    {-# LANGUAGE Trustworthy #-}
    {-# LANGUAGE CPP, NoImplicitPrelude, ScopedTypeVariables #-}
    {-# LANGUAGE BangPatterns #-}
    {-# OPTIONS_GHC -Wno-incomplete-uni-patterns #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  GHC.List
    -- Copyright   :  (c) The University of Glasgow 1994-2002
    -- License     :  see libraries/base/LICENSE
    --
    -- Maintainer  :  cvs-ghc@haskell.org
    -- Stability   :  internal
    -- Portability :  non-portable (GHC Extensions)
    --
    -- The List data type and its operations
    --
    -----------------------------------------------------------------------------

    module GHC.List (

       -- The list data type
       List,

       -- List-monomorphic Foldable methods and misc functions
       foldr, foldr', foldr1,
       foldl, foldl', foldl1,
       null, length, elem, notElem,
       maximum, minimum, sum, product, and, or, any, all,

       -- Other functions
       foldl1', concat, concatMap,
       map, (++), filter, lookup,
       head, last, tail, init, uncons, (!!),
       scanl, scanl1, scanl', scanr, scanr1,
       iterate, iterate', repeat, replicate, cycle,
       take, drop, splitAt, takeWhile, dropWhile, span, break, reverse,
       zip, zip3, zipWith, zipWith3, unzip, unzip3,
       errorEmptyList,

       -- * GHC List fusion
       augment, build,

     ) where

    import Data.Maybe
    import GHC.Base
    import GHC.Num (Num(..))
    import GHC.Num.Integer (Integer)
    import GHC.Stack.Types (HasCallStack)

    infixl 9  !!
    infix  4 `elem`, `notElem`

    -- $setup
    -- >>> import GHC.Base
    -- >>> import Prelude (Num (..), Ord (..), Int, Double, odd, not, undefined)
    -- >>> import Control.DeepSeq (force)
    --
    -- -- compiled versions are uninterruptible.
    -- https://gitlab.haskell.org/ghc/ghc/-/issues/367
    --
    -- >>> let or  = foldr (||) False
    -- >>> let and = foldr (&&) True

    --------------------------------------------------------------
    -- List-manipulation functions
    --------------------------------------------------------------

    -- | \(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty.
    --
    -- >>> head [1, 2, 3]
    -- 1
    -- >>> head [1..]
    -- 1
    -- >>> head []
    -- *** Exception: Prelude.head: empty list
    --
    -- WARNING: This function is partial. You can use case-matching, 'uncons' or
    -- 'listToMaybe' instead.
    head                    :: HasCallStack => [a] -> a
    head :: forall a. HasCallStack => [a] -> a
    head (a
    x:[a]
    _)              =  a
    x
    head []                 =  a
    forall a. HasCallStack => a
    badHead
    {-# NOINLINE [1] head #-}

    badHead :: HasCallStack => a
    badHead :: forall a. HasCallStack => a
    badHead = String -> a
    forall a. HasCallStack => String -> a
    errorEmptyList String
    "head"

    -- This rule is useful in cases like
    --      head [y | (x,y) <- ps, x==t]
    {-# RULES
    "head/build"    forall (g::forall b.(a->b->b)->b->b) .
                    head (build g) = g (\x _ -> x) badHead
    "head/augment"  forall xs (g::forall b. (a->b->b) -> b -> b) .
                    head (augment g xs) = g (\x _ -> x) (head xs)
     #-}

    -- | \(\mathcal{O}(1)\). Decompose a list into its head and tail.
    --
    -- * If the list is empty, returns 'Nothing'.
    -- * If the list is non-empty, returns @'Just' (x, xs)@,
    -- where @x@ is the head of the list and @xs@ its tail.
    --
    -- @since 4.8.0.0
    --
    -- >>> uncons []
    -- Nothing
    -- >>> uncons [1]
    -- Just (1,[])
    -- >>> uncons [1, 2, 3]
    -- Just (1,[2,3])
    uncons                  :: [a] -> Maybe (a, [a])
    uncons :: forall a. [a] -> Maybe (a, [a])
    uncons []               = Maybe (a, [a])
    forall a. Maybe a
    Nothing
    uncons (a
    x:[a]
    xs)           = (a, [a]) -> Maybe (a, [a])
    forall a. a -> Maybe a
    Just (a
    x, [a]
    xs)

    -- | \(\mathcal{O}(1)\). Extract the elements after the head of a list, which
    -- must be non-empty.
    --
    -- >>> tail [1, 2, 3]
    -- [2,3]
    -- >>> tail [1]
    -- []
    -- >>> tail []
    -- *** Exception: Prelude.tail: empty list
    --
    -- WARNING: This function is partial. You can use case-matching or 'uncons'
    -- instead.
    tail                    :: HasCallStack => [a] -> [a]
    tail :: forall a. HasCallStack => [a] -> [a]
    tail (a
    _:[a]
    xs)             =  [a]
    xs
    tail []                 =  String -> [a]
    forall a. HasCallStack => String -> a
    errorEmptyList String
    "tail"

    -- | \(\mathcal{O}(n)\). Extract the last element of a list, which must be
    -- finite and non-empty.
    --
    -- >>> last [1, 2, 3]
    -- 3
    -- >>> last [1..]
    -- * Hangs forever *
    -- >>> last []
    -- *** Exception: Prelude.last: empty list
    --
    -- WARNING: This function is partial. You can use 'reverse' with case-matching,
    -- 'uncons' or 'listToMaybe' instead.
    last                    :: HasCallStack => [a] -> a
    #if defined(USE_REPORT_PRELUDE)
    last [x]                =  x
    last (_:xs)             =  last xs
    last []                 =  errorEmptyList "last"
    #else
    -- Use foldl to make last a good consumer.
    -- This will compile to good code for the actual GHC.List.last.
    -- (At least as long it is eta-expanded, otherwise it does not, #10260.)
    last :: forall a. HasCallStack => [a] -> a
    last [a]
    xs = (a -> a -> a) -> a -> [a] -> a
    forall a b. (b -> a -> b) -> b -> [a] -> b
    foldl (\a
    _ a
    x -> a
    x) a
    forall a. HasCallStack => a
    lastError [a]
    xs
    {-# INLINE last #-}
    -- The inline pragma is required to make GHC remember the implementation via
    -- foldl.
    lastError :: HasCallStack => a
    lastError :: forall a. HasCallStack => a
    lastError = String -> a
    forall a. HasCallStack => String -> a
    errorEmptyList String
    "last"
    #endif

    -- | \(\mathcal{O}(n)\). Return all the elements of a list except the last one.
    -- The list must be non-empty.
    --
    -- >>> init [1, 2, 3]
    -- [1,2]
    -- >>> init [1]
    -- []
    -- >>> init []
    -- *** Exception: Prelude.init: empty list
    --
    -- WARNING: This function is partial. You can use 'reverse' with case-matching
    -- or 'uncons' instead.
    init                    :: HasCallStack => [a] -> [a]
    #if defined(USE_REPORT_PRELUDE)
    init [x]                =  []
    init (x:xs)             =  x : init xs
    init []                 =  errorEmptyList "init"
    #else
    -- eliminate repeated cases
    init :: forall a. HasCallStack => [a] -> [a]
    init []                 =  String -> [a]
    forall a. HasCallStack => String -> a
    errorEmptyList String
    "init"
    init (a
    x:[a]
    xs)             =  a -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    init' a
    x [a]
    xs
      where init' :: t -> [t] -> [t]
    init' t
    _ []     = []
            init' t
    y (t
    z:[t]
    zs) = t
    y t -> [t] -> [t]
    forall {t}. t -> [t] -> [t]
    : t -> [t] -> [t]
    init' t
    z [t]
    zs
    #endif

    -- | \(\mathcal{O}(1)\). Test whether a list is empty.
    --
    -- >>> null []
    -- True
    -- >>> null [1]
    -- False
    -- >>> null [1..]
    -- False
    null                    :: [a] -> Bool
    null :: forall a. [a] -> Bool
    null []                 =  Bool
    True
    null (a
    _:[a]
    _)              =  Bool
    False

    -- | \(\mathcal{O}(n)\). 'length' returns the length of a finite list as an
    -- 'Int'. It is an instance of the more general 'Data.List.genericLength', the
    -- result type of which may be any kind of number.
    --
    -- >>> length []
    -- 0
    -- >>> length ['a', 'b', 'c']
    -- 3
    -- >>> length [1..]
    -- * Hangs forever *
    {-# NOINLINE [1] length #-}
    length                  :: [a] -> Int
    length :: forall a. [a] -> Int
    length [a]
    xs               = [a] -> Int -> Int
    forall a. [a] -> Int -> Int
    lenAcc [a]
    xs Int
    0

    lenAcc          :: [a] -> Int -> Int
    lenAcc :: forall a. [a] -> Int -> Int
    lenAcc []     Int
    n = Int
    n
    lenAcc (a
    _:[a]
    ys) Int
    n = [a] -> Int -> Int
    forall a. [a] -> Int -> Int
    lenAcc [a]
    ys (Int
    nInt -> Int -> Int
    forall a. Num a => a -> a -> a
    +Int
    1)

    {-# RULES
    "length" [~1] forall xs . length xs = foldr lengthFB idLength xs 0
    "lengthList" [1] foldr lengthFB idLength = lenAcc
     #-}

    -- The lambda form turns out to be necessary to make this inline
    -- when we need it to and give good performance.
    {-# INLINE [0] lengthFB #-}
    lengthFB :: x -> (Int -> Int) -> Int -> Int
    lengthFB :: forall x. x -> (Int -> Int) -> Int -> Int
    lengthFB x
    _ Int -> Int
    r = \ !Int
    a -> Int -> Int
    r (Int
    a Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + Int
    1)

    {-# INLINE [0] idLength #-}
    idLength :: Int -> Int
    idLength :: Int -> Int
    idLength = Int -> Int
    forall a. a -> a
    id

    -- | \(\mathcal{O}(n)\). 'filter', applied to a predicate and a list, returns
    -- the list of those elements that satisfy the predicate; i.e.,
    --
    -- > filter p xs = [ x | x <- xs, p x]
    --
    -- >>> filter odd [1, 2, 3]
    -- [1,3]
    {-# NOINLINE [1] filter #-}
    filter :: (a -> Bool) -> [a] -> [a]
    filter :: forall a. (a -> Bool) -> [a] -> [a]
    filter a -> Bool
    _pred []    = []
    filter a -> Bool
    pred (a
    x:[a]
    xs)
      | a -> Bool
    pred a
    x         = a
    x a -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    : (a -> Bool) -> [a] -> [a]
    forall a. (a -> Bool) -> [a] -> [a]
    filter a -> Bool
    pred [a]
    xs
      | Bool
    otherwise      = (a -> Bool) -> [a] -> [a]
    forall a. (a -> Bool) -> [a] -> [a]
    filter a -> Bool
    pred [a]
    xs

    {-# INLINE [0] filterFB #-} -- See Note [Inline FB functions]
    filterFB :: (a -> b -> b) -> (a -> Bool) -> a -> b -> b
    filterFB :: forall a b. (a -> b -> b) -> (a -> Bool) -> a -> b -> b
    filterFB a -> b -> b
    c a -> Bool
    p a
    x b
    r | a -> Bool
    p a
    x       = a
    x a -> b -> b
    `c` b
    r
                     | Bool
    otherwise = b
    r

    {-# RULES
    "filter"     [~1] forall p xs.  filter p xs = build (\c n -> foldr (filterFB c p) n xs)
    "filterList" [1]  forall p.     foldr (filterFB (:) p) [] = filter p
    "filterFB"        forall c p q. filterFB (filterFB c p) q = filterFB c (\x -> q x && p x)
     #-}

    -- Note the filterFB rule, which has p and q the "wrong way round" in the RHS.
    --     filterFB (filterFB c p) q a b
    --   = if q a then filterFB c p a b else b
    --   = if q a then (if p a then c a b else b) else b
    --   = if q a && p a then c a b else b
    --   = filterFB c (\x -> q x && p x) a b
    -- I originally wrote (\x -> p x && q x), which is wrong, and actually
    -- gave rise to a live bug report.  SLPJ.

    -- | 'foldl', applied to a binary operator, a starting value (typically
    -- the left-identity of the operator), and a list, reduces the list
    -- using the binary operator, from left to right:
    --
    -- > foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
    --
    -- The list must be finite.
    --
    -- >>> foldl (+) 0 [1..4]
    -- 10
    -- >>> foldl (+) 42 []
    -- 42
    -- >>> foldl (-) 100 [1..4]
    -- 90
    -- >>> foldl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
    -- "dcbafoo"
    -- >>> foldl (+) 0 [1..]
    -- * Hangs forever *
    foldl :: forall a b. (b -> a -> b) -> b -> [a] -> b
    {-# INLINE foldl #-}
    foldl :: forall a b. (b -> a -> b) -> b -> [a] -> b
    foldl b -> a -> b
    k b
    z0 [a]
    xs =
      (a -> (b -> b) -> b -> b) -> (b -> b) -> [a] -> b -> b
    forall a b. (a -> b -> b) -> b -> [a] -> b
    foldr (\(a
    v::a) (b -> b
    fn::b->b) -> (b -> b) -> b -> b
    forall a b. (a -> b) -> a -> b
    oneShot (\(b
    z::b) -> b -> b
    fn (b -> a -> b
    k b
    z a
    v))) (b -> b
    forall a. a -> a
    id :: b -> b) [a]
    xs b
    z0
      -- See Note [Left folds via right fold]

    {-
    Note [Left folds via right fold]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Implementing foldl et. al. via foldr is only a good idea if the compiler can
    optimize the resulting code (eta-expand the recursive "go"). See #7994.
    We hope that one of the two measure kick in:

       * Call Arity (-fcall-arity, enabled by default) eta-expands it if it can see
         all calls and determine that the arity is large.
       * The oneShot annotation gives a hint to the regular arity analysis that
         it may assume that the lambda is called at most once.
         See [One-shot lambdas] in CoreArity and especially [Eta expanding thunks]
         in CoreArity.

    The oneShot annotations used in this module are correct, as we only use them in
    arguments to foldr, where we know how the arguments are called.

    Note [Inline FB functions]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    After fusion rules successfully fire, we are usually left with one or more calls
    to list-producing functions abstracted over cons and nil. Here we call them
    FB functions because their names usually end with 'FB'. It's a good idea to
    inline FB functions because:

    * They are higher-order functions and therefore benefit from inlining.

    * When the final consumer is a left fold, inlining the FB functions is the only
      way to make arity expansion happen. See Note [Left folds via right fold].

    For this reason we mark all FB functions INLINE [0]. The [0] phase-specifier
    ensures that calls to FB functions can be written back to the original form
    when no fusion happens.

    Without these inline pragmas, the loop in perf/should_run/T13001 won't be
    allocation-free. Also see #13001.
    -}

    -- ----------------------------------------------------------------------------

    -- | A strict version of 'foldl'.
    foldl' :: forall a b . (b -> a -> b) -> b -> [a] -> b
    {-# INLINE foldl' #-}
    foldl' :: forall a b. (b -> a -> b) -> b -> [a] -> b
    foldl' b -> a -> b
    k b
    z0 = \[a]
    xs ->
      (a -> (b -> b) -> b -> b) -> (b -> b) -> [a] -> b -> b
    forall a b. (a -> b -> b) -> b -> [a] -> b
    foldr (\(a
    v::a) (b -> b
    fn::b->b) -> (b -> b) -> b -> b
    forall a b. (a -> b) -> a -> b
    oneShot (\(b
    z::b) -> b
    z b -> b -> b
    forall a b. a -> b -> b
    `seq` b -> b
    fn (b -> a -> b
    k b
    z a
    v))) (b -> b
    forall a. a -> a
    id :: b -> b) [a]
    xs b
    z0
    {-
    Note [Definition of foldl']
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We want foldl' to be a good consumer, so:

    * We define it (rather cunningly) with `foldr`.  That way, the `fold/build`
      rule might fire.  See Note [Left folds via right fold]

    * We give it an INLINE pragma, so that it'll inline at its call sites, again
      giving the `fold/build` rule a chance to fire.

    * We eta-reduce it so that it has arity 2, not 3.  Reason: consider

         sumlen :: [Float] -> (Float, Int)
         sumlen = foldl' f (0, 0)
            where
              f (!s, !n) !x = (s + x, n + 1)

    The RHS of `sumlen` is a partial application of foldl', and is not
    eta-expanded (and it isn't, because we don't eta-expand PAPs.  See Note
    [Do not eta-expand PAPs] in GHC.Core.Opt.Simplify.Utils)

    So foldl' is partially applied to two arguments, /and it won't inline/
    if its defn is:

          {-# INLINE foldl' #-}
          foldl' k z xs = ...

    because INLINE functions only inline when saturated.

    Conclusion: move the `xs` parameter to the RHS, and define it thus

      fold' k z = \xs -> ...

    See !5259 for additional discussion.  This may result in partial applications
    of 'foldl'' inlining in some functions where they previously did not.  Absent
    an INLINE pragam for the calling function, it may become too expensive to
    automatically inline, resulting in a loss of previously accidental list
    fusion.  Such call sites may now need explicit INLINE or INLINABLE pragmas
    to make the desired list fusion robust.
    -}

    -- | 'foldl1' is a variant of 'foldl' that has no starting value argument,
    -- and thus must be applied to non-empty lists. Note that unlike 'foldl', the accumulated value must be of the same type as the list elements.
    --
    -- >>> foldl1 (+) [1..4]
    -- 10
    -- >>> foldl1 (+) []
    -- *** Exception: Prelude.foldl1: empty list
    -- >>> foldl1 (-) [1..4]
    -- -8
    -- >>> foldl1 (&&) [True, False, True, True]
    -- False
    -- >>> foldl1 (||) [False, False, True, True]
    -- True
    -- >>> foldl1 (+) [1..]
    -- * Hangs forever *
    foldl1                  :: HasCallStack => (a -> a -> a) -> [a] -> a
    foldl1 :: forall a. HasCallStack => (a -> a -> a) -> [a] -> a
    foldl1 a -> a -> a
    f (a
    x:[a]
    xs)         =  (a -> a -> a) -> a -> [a] -> a
    forall a b. (b -> a -> b) -> b -> [a] -> b
    foldl a -> a -> a
    f a
    x [a]
    xs
    foldl1 a -> a -> a
    _ []             =  String -> a
    forall a. HasCallStack => String -> a
    errorEmptyList String
    "foldl1"

    -- | A strict version of 'foldl1'.
    foldl1'                  :: HasCallStack => (a -> a -> a) -> [a] -> a
    foldl1' :: forall a. HasCallStack => (a -> a -> a) -> [a] -> a
    foldl1' a -> a -> a
    f (a
    x:[a]
    xs)         =  (a -> a -> a) -> a -> [a] -> a
    forall a b. (b -> a -> b) -> b -> [a] -> b
    foldl' a -> a -> a
    f a
    x [a]
    xs
    foldl1' a -> a -> a
    _ []             =  String -> a
    forall a. HasCallStack => String -> a
    errorEmptyList String
    "foldl1'"

    -- -----------------------------------------------------------------------------
    -- List sum and product

    -- | The 'sum' function computes the sum of a finite list of numbers.
    --
    -- >>> sum []
    -- 0
    -- >>> sum [42]
    -- 42
    -- >>> sum [1..10]
    -- 55
    -- >>> sum [4.1, 2.0, 1.7]
    -- 7.8
    -- >>> sum [1..]
    -- * Hangs forever *
    sum                     :: (Num a) => [a] -> a
    {-# INLINE sum #-}
    sum :: forall a. Num a => [a] -> a
    sum                     =  (a -> a -> a) -> a -> [a] -> a
    forall a b. (b -> a -> b) -> b -> [a] -> b
    foldl' a -> a -> a
    forall a. Num a => a -> a -> a
    (+) a
    0

    -- | The 'product' function computes the product of a finite list of numbers.
    --
    -- >>> product []
    -- 1
    -- >>> product [42]
    -- 42
    -- >>> product [1..10]
    -- 3628800
    -- >>> product [4.1, 2.0, 1.7]
    -- 13.939999999999998
    -- >>> product [1..]
    -- * Hangs forever *
    product                 :: (Num a) => [a] -> a
    {-# INLINE product #-}
    product :: forall a. Num a => [a] -> a
    product                 =  (a -> a -> a) -> a -> [a] -> a
    forall a b. (b -> a -> b) -> b -> [a] -> b
    foldl' a -> a -> a
    forall a. Num a => a -> a -> a
    (*) a
    1

    -- | \(\mathcal{O}(n)\). 'scanl' is similar to 'foldl', but returns a list 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 (+) 0 [1..4]
    -- [0,1,3,6,10]
    -- >>> scanl (+) 42 []
    -- [42]
    -- >>> scanl (-) 100 [1..4]
    -- [100,99,97,94,90]
    -- >>> scanl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
    -- ["foo","afoo","bafoo","cbafoo","dcbafoo"]
    -- >>> scanl (+) 0 [1..]
    -- * Hangs forever *

    -- This peculiar arrangement is necessary to prevent scanl being rewritten in
    -- its own right-hand side.
    {-# NOINLINE [1] scanl #-}
    scanl                   :: (b -> a -> b) -> b -> [a] -> [b]
    scanl :: forall b a. (b -> a -> b) -> b -> [a] -> [b]
    scanl                   = (b -> a -> b) -> b -> [a] -> [b]
    forall b a. (b -> a -> b) -> b -> [a] -> [b]
    scanlGo
      where
        scanlGo           :: (b -> a -> b) -> b -> [a] -> [b]
        scanlGo :: forall b a. (b -> a -> b) -> b -> [a] -> [b]
    scanlGo b -> a -> b
    f b
    q [a]
    ls    = b
    q b -> [b] -> [b]
    forall {t}. t -> [t] -> [t]
    : (case [a]
    ls of
                                   []   -> []
                                   a
    x:[a]
    xs -> (b -> a -> b) -> b -> [a] -> [b]
    forall b a. (b -> a -> b) -> b -> [a] -> [b]
    scanlGo b -> a -> b
    f (b -> a -> b
    f b
    q a
    x) [a]
    xs)

    -- See Note [scanl rewrite rules]
    {-# RULES
    "scanl"  [~1] forall f a bs . scanl f a bs =
      build (\c n -> a `c` foldr (scanlFB f c) (constScanl n) bs a)
    "scanlList" [1] forall f (a::a) bs .
        foldr (scanlFB f (:)) (constScanl []) bs a = tail (scanl f a bs)
     #-}

    {-# INLINE [0] scanlFB #-} -- See Note [Inline FB functions]
    scanlFB :: (b -> a -> b) -> (b -> c -> c) -> a -> (b -> c) -> b -> c
    scanlFB :: forall b a c.
    (b -> a -> b) -> (b -> c -> c) -> a -> (b -> c) -> b -> c
    scanlFB b -> a -> b
    f b -> c -> c
    c = \a
    b b -> c
    g -> (b -> c) -> b -> c
    forall a b. (a -> b) -> a -> b
    oneShot (\b
    x -> let b' :: b
    b' = b -> a -> b
    f b
    x a
    b in b
    b' b -> c -> c
    `c` b -> c
    g b
    b')
      -- See Note [Left folds via right fold]

    {-# INLINE [0] constScanl #-}
    constScanl :: a -> b -> a
    constScanl :: forall a b. a -> b -> a
    constScanl = a -> b -> a
    forall a b. a -> b -> a
    const

    -- | \(\mathcal{O}(n)\). 'scanl1' is a variant of 'scanl' that has no starting
    -- value argument:
    --
    -- > scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
    --
    -- >>> scanl1 (+) [1..4]
    -- [1,3,6,10]
    -- >>> scanl1 (+) []
    -- []
    -- >>> scanl1 (-) [1..4]
    -- [1,-1,-4,-8]
    -- >>> scanl1 (&&) [True, False, True, True]
    -- [True,False,False,False]
    -- >>> scanl1 (||) [False, False, True, True]
    -- [False,False,True,True]
    -- >>> scanl1 (+) [1..]
    -- * Hangs forever *
    scanl1                  :: (a -> a -> a) -> [a] -> [a]
    scanl1 :: forall a. (a -> a -> a) -> [a] -> [a]
    scanl1 a -> a -> a
    f (a
    x:[a]
    xs)         =  (a -> a -> a) -> a -> [a] -> [a]
    forall b a. (b -> a -> b) -> b -> [a] -> [b]
    scanl a -> a -> a
    f a
    x [a]
    xs
    scanl1 a -> a -> a
    _ []             =  []

    -- | \(\mathcal{O}(n)\). A strict version of 'scanl'.
    {-# NOINLINE [1] scanl' #-}
    scanl'           :: (b -> a -> b) -> b -> [a] -> [b]
    -- This peculiar form is needed to prevent scanl' from being rewritten
    -- in its own right hand side.
    scanl' :: forall b a. (b -> a -> b) -> b -> [a] -> [b]
    scanl' = (b -> a -> b) -> b -> [a] -> [b]
    forall b a. (b -> a -> b) -> b -> [a] -> [b]
    scanlGo'
      where
        scanlGo'           :: (b -> a -> b) -> b -> [a] -> [b]
        scanlGo' :: forall b a. (b -> a -> b) -> b -> [a] -> [b]
    scanlGo' b -> a -> b
    f !b
    q [a]
    ls    = b
    q b -> [b] -> [b]
    forall {t}. t -> [t] -> [t]
    : (case [a]
    ls of
                                []   -> []
                                a
    x:[a]
    xs -> (b -> a -> b) -> b -> [a] -> [b]
    forall b a. (b -> a -> b) -> b -> [a] -> [b]
    scanlGo' b -> a -> b
    f (b -> a -> b
    f b
    q a
    x) [a]
    xs)

    -- See Note [scanl rewrite rules]
    {-# RULES
    "scanl'"  [~1] forall f a bs . scanl' f a bs =
      build (\c n -> a `c` foldr (scanlFB' f c) (flipSeq n) bs a)
    "scanlList'" [1] forall f a bs .
        foldr (scanlFB' f (:)) (flipSeq []) bs a = tail (scanl' f a bs)
     #-}

    {-# INLINE [0] scanlFB' #-} -- See Note [Inline FB functions]
    scanlFB' :: (b -> a -> b) -> (b -> c -> c) -> a -> (b -> c) -> b -> c
    scanlFB' :: forall b a c.
    (b -> a -> b) -> (b -> c -> c) -> a -> (b -> c) -> b -> c
    scanlFB' b -> a -> b
    f b -> c -> c
    c = \a
    b b -> c
    g -> (b -> c) -> b -> c
    forall a b. (a -> b) -> a -> b
    oneShot (\b
    x -> let !b' :: b
    b' = b -> a -> b
    f b
    x a
    b in b
    b' b -> c -> c
    `c` b -> c
    g b
    b')
      -- See Note [Left folds via right fold]

    {-
    Note [scanl rewrite rules]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    In most cases, when we rewrite a form to one that can fuse, we try to rewrite it
    back to the original form if it does not fuse. For scanl, we do something a
    little different. In particular, we rewrite

    scanl f a bs

    to

    build (\c n -> a `c` foldr (scanlFB f c) (constScanl n) bs a)

    When build is inlined, this becomes

    a : foldr (scanlFB f (:)) (constScanl []) bs a

    To rewrite this form back to scanl, we would need a rule that looked like

    forall f a bs. a : foldr (scanlFB f (:)) (constScanl []) bs a = scanl f a bs

    The problem with this rule is that it has (:) at its head. This would have the
    effect of changing the way the inliner looks at (:), not only here but
    everywhere.  In most cases, this makes no difference, but in some cases it
    causes it to come to a different decision about whether to inline something.
    Based on nofib benchmarks, this is bad for performance. Therefore, we instead
    match on everything past the :, which is just the tail of scanl.
    -}

    -- foldr, foldr', foldr1, scanr, and scanr1 are the right-to-left duals of the
    -- above functions.

    -- | 'foldr'' is a variant of 'foldr' that begins list reduction from the last
    -- element and evaluates the accumulator strictly as it unwinds the stack back
    -- to the beginning of the list.  The input list /must/ be finite, otherwise
    -- 'foldr'' runs out of space (/diverges/).
    --
    -- Note that if the function that combines the accumulated value with each
    -- element is strict in the accumulator, other than a possible improvement
    -- in the constant factor, you get the same \(\mathcal{O}(n)\) space cost
    -- as with just 'foldr'.
    --
    -- If you want a strict right fold in constant space, you need a structure
    -- that supports faster than \(\mathcal{O}(n)\) access to the right-most
    -- element, such as @Seq@ from the @containers@ package.
    --
    -- Use of this function is a hint that the @[]@ structure may be a poor fit
    -- for the task at hand.  If the order in which the elements are combined is
    -- not important, use 'foldl'' instead.
    --
    -- >>> foldr' (+) [1..4]  -- Use foldl' instead!
    -- 10
    -- >>> foldr' (&&) [True, False, True, True] -- Use foldr instead!
    -- False
    -- >>> foldr' (||) [False, False, True, True] -- Use foldr instead!
    -- True
    foldr' :: (a -> b -> b) -> b -> [a] -> b
    foldr' :: forall a b. (a -> b -> b) -> b -> [a] -> b
    foldr' a -> b -> b
    f b
    z0 [a]
    xs = ((b -> b) -> a -> b -> b) -> (b -> b) -> [a] -> b -> b
    forall a b. (b -> a -> b) -> b -> [a] -> b
    foldl (b -> b) -> a -> b -> b
    forall {b}. (b -> b) -> a -> b -> b
    f' b -> b
    forall a. a -> a
    id [a]
    xs b
    z0
      where f' :: (b -> b) -> a -> b -> b
    f' b -> b
    k a
    x b
    z = b -> b
    k (b -> b) -> b -> b
    forall a b. (a -> b) -> a -> b
    $! a -> b -> b
    f a
    x b
    z

    -- | 'foldr1' is a variant of 'foldr' that has no starting value argument,
    -- and thus must be applied to non-empty lists. Note that unlike 'foldr', the accumulated value must be of the same type as the list elements.
    --
    -- >>> foldr1 (+) [1..4]
    -- 10
    -- >>> foldr1 (+) []
    -- *** Exception: Prelude.foldr1: empty list
    -- >>> foldr1 (-) [1..4]
    -- -2
    -- >>> foldr1 (&&) [True, False, True, True]
    -- False
    -- >>> foldr1 (||) [False, False, True, True]
    -- True
    -- >>> force $ foldr1 (+) [1..]
    -- *** Exception: stack overflow
    foldr1                  :: HasCallStack => (a -> a -> a) -> [a] -> a
    foldr1 :: forall a. HasCallStack => (a -> a -> a) -> [a] -> a
    foldr1 a -> a -> a
    f = [a] -> a
    go
      where go :: [a] -> a
    go [a
    x]            =  a
    x
            go (a
    x:[a]
    xs)         =  a -> a -> a
    f a
    x ([a] -> a
    go [a]
    xs)
            go []             =  String -> a
    forall a. HasCallStack => String -> a
    errorEmptyList String
    "foldr1"
    {-# INLINE [0] foldr1 #-}

    -- | \(\mathcal{O}(n)\). 'scanr' is the right-to-left dual of 'scanl'. Note that the order of parameters on the accumulating function are reversed compared to 'scanl'.
    -- Also note that
    --
    -- > head (scanr f z xs) == foldr f z xs.
    --
    -- >>> scanr (+) 0 [1..4]
    -- [10,9,7,4,0]
    -- >>> scanr (+) 42 []
    -- [42]
    -- >>> scanr (-) 100 [1..4]
    -- [98,-97,99,-96,100]
    -- >>> scanr (\nextChar reversedString -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
    -- ["abcdfoo","bcdfoo","cdfoo","dfoo","foo"]
    -- >>> force $ scanr (+) 0 [1..]
    -- *** Exception: stack overflow
    {-# NOINLINE [1] scanr #-}
    scanr                   :: (a -> b -> b) -> b -> [a] -> [b]
    scanr :: forall a b. (a -> b -> b) -> b -> [a] -> [b]
    scanr a -> b -> b
    _ b
    q0 []           =  [b
    q0]
    scanr a -> b -> b
    f b
    q0 (a
    x:[a]
    xs)       =  a -> b -> b
    f a
    x b
    q b -> [b] -> [b]
    forall {t}. t -> [t] -> [t]
    : [b]
    qs
                               where qs :: [b]
    qs@(b
    q:[b]
    _) = (a -> b -> b) -> b -> [a] -> [b]
    forall a b. (a -> b -> b) -> b -> [a] -> [b]
    scanr a -> b -> b
    f b
    q0 [a]
    xs

    {-# INLINE [0] strictUncurryScanr #-}
    strictUncurryScanr :: (a -> b -> c) -> (a, b) -> c
    strictUncurryScanr :: forall a b c. (a -> b -> c) -> (a, b) -> c
    strictUncurryScanr a -> b -> c
    f (a, b)
    pair = case (a, b)
    pair of
                                  (a
    x, b
    y) -> a -> b -> c
    f a
    x b
    y

    {-# INLINE [0] scanrFB #-} -- See Note [Inline FB functions]
    scanrFB :: (a -> b -> b) -> (b -> c -> c) -> a -> (b, c) -> (b, c)
    scanrFB :: forall a b c.
    (a -> b -> b) -> (b -> c -> c) -> a -> (b, c) -> (b, c)
    scanrFB a -> b -> b
    f b -> c -> c
    c = \a
    x ~(b
    r, c
    est) -> (a -> b -> b
    f a
    x b
    r, b
    r b -> c -> c
    `c` c
    est)
    -- This lazy pattern match on the tuple is necessary to prevent
    -- an infinite loop when scanr receives a fusable infinite list,
    -- which was the reason for #16943.
    -- See Note [scanrFB and evaluation] below

    {-# RULES
    "scanr" [~1] forall f q0 ls . scanr f q0 ls =
      build (\c n -> strictUncurryScanr c (foldr (scanrFB f c) (q0,n) ls))
    "scanrList" [1] forall f q0 ls .
                   strictUncurryScanr (:) (foldr (scanrFB f (:)) (q0,[]) ls) =
                     scanr f q0 ls
     #-}

    {-
    Note [scanrFB and evaluation]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In a previous Version, the pattern match on the tuple in scanrFB used to be
    strict. If scanr is called with a build expression, the following would happen:
    The rule "scanr" would fire, and we obtain
        build (\c n -> strictUncurryScanr c (foldr (scanrFB f c) (q0,n) (build g))))
    The rule "foldr/build" now fires, and the second argument of strictUncurryScanr
    will be the expression
        g (scanrFB f c) (q0,n)
    which will be evaluated, thanks to strictUncurryScanr.
    The type of (g :: (a -> b -> b) -> b -> b) allows us to apply parametricity:
    Either the tuple is returned (trivial), or scanrFB is called:
        g (scanrFB f c) (q0,n) = scanrFB ... (g' (scanrFB f c) (q0,n))
    Notice that thanks to the strictness of scanrFB, the expression
    g' (scanrFB f c) (q0,n) gets evaluated as well. In particular, if g' is a
    recursive case of g, parametricity applies again and we will again have a
    possible call to scanrFB. In short, g (scanrFB f c) (q0,n) will end up being
    completely evaluated. This is resource consuming for large lists and if the
    recursion has no exit condition (and this will be the case in functions like
    repeat or cycle), the program will crash (see #16943).
    The solution: Don't make scanrFB strict in its last argument. Doing so will
    remove the cause for the chain of evaluations, and all is well.
    -}

    -- | \(\mathcal{O}(n)\). 'scanr1' is a variant of 'scanr' that has no starting
    -- value argument.
    --
    -- >>> scanr1 (+) [1..4]
    -- [10,9,7,4]
    -- >>> scanr1 (+) []
    -- []
    -- >>> scanr1 (-) [1..4]
    -- [-2,3,-1,4]
    -- >>> scanr1 (&&) [True, False, True, True]
    -- [False,False,True,True]
    -- >>> scanr1 (||) [True, True, False, False]
    -- [True,True,False,False]
    -- >>> force $ scanr1 (+) [1..]
    -- *** Exception: stack overflow
    scanr1                  :: (a -> a -> a) -> [a] -> [a]
    scanr1 :: forall a. (a -> a -> a) -> [a] -> [a]
    scanr1 a -> a -> a
    _ []             =  []
    scanr1 a -> a -> a
    _ [a
    x]            =  [a
    x]
    scanr1 a -> a -> a
    f (a
    x:[a]
    xs)         =  a -> a -> a
    f a
    x a
    q a -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    : [a]
    qs
                               where qs :: [a]
    qs@(a
    q:[a]
    _) = (a -> a -> a) -> [a] -> [a]
    forall a. (a -> a -> a) -> [a] -> [a]
    scanr1 a -> a -> a
    f [a]
    xs

    -- | 'maximum' returns the maximum value from a list,
    -- which must be non-empty, finite, and of an ordered type.
    -- It is a special case of 'Data.List.maximumBy', which allows the
    -- programmer to supply their own comparison function.
    --
    -- >>> maximum []
    -- *** Exception: Prelude.maximum: empty list
    -- >>> maximum [42]
    -- 42
    -- >>> maximum [55, -12, 7, 0, -89]
    -- 55
    -- >>> maximum [1..]
    -- * Hangs forever *
    maximum                 :: (Ord a, HasCallStack) => [a] -> a
    {-# INLINABLE maximum #-}
    maximum :: forall a. (Ord a, HasCallStack) => [a] -> a
    maximum []              =  String -> a
    forall a. HasCallStack => String -> a
    errorEmptyList String
    "maximum"
    maximum [a]
    xs              =  (a -> a -> a) -> [a] -> a
    forall a. HasCallStack => (a -> a -> a) -> [a] -> a
    foldl1' a -> a -> a
    forall a. Ord a => a -> a -> a
    max [a]
    xs

    -- We want this to be specialized so that with a strict max function, GHC
    -- produces good code. Note that to see if this is happening, one has to
    -- look at -ddump-prep, not -ddump-core!
    {-# SPECIALIZE  maximum :: [Int] -> Int #-}
    {-# SPECIALIZE  maximum :: [Integer] -> Integer #-}

    -- | 'minimum' returns the minimum value from a list,
    -- which must be non-empty, finite, and of an ordered type.
    -- It is a special case of 'Data.List.minimumBy', which allows the
    -- programmer to supply their own comparison function.
    --
    -- >>> minimum []
    -- *** Exception: Prelude.minimum: empty list
    -- >>> minimum [42]
    -- 42
    -- >>> minimum [55, -12, 7, 0, -89]
    -- -89
    -- >>> minimum [1..]
    -- * Hangs forever *
    minimum                 :: (Ord a, HasCallStack) => [a] -> a
    {-# INLINABLE minimum #-}
    minimum :: forall a. (Ord a, HasCallStack) => [a] -> a
    minimum []              =  String -> a
    forall a. HasCallStack => String -> a
    errorEmptyList String
    "minimum"
    minimum [a]
    xs              =  (a -> a -> a) -> [a] -> a
    forall a. HasCallStack => (a -> a -> a) -> [a] -> a
    foldl1' a -> a -> a
    forall a. Ord a => a -> a -> a
    min [a]
    xs

    {-# SPECIALIZE  minimum :: [Int] -> Int #-}
    {-# SPECIALIZE  minimum :: [Integer] -> Integer #-}

    -- | 'iterate' @f x@ returns an infinite list of repeated applications
    -- of @f@ to @x@:
    --
    -- > iterate f x == [x, f x, f (f x), ...]
    --
    -- Note that 'iterate' is lazy, potentially leading to thunk build-up if
    -- the consumer doesn't force each iterate. See 'iterate'' for a strict
    -- variant of this function.
    --
    -- >>> take 10 $ iterate not True
    -- [True,False,True,False...
    -- >>> take 10 $ iterate (+3) 42
    -- [42,45,48,51,54,57,60,63...
    {-# NOINLINE [1] iterate #-}
    iterate :: (a -> a) -> a -> [a]
    iterate :: forall a. (a -> a) -> a -> [a]
    iterate a -> a
    f a
    x =  a
    x a -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    : (a -> a) -> a -> [a]
    forall a. (a -> a) -> a -> [a]
    iterate a -> a
    f (a -> a
    f a
    x)

    {-# INLINE [0] iterateFB #-} -- See Note [Inline FB functions]
    iterateFB :: (a -> b -> b) -> (a -> a) -> a -> b
    iterateFB :: forall a b. (a -> b -> b) -> (a -> a) -> a -> b
    iterateFB a -> b -> b
    c a -> a
    f a
    x0 = a -> b
    go a
    x0
      where go :: a -> b
    go a
    x = a
    x a -> b -> b
    `c` a -> b
    go (a -> a
    f a
    x)

    {-# RULES
    "iterate"    [~1] forall f x.   iterate f x = build (\c _n -> iterateFB c f x)
    "iterateFB"  [1]                iterateFB (:) = iterate
     #-}

    -- | 'iterate'' is the strict version of 'iterate'.
    --
    -- It forces the result of each application of the function to weak head normal
    -- form (WHNF)
    -- before proceeding.
    {-# NOINLINE [1] iterate' #-}
    iterate' :: (a -> a) -> a -> [a]
    iterate' :: forall a. (a -> a) -> a -> [a]
    iterate' a -> a
    f a
    x =
        let x' :: a
    x' = a -> a
    f a
    x
        in a
    x' a -> [a] -> [a]
    forall a b. a -> b -> b
    `seq` (a
    x a -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    : (a -> a) -> a -> [a]
    forall a. (a -> a) -> a -> [a]
    iterate' a -> a
    f a
    x')

    {-# INLINE [0] iterate'FB #-} -- See Note [Inline FB functions]
    iterate'FB :: (a -> b -> b) -> (a -> a) -> a -> b
    iterate'FB :: forall a b. (a -> b -> b) -> (a -> a) -> a -> b
    iterate'FB a -> b -> b
    c a -> a
    f a
    x0 = a -> b
    go a
    x0
      where go :: a -> b
    go a
    x =
                let x' :: a
    x' = a -> a
    f a
    x
                in a
    x' a -> b -> b
    forall a b. a -> b -> b
    `seq` (a
    x a -> b -> b
    `c` a -> b
    go a
    x')

    {-# RULES
    "iterate'"    [~1] forall f x.   iterate' f x = build (\c _n -> iterate'FB c f x)
    "iterate'FB"  [1]                iterate'FB (:) = iterate'
     #-}

    -- | 'repeat' @x@ is an infinite list, with @x@ the value of every element.
    --
    -- >>> repeat 17
    -- [17,17,17,17,17,17,17,17,17...
    repeat :: a -> [a]
    {-# INLINE [0] repeat #-}
    -- The pragma just gives the rules more chance to fire
    repeat :: forall a. a -> [a]
    repeat a
    x = [a]
    xs where xs :: [a]
    xs = a
    x a -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    : [a]
    xs

    {-# INLINE [0] repeatFB #-}     -- ditto -- See Note [Inline FB functions]
    repeatFB :: (a -> b -> b) -> a -> b
    repeatFB :: forall a b. (a -> b -> b) -> a -> b
    repeatFB a -> b -> b
    c a
    x = b
    xs where xs :: b
    xs = a
    x a -> b -> b
    `c` b
    xs

    {-# RULES
    "repeat"    [~1] forall x. repeat x = build (\c _n -> repeatFB c x)
    "repeatFB"  [1]  repeatFB (:)       = repeat
     #-}

    -- | 'replicate' @n x@ is a list of length @n@ with @x@ the value of
    -- every element.
    -- It is an instance of the more general 'Data.List.genericReplicate',
    -- in which @n@ may be of any integral type.
    --
    -- >>> replicate 0 True
    -- []
    -- >>> replicate (-1) True
    -- []
    -- >>> replicate 4 True
    -- [True,True,True,True]
    {-# INLINE replicate #-}
    replicate               :: Int -> a -> [a]
    replicate :: forall a. Int -> a -> [a]
    replicate Int
    n a
    x           =  Int -> [a] -> [a]
    forall a. Int -> [a] -> [a]
    take Int
    n (a -> [a]
    forall a. a -> [a]
    repeat a
    x)

    -- | 'cycle' ties a finite list into a circular one, or equivalently,
    -- the infinite repetition of the original list.  It is the identity
    -- on infinite lists.
    --
    -- >>> cycle []
    -- *** Exception: Prelude.cycle: empty list
    -- >>> cycle [42]
    -- [42,42,42,42,42,42,42,42,42,42...
    -- >>> cycle [2, 5, 7]
    -- [2,5,7,2,5,7,2,5,7,2,5,7...
    cycle                   :: HasCallStack => [a] -> [a]
    cycle :: forall a. HasCallStack => [a] -> [a]
    cycle []                = String -> [a]
    forall a. HasCallStack => String -> a
    errorEmptyList String
    "cycle"
    cycle [a]
    xs                = [a]
    xs' where xs' :: [a]
    xs' = [a]
    xs [a] -> [a] -> [a]
    forall a. [a] -> [a] -> [a]
    ++ [a]
    xs'

    -- | 'takeWhile', applied to a predicate @p@ and a list @xs@, returns the
    -- longest prefix (possibly empty) of @xs@ of elements that satisfy @p@.
    --
    -- >>> takeWhile (< 3) [1,2,3,4,1,2,3,4]
    -- [1,2]
    -- >>> takeWhile (< 9) [1,2,3]
    -- [1,2,3]
    -- >>> takeWhile (< 0) [1,2,3]
    -- []
    {-# NOINLINE [1] takeWhile #-}
    takeWhile               :: (a -> Bool) -> [a] -> [a]
    takeWhile :: forall a. (a -> Bool) -> [a] -> [a]
    takeWhile a -> Bool
    _ []          =  []
    takeWhile a -> Bool
    p (a
    x:[a]
    xs)
                | a -> Bool
    p a
    x       =  a
    x a -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    : (a -> Bool) -> [a] -> [a]
    forall a. (a -> Bool) -> [a] -> [a]
    takeWhile a -> Bool
    p [a]
    xs
                | Bool
    otherwise =  []

    {-# INLINE [0] takeWhileFB #-} -- See Note [Inline FB functions]
    takeWhileFB :: (a -> Bool) -> (a -> b -> b) -> b -> a -> b -> b
    takeWhileFB :: forall a b. (a -> Bool) -> (a -> b -> b) -> b -> a -> b -> b
    takeWhileFB a -> Bool
    p a -> b -> b
    c b
    n = \a
    x b
    r -> if a -> Bool
    p a
    x then a
    x a -> b -> b
    `c` b
    r else b
    n

    -- The takeWhileFB rule is similar to the filterFB rule. It works like this:
    -- takeWhileFB q (takeWhileFB p c n) n =
    -- \x r -> if q x then (takeWhileFB p c n) x r else n =
    -- \x r -> if q x then (\x' r' -> if p x' then x' `c` r' else n) x r else n =
    -- \x r -> if q x then (if p x then x `c` r else n) else n =
    -- \x r -> if q x && p x then x `c` r else n =
    -- takeWhileFB (\x -> q x && p x) c n
    {-# RULES
    "takeWhile"     [~1] forall p xs. takeWhile p xs =
                                    build (\c n -> foldr (takeWhileFB p c n) n xs)
    "takeWhileList" [1]  forall p.    foldr (takeWhileFB p (:) []) [] = takeWhile p
    "takeWhileFB"        forall c n p q. takeWhileFB q (takeWhileFB p c n) n =
                            takeWhileFB (\x -> q x && p x) c n
     #-}

    -- | 'dropWhile' @p xs@ returns the suffix remaining after 'takeWhile' @p xs@.
    --
    -- >>> dropWhile (< 3) [1,2,3,4,5,1,2,3]
    -- [3,4,5,1,2,3]
    -- >>> dropWhile (< 9) [1,2,3]
    -- []
    -- >>> dropWhile (< 0) [1,2,3]
    -- [1,2,3]
    dropWhile               :: (a -> Bool) -> [a] -> [a]
    dropWhile :: forall a. (a -> Bool) -> [a] -> [a]
    dropWhile a -> Bool
    _ []          =  []
    dropWhile a -> Bool
    p xs :: [a]
    xs@(a
    x:[a]
    xs')
                | a -> Bool
    p a
    x       =  (a -> Bool) -> [a] -> [a]
    forall a. (a -> Bool) -> [a] -> [a]
    dropWhile a -> Bool
    p [a]
    xs'
                | Bool
    otherwise =  [a]
    xs

    -- | 'take' @n@, applied to a list @xs@, returns the prefix of @xs@
    -- of length @n@, or @xs@ itself if @n >= 'length' xs@.
    --
    -- >>> take 5 "Hello World!"
    -- "Hello"
    -- >>> take 3 [1,2,3,4,5]
    -- [1,2,3]
    -- >>> take 3 [1,2]
    -- [1,2]
    -- >>> take 3 []
    -- []
    -- >>> take (-1) [1,2]
    -- []
    -- >>> take 0 [1,2]
    -- []
    --
    -- It is an instance of the more general 'Data.List.genericTake',
    -- in which @n@ may be of any integral type.
    take                   :: Int -> [a] -> [a]
    #if defined(USE_REPORT_PRELUDE)
    take n _      | n <= 0 =  []
    take _ []              =  []
    take n (x:xs)          =  x : take (n-1) xs
    #else

    {- We always want to inline this to take advantage of a known length argument
    sign. Note, however, that it's important for the RULES to grab take, rather
    than trying to INLINE take immediately and then letting the RULES grab
    unsafeTake. Presumably the latter approach doesn't grab it early enough; it led
    to an allocation regression in nofib/fft2. -}
    {-# INLINE [1] take #-}
    take :: forall a. Int -> [a] -> [a]
    take Int
    n [a]
    xs | Int
    0 Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    n     = Int -> [a] -> [a]
    forall a. Int -> [a] -> [a]
    unsafeTake Int
    n [a]
    xs
              | Bool
    otherwise = []

    -- A version of take that takes the whole list if it's given an argument less
    -- than 1.
    {-# NOINLINE [0] unsafeTake #-} -- See Note [Inline FB functions]
    unsafeTake :: Int -> [a] -> [a]
    unsafeTake :: forall a. Int -> [a] -> [a]
    unsafeTake !Int
    _  []     = []
    unsafeTake Int
    1   (a
    x: [a]
    _) = [a
    x]
    unsafeTake Int
    m   (a
    x:[a]
    xs) = a
    x a -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    : Int -> [a] -> [a]
    forall a. Int -> [a] -> [a]
    unsafeTake (Int
    m Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - Int
    1) [a]
    xs

    {-# RULES
    "take"     [~1] forall n xs . take n xs =
      build (\c nil -> if 0 < n
                       then foldr (takeFB c nil) (flipSeq nil) xs n
                       else nil)
    "unsafeTakeList"  [1] forall n xs . foldr (takeFB (:) []) (flipSeq []) xs n
                                            = unsafeTake n xs
     #-}

    {-# INLINE [0] flipSeq #-}
    -- Just flip seq, but not inlined too early.
    -- It's important to force the argument here, even though it's not used.
    -- Otherwise, take n [] can't unbox n, leading to increased allocation in T7257.
    flipSeq :: a -> b -> a
    flipSeq :: forall a b. a -> b -> a
    flipSeq a
    x !b
    _n = a
    x

    {-# INLINE [0] takeFB #-} -- See Note [Inline FB functions]
    takeFB :: (a -> b -> b) -> b -> a -> (Int -> b) -> Int -> b
    -- The \m accounts for the fact that takeFB is used in a higher-order
    -- way by takeFoldr, so it's better to inline.  A good example is
    --     take n (repeat x)
    -- for which we get excellent code... but only if we inline takeFB
    -- when given four arguments
    takeFB :: forall a b. (a -> b -> b) -> b -> a -> (Int -> b) -> Int -> b
    takeFB a -> b -> b
    c b
    n a
    x Int -> b
    xs
      = \ Int
    m -> case Int
    m of
                Int
    1 -> a
    x a -> b -> b
    `c` b
    n
                Int
    _ -> a
    x a -> b -> b
    `c` Int -> b
    xs (Int
    m Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - Int
    1)
    #endif

    -- | 'drop' @n xs@ returns the suffix of @xs@
    -- after the first @n@ elements, or @[]@ if @n >= 'length' xs@.
    --
    -- >>> drop 6 "Hello World!"
    -- "World!"
    -- >>> drop 3 [1,2,3,4,5]
    -- [4,5]
    -- >>> drop 3 [1,2]
    -- []
    -- >>> drop 3 []
    -- []
    -- >>> drop (-1) [1,2]
    -- [1,2]
    -- >>> drop 0 [1,2]
    -- [1,2]
    --
    -- It is an instance of the more general 'Data.List.genericDrop',
    -- in which @n@ may be of any integral type.
    drop                   :: Int -> [a] -> [a]
    #if defined(USE_REPORT_PRELUDE)
    drop n xs     | n <= 0 =  xs
    drop _ []              =  []
    drop n (_:xs)          =  drop (n-1) xs
    #else /* hack away */
    {-# INLINE drop #-}
    drop :: forall a. Int -> [a] -> [a]
    drop Int
    n [a]
    ls
      | Int
    n Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    <= Int
    0     = [a]
    ls
      | Bool
    otherwise  = Int -> [a] -> [a]
    forall a. Int -> [a] -> [a]
    unsafeDrop Int
    n [a]
    ls
      where
        -- A version of drop that drops the whole list if given an argument
        -- less than 1
        unsafeDrop :: Int -> [a] -> [a]
        unsafeDrop :: forall a. Int -> [a] -> [a]
    unsafeDrop !Int
    _ []     = []
        unsafeDrop Int
    1  (a
    _:[a]
    xs) = [a]
    xs
        unsafeDrop Int
    m  (a
    _:[a]
    xs) = Int -> [a] -> [a]
    forall a. Int -> [a] -> [a]
    unsafeDrop (Int
    m Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - Int
    1) [a]
    xs
    #endif

    -- | 'splitAt' @n xs@ returns a tuple where first element is @xs@ prefix of
    -- length @n@ and second element is the remainder of the list:
    --
    -- >>> splitAt 6 "Hello World!"
    -- ("Hello ","World!")
    -- >>> splitAt 3 [1,2,3,4,5]
    -- ([1,2,3],[4,5])
    -- >>> splitAt 1 [1,2,3]
    -- ([1],[2,3])
    -- >>> splitAt 3 [1,2,3]
    -- ([1,2,3],[])
    -- >>> splitAt 4 [1,2,3]
    -- ([1,2,3],[])
    -- >>> splitAt 0 [1,2,3]
    -- ([],[1,2,3])
    -- >>> splitAt (-1) [1,2,3]
    -- ([],[1,2,3])
    --
    -- It is equivalent to @('take' n xs, 'drop' n xs)@ when @n@ is not @_|_@
    -- (@splitAt _|_ xs = _|_@).
    -- 'splitAt' is an instance of the more general 'Data.List.genericSplitAt',
    -- in which @n@ may be of any integral type.
    splitAt                :: Int -> [a] -> ([a],[a])

    #if defined(USE_REPORT_PRELUDE)
    splitAt n xs           =  (take n xs, drop n xs)
    #else
    splitAt :: forall a. Int -> [a] -> ([a], [a])
    splitAt Int
    n [a]
    ls
      | Int
    n Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    <= Int
    0 = ([], [a]
    ls)
      | Bool
    otherwise          = Int -> [a] -> ([a], [a])
    forall a. Int -> [a] -> ([a], [a])
    splitAt' Int
    n [a]
    ls
        where
            splitAt' :: Int -> [a] -> ([a], [a])
            splitAt' :: forall a. Int -> [a] -> ([a], [a])
    splitAt' Int
    _  []     = ([], [])
            splitAt' Int
    1  (a
    x:[a]
    xs) = ([a
    x], [a]
    xs)
            splitAt' Int
    m  (a
    x:[a]
    xs) = (a
    xa -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    :[a]
    xs', [a]
    xs'')
              where
                ([a]
    xs', [a]
    xs'') = Int -> [a] -> ([a], [a])
    forall a. Int -> [a] -> ([a], [a])
    splitAt' (Int
    m Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - Int
    1) [a]
    xs
    #endif /* USE_REPORT_PRELUDE */

    -- | 'span', applied to a predicate @p@ and a list @xs@, returns a tuple where
    -- first element is longest prefix (possibly empty) of @xs@ of elements that
    -- satisfy @p@ and second element is the remainder of the list:
    --
    -- >>> span (< 3) [1,2,3,4,1,2,3,4]
    -- ([1,2],[3,4,1,2,3,4])
    -- >>> span (< 9) [1,2,3]
    -- ([1,2,3],[])
    -- >>> span (< 0) [1,2,3]
    -- ([],[1,2,3])
    --
    -- 'span' @p xs@ is equivalent to @('takeWhile' p xs, 'dropWhile' p xs)@
    span                    :: (a -> Bool) -> [a] -> ([a],[a])
    span :: forall a. (a -> Bool) -> [a] -> ([a], [a])
    span a -> Bool
    _ xs :: [a]
    xs@[]            =  ([a]
    xs, [a]
    xs)
    span a -> Bool
    p xs :: [a]
    xs@(a
    x:[a]
    xs')
             | a -> Bool
    p a
    x          =  let ([a]
    ys,[a]
    zs) = (a -> Bool) -> [a] -> ([a], [a])
    forall a. (a -> Bool) -> [a] -> ([a], [a])
    span a -> Bool
    p [a]
    xs' in (a
    xa -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    :[a]
    ys,[a]
    zs)
             | Bool
    otherwise    =  ([],[a]
    xs)

    -- | 'break', applied to a predicate @p@ and a list @xs@, returns a tuple where
    -- first element is longest prefix (possibly empty) of @xs@ of elements that
    -- /do not satisfy/ @p@ and second element is the remainder of the list:
    --
    -- >>> break (> 3) [1,2,3,4,1,2,3,4]
    -- ([1,2,3],[4,1,2,3,4])
    -- >>> break (< 9) [1,2,3]
    -- ([],[1,2,3])
    -- >>> break (> 9) [1,2,3]
    -- ([1,2,3],[])
    --
    -- 'break' @p@ is equivalent to @'span' ('not' . p)@.
    break                   :: (a -> Bool) -> [a] -> ([a],[a])
    #if defined(USE_REPORT_PRELUDE)
    break p                 =  span (not . p)
    #else
    -- HBC version (stolen)
    break :: forall a. (a -> Bool) -> [a] -> ([a], [a])
    break a -> Bool
    _ xs :: [a]
    xs@[]           =  ([a]
    xs, [a]
    xs)
    break a -> Bool
    p xs :: [a]
    xs@(a
    x:[a]
    xs')
               | a -> Bool
    p a
    x        =  ([],[a]
    xs)
               | Bool
    otherwise  =  let ([a]
    ys,[a]
    zs) = (a -> Bool) -> [a] -> ([a], [a])
    forall a. (a -> Bool) -> [a] -> ([a], [a])
    break a -> Bool
    p [a]
    xs' in (a
    xa -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    :[a]
    ys,[a]
    zs)
    #endif

    -- | 'reverse' @xs@ returns the elements of @xs@ in reverse order.
    -- @xs@ must be finite.
    --
    -- >>> reverse []
    -- []
    -- >>> reverse [42]
    -- [42]
    -- >>> reverse [2,5,7]
    -- [7,5,2]
    -- >>> reverse [1..]
    -- * Hangs forever *
    reverse                 :: [a] -> [a]
    #if defined(USE_REPORT_PRELUDE)
    reverse                 =  foldl (flip (:)) []
    #else
    reverse :: forall a. [a] -> [a]
    reverse [a]
    l =  [a] -> [a] -> [a]
    forall a. [a] -> [a] -> [a]
    rev [a]
    l []
      where
        rev :: [a] -> [a] -> [a]
    rev []     [a]
    a = [a]
    a
        rev (a
    x:[a]
    xs) [a]
    a = [a] -> [a] -> [a]
    rev [a]
    xs (a
    xa -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    :[a]
    a)
    #endif

    -- | 'and' returns the conjunction of a Boolean list. For the result to be
    -- 'True', the list must be finite; 'False', however, results from a 'False'
    -- value at a finite index of a finite or infinite list.
    --
    -- >>> and []
    -- True
    -- >>> and [True]
    -- True
    -- >>> and [False]
    -- False
    -- >>> and [True, True, False]
    -- False
    -- >>> and (False : repeat True) -- Infinite list [False,True,True,True,True,True,True...
    -- False
    -- >>> and (repeat True)
    -- * Hangs forever *
    and                     :: [Bool] -> Bool
    #if defined(USE_REPORT_PRELUDE)
    and                     =  foldr (&&) True
    #else
    and :: [Bool] -> Bool
    and []          =  Bool
    True
    and (Bool
    x:[Bool]
    xs)      =  Bool
    x Bool -> Bool -> Bool
    && [Bool] -> Bool
    and [Bool]
    xs
    {-# NOINLINE [1] and #-}

    {-# RULES
    "and/build"     forall (g::forall b.(Bool->b->b)->b->b) .
                    and (build g) = g (&&) True
     #-}
    #endif

    -- | 'or' returns the disjunction of a Boolean list. For the result to be
    -- 'False', the list must be finite; 'True', however, results from a 'True'
    -- value at a finite index of a finite or infinite list.
    --
    -- >>> or []
    -- False
    -- >>> or [True]
    -- True
    -- >>> or [False]
    -- False
    -- >>> or [True, True, False]
    -- True
    -- >>> or (True : repeat False) -- Infinite list [True,False,False,False,False,False,False...
    -- True
    -- >>> or (repeat False)
    -- * Hangs forever *
    or                      :: [Bool] -> Bool
    #if defined(USE_REPORT_PRELUDE)
    or                      =  foldr (||) False
    #else
    or :: [Bool] -> Bool
    or []           =  Bool
    False
    or (Bool
    x:[Bool]
    xs)       =  Bool
    x Bool -> Bool -> Bool
    || [Bool] -> Bool
    or [Bool]
    xs
    {-# NOINLINE [1] or #-}

    {-# RULES
    "or/build"      forall (g::forall b.(Bool->b->b)->b->b) .
                    or (build g) = g (||) False
     #-}
    #endif

    -- | Applied to a predicate and a list, 'any' determines if any element
    -- of the list satisfies the predicate. For the result to be
    -- 'False', the list must be finite; 'True', however, results from a 'True'
    -- value for the predicate applied to an element at a finite index of a finite
    -- or infinite list.
    --
    -- >>> any (> 3) []
    -- False
    -- >>> any (> 3) [1,2]
    -- False
    -- >>> any (> 3) [1,2,3,4,5]
    -- True
    -- >>> any (> 3) [1..]
    -- True
    -- >>> any (> 3) [0, -1..]
    -- * Hangs forever *
    any                     :: (a -> Bool) -> [a] -> Bool
    #if defined(USE_REPORT_PRELUDE)
    any p                   =  or . map p
    #else
    any :: forall a. (a -> Bool) -> [a] -> Bool
    any a -> Bool
    _ []        = Bool
    False
    any a -> Bool
    p (a
    x:[a]
    xs)    = a -> Bool
    p a
    x Bool -> Bool -> Bool
    || (a -> Bool) -> [a] -> Bool
    forall a. (a -> Bool) -> [a] -> Bool
    any a -> Bool
    p [a]
    xs

    {-# NOINLINE [1] any #-}

    {-# RULES
    "any/build"     forall p (g::forall b.(a->b->b)->b->b) .
                    any p (build g) = g ((||) . p) False
     #-}
    #endif

    -- | Applied to a predicate and a list, 'all' determines if all elements
    -- of the list satisfy the predicate. For the result to be
    -- 'True', the list must be finite; 'False', however, results from a 'False'
    -- value for the predicate applied to an element at a finite index of a finite
    -- or infinite list.
    --
    -- >>> all (> 3) []
    -- True
    -- >>> all (> 3) [1,2]
    -- False
    -- >>> all (> 3) [1,2,3,4,5]
    -- False
    -- >>> all (> 3) [1..]
    -- False
    -- >>> all (> 3) [4..]
    -- * Hangs forever *
    all                     :: (a -> Bool) -> [a] -> Bool
    #if defined(USE_REPORT_PRELUDE)
    all p                   =  and . map p
    #else
    all :: forall a. (a -> Bool) -> [a] -> Bool
    all a -> Bool
    _ []        =  Bool
    True
    all a -> Bool
    p (a
    x:[a]
    xs)    =  a -> Bool
    p a
    x Bool -> Bool -> Bool
    && (a -> Bool) -> [a] -> Bool
    forall a. (a -> Bool) -> [a] -> Bool
    all a -> Bool
    p [a]
    xs

    {-# NOINLINE [1] all #-}

    {-# RULES
    "all/build"     forall p (g::forall b.(a->b->b)->b->b) .
                    all p (build g) = g ((&&) . p) True
     #-}
    #endif

    -- | 'elem' is the list membership predicate, usually written in infix form,
    -- e.g., @x \`elem\` xs@.  For the result to be
    -- 'False', the list must be finite; 'True', however, results from an element
    -- equal to @x@ found at a finite index of a finite or infinite list.
    --
    -- >>> 3 `elem` []
    -- False
    -- >>> 3 `elem` [1,2]
    -- False
    -- >>> 3 `elem` [1,2,3,4,5]
    -- True
    -- >>> 3 `elem` [1..]
    -- True
    -- >>> 3 `elem` [4..]
    -- * Hangs forever *
    elem                    :: (Eq a) => a -> [a] -> Bool
    #if defined(USE_REPORT_PRELUDE)
    elem x                  =  any (== x)
    #else
    elem :: forall a. Eq a => a -> [a] -> Bool
    elem a
    _ []       = Bool
    False
    elem a
    x (a
    y:[a]
    ys)   = a
    xa -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    ==a
    y Bool -> Bool -> Bool
    || a -> [a] -> Bool
    forall a. Eq a => a -> [a] -> Bool
    elem a
    x [a]
    ys
    {-# NOINLINE [1] elem #-}
    {-# RULES
    "elem/build"    forall x (g :: forall b . (a -> b -> b) -> b -> b)
       . elem x (build g) = g (\ y r -> (x == y) || r) False
     #-}
    #endif

    -- | 'notElem' is the negation of 'elem'.
    --
    -- >>> 3 `notElem` []
    -- True
    -- >>> 3 `notElem` [1,2]
    -- True
    -- >>> 3 `notElem` [1,2,3,4,5]
    -- False
    -- >>> 3 `notElem` [1..]
    -- False
    -- >>> 3 `notElem` [4..]
    -- * Hangs forever *
    notElem                 :: (Eq a) => a -> [a] -> Bool
    #if defined(USE_REPORT_PRELUDE)
    notElem x               =  all (/= x)
    #else
    notElem :: forall a. Eq a => a -> [a] -> Bool
    notElem a
    _ []    =  Bool
    True
    notElem a
    x (a
    y:[a]
    ys)=  a
    x a -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    /= a
    y Bool -> Bool -> Bool
    && a -> [a] -> Bool
    forall a. Eq a => a -> [a] -> Bool
    notElem a
    x [a]
    ys
    {-# NOINLINE [1] notElem #-}
    {-# RULES
    "notElem/build" forall x (g :: forall b . (a -> b -> b) -> b -> b)
       . notElem x (build g) = g (\ y r -> (x /= y) && r) True
     #-}
    #endif

    -- | \(\mathcal{O}(n)\). 'lookup' @key assocs@ looks up a key in an association
    -- list.
    -- For the result to be 'Nothing', the list must be finite.
    --
    -- >>> lookup 2 []
    -- Nothing
    -- >>> lookup 2 [(1, "first")]
    -- Nothing
    -- >>> lookup 2 [(1, "first"), (2, "second"), (3, "third")]
    -- Just "second"
    --
    lookup                  :: (Eq a) => a -> [(a,b)] -> Maybe b
    lookup :: forall a b. Eq a => a -> [(a, b)] -> Maybe b
    lookup a
    _key []          =  Maybe b
    forall a. Maybe a
    Nothing
    lookup  a
    key ((a
    x,b
    y):[(a, b)]
    xys)
        | a
    key a -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    == a
    x           =  b -> Maybe b
    forall a. a -> Maybe a
    Just b
    y
        | Bool
    otherwise         =  a -> [(a, b)] -> Maybe b
    forall a b. Eq a => a -> [(a, b)] -> Maybe b
    lookup a
    key [(a, b)]
    xys

    -- | Map a function returning a list over a list and concatenate the results.
    -- 'concatMap' can be seen as the composition of 'concat' and 'map'.
    --
    -- > concatMap f xs == (concat . map f) xs
    --
    -- >>> concatMap (\i -> [-i,i]) []
    -- []
    -- >>> concatMap (\i -> [-i,i]) [1,2,3]
    -- [-1,1,-2,2,-3,3]
    concatMap               :: (a -> [b]) -> [a] -> [b]
    concatMap :: forall a b. (a -> [b]) -> [a] -> [b]
    concatMap a -> [b]
    f             =  (a -> [b] -> [b]) -> [b] -> [a] -> [b]
    forall a b. (a -> b -> b) -> b -> [a] -> b
    foldr ([b] -> [b] -> [b]
    forall a. [a] -> [a] -> [a]
    (++) ([b] -> [b] -> [b]) -> (a -> [b]) -> a -> [b] -> [b]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . a -> [b]
    f) []

    {-# NOINLINE [1] concatMap #-}

    {-# RULES
    "concatMap" forall f xs . concatMap f xs =
        build (\c n -> foldr (\x b -> foldr c b (f x)) n xs)
     #-}

    -- | Concatenate a list of lists.
    --
    -- >>> concat []
    -- []
    -- >>> concat [[42]]
    -- [42]
    -- >>> concat [[1,2,3], [4,5], [6], []]
    -- [1,2,3,4,5,6]
    concat :: [[a]] -> [a]
    concat :: forall a. [[a]] -> [a]
    concat = ([a] -> [a] -> [a]) -> [a] -> [[a]] -> [a]
    forall a b. (a -> b -> b) -> b -> [a] -> b
    foldr [a] -> [a] -> [a]
    forall a. [a] -> [a] -> [a]
    (++) []

    {-# NOINLINE [1] concat #-}

    {-# RULES
      "concat" forall xs. concat xs =
         build (\c n -> foldr (\x y -> foldr c y x) n xs)
    -- We don't bother to turn non-fusible applications of concat back into concat
     #-}

    -- | List index (subscript) operator, starting from 0.
    -- It is an instance of the more general 'Data.List.genericIndex',
    -- which takes an index of any integral type.
    --
    -- >>> ['a', 'b', 'c'] !! 0
    -- 'a'
    -- >>> ['a', 'b', 'c'] !! 2
    -- 'c'
    -- >>> ['a', 'b', 'c'] !! 3
    -- *** Exception: Prelude.!!: index too large
    -- >>> ['a', 'b', 'c'] !! (-1)
    -- *** Exception: Prelude.!!: negative index
    --
    -- WARNING: This function is partial. You can use
    -- <https://hackage.haskell.org/package/safe/docs/Safe.html#v:atMay atMay>
    -- instead.
    #if defined(USE_REPORT_PRELUDE)
    (!!)                    :: [a] -> Int -> a
    xs     !! n | n < 0 =  errorWithoutStackTrace "Prelude.!!: negative index"
    []     !! _         =  errorWithoutStackTrace "Prelude.!!: index too large"
    (x:_)  !! 0         =  x
    (_:xs) !! n         =  xs !! (n-1)
    -- Prelude version is without HasCallStack to avoid building linear one
    #else
    (!!)                    :: HasCallStack => [a] -> Int -> a

    -- We don't really want the errors to inline with (!!).
    -- We may want to fuss around a bit with NOINLINE, and
    -- if so we should be careful not to trip up known-bottom
    -- optimizations.
    tooLarge :: HasCallStack => Int -> a
    tooLarge :: forall a. HasCallStack => Int -> a
    tooLarge Int
    _ = String -> a
    forall a. HasCallStack => String -> a
    error (String
    prel_list_str String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ String
    "!!: index too large")

    negIndex :: HasCallStack => a
    negIndex :: forall a. HasCallStack => a
    negIndex = String -> a
    forall a. HasCallStack => String -> a
    error (String -> a) -> String -> a
    forall a b. (a -> b) -> a -> b
    $ String
    prel_list_str String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ String
    "!!: negative index"

    {-# INLINABLE (!!) #-}
    [a]
    xs !! :: forall a. HasCallStack => [a] -> Int -> a
    !! Int
    n
      | Int
    n Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0     = a
    forall a. HasCallStack => a
    negIndex
      | Bool
    otherwise = (a -> (Int -> a) -> Int -> a) -> (Int -> a) -> [a] -> Int -> a
    forall a b. (a -> b -> b) -> b -> [a] -> b
    foldr (\a
    x Int -> a
    r Int
    k -> case Int
    k of
                                       Int
    0 -> a
    x
                                       Int
    _ -> Int -> a
    r (Int
    kInt -> Int -> Int
    forall a. Num a => a -> a -> a
    -Int
    1)) Int -> a
    forall a. HasCallStack => Int -> a
    tooLarge [a]
    xs Int
    n
    #endif

    --------------------------------------------------------------
    -- The zip family
    --------------------------------------------------------------

    foldr2 :: (a -> b -> c -> c) -> c -> [a] -> [b] -> c
    foldr2 :: forall a b c. (a -> b -> c -> c) -> c -> [a] -> [b] -> c
    foldr2 a -> b -> c -> c
    k c
    z = [a] -> [b] -> c
    go
      where
            go :: [a] -> [b] -> c
    go []    [b]
    _ys     = c
    z
            go [a]
    _xs   []      = c
    z
            go (a
    x:[a]
    xs) (b
    y:[b]
    ys) = a -> b -> c -> c
    k a
    x b
    y ([a] -> [b] -> c
    go [a]
    xs [b]
    ys)
    {-# INLINE [0] foldr2 #-}  -- See Note [Fusion for foldrN]

    foldr2_left :: (a -> b -> c -> d) -> d -> a -> ([b] -> c) -> [b] -> d
    foldr2_left :: forall a b c d.
    (a -> b -> c -> d) -> d -> a -> ([b] -> c) -> [b] -> d
    foldr2_left a -> b -> c -> d
    _k  d
    z a
    _x [b] -> c
    _r []     = d
    z
    foldr2_left  a -> b -> c -> d
    k d
    _z  a
    x  [b] -> c
    r (b
    y:[b]
    ys) = a -> b -> c -> d
    k a
    x b
    y ([b] -> c
    r [b]
    ys)

    -- foldr2 k z xs ys = foldr (foldr2_left k z)  (\_ -> z) xs ys
    {-# RULES   -- See Note [Fusion for foldrN]
    "foldr2/left"   forall k z ys (g::forall b.(a->b->b)->b->b) .
                      foldr2 k z (build g) ys = g (foldr2_left  k z) (\_ -> z) ys
     #-}

    foldr3 :: (a -> b -> c -> d -> d) -> d -> [a] -> [b] -> [c] -> d
    foldr3 :: forall a b c d.
    (a -> b -> c -> d -> d) -> d -> [a] -> [b] -> [c] -> d
    foldr3 a -> b -> c -> d -> d
    k d
    z = [a] -> [b] -> [c] -> d
    go
      where
        go :: [a] -> [b] -> [c] -> d
    go  []    [b]
    _      [c]
    _      = d
    z
        go  [a]
    _     []     [c]
    _      = d
    z
        go  [a]
    _     [b]
    _      []     = d
    z
        go (a
    a:[a]
    as) (b
    b:[b]
    bs) (c
    c:[c]
    cs) = a -> b -> c -> d -> d
    k a
    a b
    b c
    c ([a] -> [b] -> [c] -> d
    go [a]
    as [b]
    bs [c]
    cs)
    {-# INLINE [0] foldr3 #-}  -- See Note [Fusion for foldrN]

    foldr3_left :: (a -> b -> c -> d -> e) -> e -> a ->
                   ([b] -> [c] -> d) -> [b] -> [c] -> e
    foldr3_left :: forall a b c d e.
    (a -> b -> c -> d -> e)
    -> e -> a -> ([b] -> [c] -> d) -> [b] -> [c] -> e
    foldr3_left a -> b -> c -> d -> e
    k e
    _z a
    a [b] -> [c] -> d
    r (b
    b:[b]
    bs) (c
    c:[c]
    cs) = a -> b -> c -> d -> e
    k a
    a b
    b c
    c ([b] -> [c] -> d
    r [b]
    bs [c]
    cs)
    foldr3_left a -> b -> c -> d -> e
    _  e
    z a
    _ [b] -> [c] -> d
    _  [b]
    _      [c]
    _     = e
    z

    -- foldr3 k n xs ys zs = foldr (foldr3_left k n) (\_ _ -> n) xs ys zs
    {-# RULES   -- See Note [Fusion for foldrN]
    "foldr3/left"   forall k z (g::forall b.(a->b->b)->b->b).
                      foldr3 k z (build g) = g (foldr3_left k z) (\_ _ -> z)
     #-}

    {-
    Note [Fusion for foldrN]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    We arrange that foldr2, foldr3, etc is a good consumer for its first
    (left) list argument. Here's how. See below for the second, third
    etc list arguments

    * The rule "foldr2/left" (active only before phase 1) does this:
         foldr2 k z (build g) ys = g (foldr2_left  k z) (\_ -> z) ys
      thereby fusing away the 'build' on the left argument

    * To ensure this rule has a chance to fire, foldr2 has a NOINLINE[1] pragma

    There used to be a "foldr2/right" rule, allowing foldr2 to fuse with a build
    form on the right. However, this causes trouble if the right list ends in
    a bottom that is only avoided by the left list ending at that spot. That is,
    foldr2 f z [a,b,c] (d:e:f:_|_), where the right list is produced by a build
    form, would cause the foldr2/right rule to introduce bottom. Example:
      zip [1,2,3,4] (unfoldr (\s -> if s > 4 then undefined else Just (s,s+1)) 1)
    should produce
      [(1,1),(2,2),(3,3),(4,4)]
    but with the foldr2/right rule it would instead produce
      (1,1):(2,2):(3,3):(4,4):_|_

    Note [Fusion for zipN/zipWithN]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We arrange that zip, zip3, etc, and zipWith, zipWit3 etc, are all
    good consumers for their first (left) argument, and good producers.
    Here's how.  See Note [Fusion for foldrN] for why it can't fuse its
    second (right) list argument.

    NB: Zips for larger tuples are in the List module.

    * Rule "zip" (active only before phase 1) rewrites
        zip xs ys = build (\c n -> foldr2 (zipFB c) n xs ys)
      See also Note [Inline FB functions]

      Ditto rule "zipWith".

    * To give this rule a chance to fire, we give zip a NOLINLINE[1]
      pragma (although since zip is recursive it might not need it)

    * Now the rules for foldr2 (see Note [Fusion for foldrN]) may fire,
      or rules that fuse the build-produced output of zip.

    * If none of these fire, rule "zipList" (active only in phase 1)
      rewrites the foldr2 call back to zip
         foldr2 (zipFB (:)) []   = zip
      This rule will only fire when build has inlined, which also
      happens in phase 1.

      Ditto rule "zipWithList".
    -}

    ----------------------------------------------
    -- | \(\mathcal{O}(\min(m,n))\). 'zip' takes two lists and returns a list of
    -- corresponding pairs.
    --
    -- >>> zip [1, 2] ['a', 'b']
    -- [(1,'a'),(2,'b')]
    --
    -- If one input list is shorter than the other, excess elements of the longer
    -- list are discarded, even if one of the lists is infinite:
    --
    -- >>> zip [1] ['a', 'b']
    -- [(1,'a')]
    -- >>> zip [1, 2] ['a']
    -- [(1,'a')]
    -- >>> zip [] [1..]
    -- []
    -- >>> zip [1..] []
    -- []
    --
    -- 'zip' is right-lazy:
    --
    -- >>> zip [] undefined
    -- []
    -- >>> zip undefined []
    -- *** Exception: Prelude.undefined
    -- ...
    --
    -- 'zip' is capable of list fusion, but it is restricted to its
    -- first list argument and its resulting list.
    {-# NOINLINE [1] zip #-}  -- See Note [Fusion for zipN/zipWithN]
    zip :: [a] -> [b] -> [(a,b)]
    zip :: forall a b. [a] -> [b] -> [(a, b)]
    zip []     [b]
    _bs    = []
    zip [a]
    _as    []     = []
    zip (a
    a:[a]
    as) (b
    b:[b]
    bs) = (a
    a,b
    b) (a, b) -> [(a, b)] -> [(a, b)]
    forall {t}. t -> [t] -> [t]
    : [a] -> [b] -> [(a, b)]
    forall a b. [a] -> [b] -> [(a, b)]
    zip [a]
    as [b]
    bs

    {-# INLINE [0] zipFB #-} -- See Note [Inline FB functions]
    zipFB :: ((a, b) -> c -> d) -> a -> b -> c -> d
    zipFB :: forall a b c d. ((a, b) -> c -> d) -> a -> b -> c -> d
    zipFB (a, b) -> c -> d
    c = \a
    x b
    y c
    r -> (a
    x,b
    y) (a, b) -> c -> d
    `c` c
    r

    {-# RULES  -- See Note [Fusion for zipN/zipWithN]
    "zip"      [~1] forall xs ys. zip xs ys = build (\c n -> foldr2 (zipFB c) n xs ys)
    "zipList"  [1]  foldr2 (zipFB (:)) []   = zip
     #-}

    ----------------------------------------------
    -- | 'zip3' takes three lists and returns a list of triples, analogous to
    -- 'zip'.
    -- It is capable of list fusion, but it is restricted to its
    -- first list argument and its resulting list.
    {-# NOINLINE [1] zip3 #-}
    zip3 :: [a] -> [b] -> [c] -> [(a,b,c)]
    -- Specification
    -- zip3 =  zipWith3 (,,)
    zip3 :: forall a b c. [a] -> [b] -> [c] -> [(a, b, c)]
    zip3 (a
    a:[a]
    as) (b
    b:[b]
    bs) (c
    c:[c]
    cs) = (a
    a,b
    b,c
    c) (a, b, c) -> [(a, b, c)] -> [(a, b, c)]
    forall {t}. t -> [t] -> [t]
    : [a] -> [b] -> [c] -> [(a, b, c)]
    forall a b c. [a] -> [b] -> [c] -> [(a, b, c)]
    zip3 [a]
    as [b]
    bs [c]
    cs
    zip3 [a]
    _      [b]
    _      [c]
    _      = []

    {-# INLINE [0] zip3FB #-} -- See Note [Inline FB functions]
    zip3FB :: ((a,b,c) -> xs -> xs') -> a -> b -> c -> xs -> xs'
    zip3FB :: forall a b c xs xs'.
    ((a, b, c) -> xs -> xs') -> a -> b -> c -> xs -> xs'
    zip3FB (a, b, c) -> xs -> xs'
    cons = \a
    a b
    b c
    c xs
    r -> (a
    a,b
    b,c
    c) (a, b, c) -> xs -> xs'
    `cons` xs
    r

    {-# RULES    -- See Note [Fusion for zipN/zipWithN]
    "zip3"       [~1] forall as bs cs. zip3 as bs cs = build (\c n -> foldr3 (zip3FB c) n as bs cs)
    "zip3List"   [1]          foldr3 (zip3FB (:)) [] = zip3
     #-}

    -- The zipWith family generalises the zip family by zipping with the
    -- function given as the first argument, instead of a tupling function.

    ----------------------------------------------
    -- | \(\mathcal{O}(\min(m,n))\). 'zipWith' generalises 'zip' by zipping with the
    -- function given as the first argument, instead of a tupling function.
    --
    -- > zipWith (,) xs ys == zip xs ys
    -- > zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]
    --
    -- For example, @'zipWith' (+)@ is applied to two lists to produce the list of
    -- corresponding sums:
    --
    -- >>> zipWith (+) [1, 2, 3] [4, 5, 6]
    -- [5,7,9]
    --
    -- 'zipWith' is right-lazy:
    --
    -- >>> let f = undefined
    -- >>> zipWith f [] undefined
    -- []
    --
    -- 'zipWith' is capable of list fusion, but it is restricted to its
    -- first list argument and its resulting list.
    {-# NOINLINE [1] zipWith #-}  -- See Note [Fusion for zipN/zipWithN]
    zipWith :: (a->b->c) -> [a]->[b]->[c]
    zipWith :: forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    zipWith a -> b -> c
    f = [a] -> [b] -> [c]
    go
      where
        go :: [a] -> [b] -> [c]
    go [] [b]
    _ = []
        go [a]
    _ [] = []
        go (a
    x:[a]
    xs) (b
    y:[b]
    ys) = a -> b -> c
    f a
    x b
    y c -> [c] -> [c]
    forall {t}. t -> [t] -> [t]
    : [a] -> [b] -> [c]
    go [a]
    xs [b]
    ys

    -- zipWithFB must have arity 2 since it gets two arguments in the "zipWith"
    -- rule; it might not get inlined otherwise
    {-# INLINE [0] zipWithFB #-} -- See Note [Inline FB functions]
    zipWithFB :: (a -> b -> c) -> (d -> e -> a) -> d -> e -> b -> c
    zipWithFB :: forall a b c d e.
    (a -> b -> c) -> (d -> e -> a) -> d -> e -> b -> c
    zipWithFB a -> b -> c
    c d -> e -> a
    f = \d
    x e
    y b
    r -> (d
    x d -> e -> a
    `f` e
    y) a -> b -> c
    `c` b
    r

    {-# RULES       -- See Note [Fusion for zipN/zipWithN]
    "zipWith"       [~1] forall f xs ys.    zipWith f xs ys = build (\c n -> foldr2 (zipWithFB c f) n xs ys)
    "zipWithList"   [1]  forall f.  foldr2 (zipWithFB (:) f) [] = zipWith f
      #-}

    -- | The 'zipWith3' function takes a function which combines three
    -- elements, as well as three lists and returns a list of the function applied
    -- to corresponding elements, analogous to 'zipWith'.
    -- It is capable of list fusion, but it is restricted to its
    -- first list argument and its resulting list.
    --
    -- > zipWith3 (,,) xs ys zs == zip3 xs ys zs
    -- > zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..]
    {-# NOINLINE [1] zipWith3 #-}
    zipWith3                :: (a->b->c->d) -> [a]->[b]->[c]->[d]
    zipWith3 :: forall a b c d. (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
    zipWith3 a -> b -> c -> d
    z = [a] -> [b] -> [c] -> [d]
    go
      where
        go :: [a] -> [b] -> [c] -> [d]
    go (a
    a:[a]
    as) (b
    b:[b]
    bs) (c
    c:[c]
    cs) = a -> b -> c -> d
    z a
    a b
    b c
    c d -> [d] -> [d]
    forall {t}. t -> [t] -> [t]
    : [a] -> [b] -> [c] -> [d]
    go [a]
    as [b]
    bs [c]
    cs
        go [a]
    _ [b]
    _ [c]
    _                = []

    {-# INLINE [0] zipWith3FB #-} -- See Note [Inline FB functions]
    zipWith3FB :: (d -> xs -> xs') -> (a -> b -> c -> d) -> a -> b -> c -> xs -> xs'
    zipWith3FB :: forall d xs xs' a b c.
    (d -> xs -> xs') -> (a -> b -> c -> d) -> a -> b -> c -> xs -> xs'
    zipWith3FB d -> xs -> xs'
    cons a -> b -> c -> d
    func = \a
    a b
    b c
    c xs
    r -> (a -> b -> c -> d
    func a
    a b
    b c
    c) d -> xs -> xs'
    `cons` xs
    r

    {-# RULES
    "zipWith3"      [~1] forall f as bs cs.   zipWith3 f as bs cs = build (\c n -> foldr3 (zipWith3FB c f) n as bs cs)
    "zipWith3List"  [1]  forall f.   foldr3 (zipWith3FB (:) f) [] = zipWith3 f
     #-}

    -- | 'unzip' transforms a list of pairs into a list of first components
    -- and a list of second components.
    --
    -- >>> unzip []
    -- ([],[])
    -- >>> unzip [(1, 'a'), (2, 'b')]
    -- ([1,2],"ab")
    unzip    :: [(a,b)] -> ([a],[b])
    {-# INLINE unzip #-}
    -- Inline so that fusion `foldr` has an opportunity to fire.
    -- See Note [Inline @unzipN@ functions] in GHC/OldList.hs.
    unzip :: forall a b. [(a, b)] -> ([a], [b])
    unzip    =  ((a, b) -> ([a], [b]) -> ([a], [b]))
    -> ([a], [b]) -> [(a, b)] -> ([a], [b])
    forall a b. (a -> b -> b) -> b -> [a] -> b
    foldr (\(a
    a,b
    b) ~([a]
    as,[b]
    bs) -> (a
    aa -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    :[a]
    as,b
    bb -> [b] -> [b]
    forall {t}. t -> [t] -> [t]
    :[b]
    bs)) ([],[])

    -- | The 'unzip3' function takes a list of triples and returns three
    -- lists, analogous to 'unzip'.
    --
    -- >>> unzip3 []
    -- ([],[],[])
    -- >>> unzip3 [(1, 'a', True), (2, 'b', False)]
    -- ([1,2],"ab",[True,False])
    unzip3   :: [(a,b,c)] -> ([a],[b],[c])
    {-# INLINE unzip3 #-}
    -- Inline so that fusion `foldr` has an opportunity to fire.
    -- See Note [Inline @unzipN@ functions] in GHC/OldList.hs.
    unzip3 :: forall a b c. [(a, b, c)] -> ([a], [b], [c])
    unzip3   =  ((a, b, c) -> ([a], [b], [c]) -> ([a], [b], [c]))
    -> ([a], [b], [c]) -> [(a, b, c)] -> ([a], [b], [c])
    forall a b. (a -> b -> b) -> b -> [a] -> b
    foldr (\(a
    a,b
    b,c
    c) ~([a]
    as,[b]
    bs,[c]
    cs) -> (a
    aa -> [a] -> [a]
    forall {t}. t -> [t] -> [t]
    :[a]
    as,b
    bb -> [b] -> [b]
    forall {t}. t -> [t] -> [t]
    :[b]
    bs,c
    cc -> [c] -> [c]
    forall {t}. t -> [t] -> [t]
    :[c]
    cs))
                      ([],[],[])

    --------------------------------------------------------------
    -- Error code
    --------------------------------------------------------------

    -- Common up near identical calls to `error' to reduce the number
    -- constant strings created when compiled:

    errorEmptyList :: HasCallStack => String -> a
    errorEmptyList :: forall a. HasCallStack => String -> a
    errorEmptyList String
    fun =
      String -> a
    forall a. HasCallStack => String -> a
    error (String
    prel_list_str String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ String
    fun String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ String
    ": empty list")

    prel_list_str :: String
    prel_list_str :: String
    prel_list_str = String
    "Prelude."