying the unfolding
-- function to the seed value to produce an element of type @[email protected] and a new
-- seed value.  When the unfolding function returns 'Nothing' instead of
-- a new seed value, the stream ends.
unfold :: (a -> (b, Maybe a)) -> a -> NonEmpty b
unfold f a = case f a of
  (b, Nothing) -> b :| []
  (b, Just c)  -> b <| unfold f c
{-# DEPRECATED unfold "Use unfoldr" #-}
-- Deprecated in 8.2.1, remove in 8.4

-- | 'nonEmpty' efficiently turns a normal list into a 'NonEmpty' stream,
-- producing 'Nothing' if the input is empty.
nonEmpty :: [a] -> Maybe (NonEmpty a)
nonEmpty []     = Nothing
nonEmpty (a:as) = Just (a :| as)

-- | 'uncons' produces the first element of the stream, and a stream of the
-- remaining elements, if any.
uncons :: NonEmpty a -> (a, Maybe (NonEmpty a))
uncons ~(a :| as) = (a, nonEmpty as)

-- | The 'unfoldr' function is analogous to "Data.List"'s
-- 'Data.List.unfoldr' operation.
unfoldr :: (a -> (b, Maybe a)) -> a -> NonEmpty b
unfoldr f a = case f a of
  (b, mc) -> b :| maybe [] go mc
 where
    go c = case f c of
      (d, me) -> d : maybe [] go me

-- | Extract the first element of the stream.
head :: NonEmpty a -> a
head ~(a :| _) = a

-- | Extract the possibly-empty tail of the stream.
tail :: NonEmpty a -> [a]
tail ~(_ :| as) = as

-- | Extract the last element of the stream.
last :: NonEmpty a -> a
last ~(a :| as) = List.last (a : as)

-- | Extract everything except the last element of the stream.
init :: NonEmpty a -> [a]
init ~(a :| as) = List.init (a : as)

-- | Prepend an element to the stream.
(<|) :: a -> NonEmpty a -> NonEmpty a
a <| ~(b :| bs) = a :| b : bs

-- | Synonym for '<|'.
cons :: a -> NonEmpty a -> NonEmpty a
cons = (<|)

-- | Sort a stream.
sort :: Ord a => NonEmpty a -> NonEmpty a
sort = lift List.sort

-- | Converts a normal list to a 'NonEmpty' stream.
--
-- Raises an error if given an empty list.
fromList :: [a] -> NonEmpty a
fromList (a:as) = a :| as
fromList [] = errorWithoutStackTrace "NonEmpty.fromList: empty list"

-- | Convert a stream to a normal list efficiently.
toList :: NonEmpty a -> [a]
toList ~(a :| as) = a : as

-- | Lift list operations to work on a 'NonEmpty' stream.
--
-- /Beware/: If the provided function returns an empty list,
-- this will raise an error.
lift :: Foldable f => ([a] -> [b]) -> f a -> NonEmpty b
lift f = fromList . f . Foldable.toList

-- | Map a function over a 'NonEmpty' stream.
map :: (a -> b) -> NonEmpty a -> NonEmpty b
map f ~(a :| as) = f a :| fmap f as

-- | The 'inits' function takes a stream @[email protected] and returns all the
-- finite prefixes of @[email protected]
inits :: Foldable f => f a -> NonEmpty [a]
inits = fromList . List.inits . Foldable.toList

-- | The 'tails' function takes a stream @[email protected] and returns all the
-- suffixes of @[email protected]
tails   :: Foldable f => f a -> NonEmpty [a]
tails = fromList . List.tails . Foldable.toList

-- | @'insert' x [email protected] inserts @[email protected] into the last position in @[email protected] where it
-- is still less than or equal to the next element. In particular, if the
-- list is sorted beforehand, the result will also be sorted.
insert  :: (Foldable f, Ord a) => a -> f a -> NonEmpty a
insert a = fromList . List.insert a . Foldable.toList

-- | @'some1' [email protected] sequences @[email protected] one or more times.
some1 :: Alternative f => f a -> f (NonEmpty a)
some1 x = liftA2 (:|) x (many x)

-- | 'scanl' is similar to 'foldl', but returns a stream of successive
-- reduced values from the left:
--
-- > scanl f z [x1, x2, ...] == z :| [z `f` x1, (z `f` x1) `f` x2, ...]
--
-- Note that
--
-- > last (scanl f z xs) == foldl f z xs.
scanl   :: Foldable f => (b -> a -> b) -> b -> f a -> NonEmpty b
scanl f z = fromList . List.scanl f z . Foldable.toList

-- | 'scanr' is the right-to-left dual of 'scanl'.
-- Note that
--
-- > head (scanr f z xs) == foldr f z xs.
scanr   :: Foldable f => (a -> b -> b) -> b -> f a -> NonEmpty b
scanr f z = fromList . List.scanr f z . Foldable.toList

-- | 'scanl1' is a variant of 'scanl' that has no starting value argument:
--
-- > scanl1 f [x1, x2, ...] == x1 :| [x1 `f` x2, x1 `f` (x2 `f` x3), ...]
scanl1 :: (a -> a -> a) -> NonEmpty a -> NonEmpty a
scanl1 f ~(a :| as) = fromList (List.scanl f a as)

-- | 'scanr1' is a variant of 'scanr' that has no starting value argument.
scanr1 :: (a -> a -> a) -> NonEmpty a -> NonEmpty a
scanr1 f ~(a :| as) = fromList (List.scanr1 f (a:as))

-- | 'intersperse x xs' alternates elements of the list with copies of @[email protected]
--
-- > intersperse 0 (1 :| [2,3]) == 1 :| [0,2,0,3]
intersperse :: a -> NonEmpty a -> NonEmpty a
intersperse a ~(b :| bs) = b :| case bs of
    [] -> []
    _ -> a : List.intersperse a bs

-- | @'iterate' f [email protected] produces the infinite sequence
-- of repeated applications of @[email protected] to @[email protected]
--
-- > iterate f x = x :| [f x, f (f x), ..]
iterate :: (a -> a) -> a -> NonEmpty a
iterate f a = a :| List.iterate f (f a)

-- | @'cycle' [email protected] returns the infinite repetition of @[email protected]:
--
-- > cycle (1 :| [2,3]) = 1 :| [2,3,1,2,3,...]
cycle :: NonEmpty a -> NonEmpty a
cycle = fromList . List.cycle . toList

-- | 'reverse' a finite NonEmpty stream.
reverse :: NonEmpty a -> NonEmpty a
reverse = lift List.reverse

-- | @'repeat' [email protected] returns a constant stream, where all elements are
-- equal to @[email protected]
repeat :: a -> NonEmpty a
repeat a = a :| List.repeat a

-- | @'take' n [email protected] returns the first @[email protected] elements of @[email protected]
take :: Int -> NonEmpty a -> [a]
take n = List.take n . toList

-- | @'drop' n [email protected] drops the first @[email protected] elements off the front of
-- the sequence @[email protected]
drop :: Int -> NonEmpty a -> [a]
drop n = List.drop n . toList

-- | @'splitAt' n [email protected] returns a pair consisting of the prefix of @x[email protected]
-- of length @[email protected] and the remaining stream immediately following this prefix.
--
-- > 'splitAt' n xs == ('take' n xs, 'drop' n xs)
-- > xs == ys ++ zs where (ys, zs) = 'splitAt' n xs
splitAt :: Int -> NonEmpty a -> ([a],[a])
splitAt n = List.splitAt n . toList

-- | @'takeWhile' p [email protected] returns the longest prefix of the stream
-- @[email protected] for which the predicate @[email protected] holds.
takeWhile :: (a -> Bool) -> NonEmpty a -> [a]
takeWhile p = List.takeWhile p . toList

-- | @'dropWhile' p [email protected] returns the suffix remaining after
-- @'takeWhile' p [email protected]
dropWhile :: (a -> Bool) -> NonEmpty a -> [a]
dropWhile p = List.dropWhile p . toList

-- | @'span' p [email protected] returns the longest prefix of @[email protected] that satisfies
-- @[email protected], together with the remainder of the stream.
--
-- > 'span' p xs == ('takeWhile' p xs, 'dropWhile' p xs)
-- > xs == ys ++ zs where (ys, zs) = 'span' p xs
span :: (a -> Bool) -> NonEmpty a -> ([a], [a])
span p = List.span p . toList

-- | The @'break' [email protected] function is equivalent to @'span' (not . p)@.
break :: (a -> Bool) -> NonEmpty a -> ([a], [a])
break p = span (not . p)

-- | @'filter' p [email protected] removes any elements from @[email protected] that do not satisfy @[email protected]
filter :: (a -> Bool) -> NonEmpty a -> [a]
filter p = List.filter p . toList

-- | The 'partition' function takes a predicate @[email protected] and a stream
-- @[email protected], and returns a pair of lists. The first list corresponds to the
-- elements of @[email protected] for which @[email protected] holds; the second corresponds to the
-- elements of @[email protected] for which @[email protected] does not hold.
--
-- > 'partition' p xs = ('filter' p xs, 'filter' (not . p) xs)
partition :: (a -> Bool) -> NonEmpty a -> ([a], [a])
partition p = List.partition p . toList

-- | The 'group' function takes a stream and returns a list of
-- streams such that flattening the resulting list is equal to the
-- argument.  Moreover, each stream in the resulting list
-- contains only equal elements.  For example, in list notation:
--
-- > 'group' $ 'cycle' "Mississippi"
-- >   = "M" : "i" : "ss" : "i" : "ss" : "i" : "pp" : "i" : "M" : "i" : ...
group :: (Foldable f, Eq a) => f a -> [NonEmpty a]
group = groupBy (==)

-- | 'groupBy' operates like 'group', but uses the provided equality
-- predicate instead of `==`.
groupBy :: Foldable f => (a -> a -> Bool) -> f a -> [NonEmpty a]
groupBy eq0 = go eq0 . Foldable.toList
  where
    go _  [] = []
    go eq (x : xs) = (x :| ys) : groupBy eq zs
      where (ys, zs) = List.span (eq x) xs

-- | 'groupWith' operates like 'group', but uses the provided projection when
-- comparing for equality
groupWith :: (Foldable f, Eq b) => (a -> b) -> f a -> [NonEmpty a]
groupWith f = groupBy ((==) `on` f)

-- | 'groupAllWith' operates like 'groupWith', but sorts the list
-- first so that each equivalence class has, at most, one list in the
-- output
groupAllWith :: (Ord b) => (a -> b) -> [a] -> [NonEmpty a]
groupAllWith f = groupWith f . List.sortBy (compare `on` f)

-- | 'group1' operates like 'group', but uses the knowledge that its
-- input is non-empty to produce guaranteed non-empty output.
group1 :: Eq a => NonEmpty a -> NonEmpty (NonEmpty a)
group1 = groupBy1 (==)

-- | 'groupBy1' is to 'group1' as 'groupBy' is to 'group'.
groupBy1 :: (a -> a -> Bool) -> NonEmpty a -> NonEmpty (NonEmpty a)
groupBy1 eq (x :| xs) = (x :| ys) :| groupBy eq zs
  where (ys, zs) = List.span (eq x) xs

-- | 'groupWith1' is to 'group1' as 'groupWith' is to 'group'
groupWith1 :: (Eq b) => (a -> b) -> NonEmpty a -> NonEmpty (NonEmpty a)
groupWith1 f = groupBy1 ((==) `on` f)

-- | 'groupAllWith1' is to 'groupWith1' as 'groupAllWith' is to 'groupWith'
groupAllWith1 :: (Ord b) => (a -> b) -> NonEmpty a -> NonEmpty (NonEmpty a)
groupAllWith1 f = groupWith1 f . sortWith f

-- | The 'isPrefix' function returns @[email protected] if the first argument is
-- a prefix of the second.
isPrefixOf :: Eq a => [a] -> NonEmpty a -> Bool
isPrefixOf [] _ = True
isPrefixOf (y:ys) (x :| xs) = (y == x) && List.isPrefixOf ys xs

-- | @xs !! [email protected] returns the element of the stream @[email protected] at index
-- @[email protected] Note that the head of the stream has index 0.
--
-- /Beware/: a negative or out-of-bounds index will cause an error.
(!!) :: NonEmpty a -> Int -> a
(!!) ~(x :| xs) n
  | n == 0 = x
  | n > 0  = xs List.!! (n - 1)
  | otherwise = errorWithoutStackTrace "NonEmpty.!! negative argument"
infixl 9 !!

-- | The 'zip' function takes two streams and returns a stream of
-- corresponding pairs.
zip :: NonEmpty a -> NonEmpty b -> NonEmpty (a,b)
zip ~(x :| xs) ~(y :| ys) = (x, y) :| List.zip xs ys

-- | The 'zipWith' function generalizes 'zip'. Rather than tupling
-- the elements, the elements are combined using the function
-- passed as the first argument.
zipWith :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c
zipWith f ~(x :| xs) ~(y :| ys) = f x y :| List.zipWith f xs ys

-- | The 'unzip' function is the inverse of the 'zip' function.
unzip :: Functor f => f (a,b) -> (f a, f b)
unzip xs = (fst <$> xs, snd <$> xs)

-- | The 'nub' function removes duplicate elements from a list. In
-- particular, it keeps only the first occurrence of each element.
-- (The name 'nub' means \'essence\'.)
-- It is a special case of 'nubBy', which allows the programmer to
-- supply their own inequality test.
nub :: Eq a => NonEmpty a -> NonEmpty a
nub = nubBy (==)

-- | The 'nubBy' function behaves just like 'nub', except it uses a
-- user-supplied equality predicate instead of the overloaded '=='
-- function.
nubBy :: (a -> a -> Bool) -> NonEmpty a -> NonEmpty a
nubBy eq (a :| as) = a :| List.nubBy eq (List.filter (\b -> not (eq a b)) as)

-- | 'transpose' for 'NonEmpty', behaves the same as 'Data.List.transpose'
-- The rows/columns need not be the same length, in which case
-- > transpose . transpose /= id
transpose :: NonEmpty (NonEmpty a) -> NonEmpty (NonEmpty a)
transpose = fmap fromList
          . fromList . List.transpose . toList
          . fmap toList

-- | 'sortBy' for 'NonEmpty', behaves the same as 'Data.List.sortBy'
sortBy :: (a -> a -> Ordering) -> NonEmpty a -> NonEmpty a
sortBy f = lift (List.sortBy f)

-- | 'sortWith' for 'NonEmpty', behaves the same as:
--
-- > sortBy . comparing
sortWith :: Ord o => (a -> o) -> NonEmpty a -> NonEmpty a
sortWith = sortBy . comparing