GHC/Arr.hs

    {-# LANGUAGE Unsafe #-}
    {-# LANGUAGE NoImplicitPrelude, MagicHash, UnboxedTuples, RoleAnnotations #-}
    {-# OPTIONS_HADDOCK hide #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  GHC.Arr
    -- Copyright   :  (c) The University of Glasgow, 1994-2000
    -- License     :  see libraries/base/LICENSE
    --
    -- Maintainer  :  cvs-ghc@haskell.org
    -- Stability   :  internal
    -- Portability :  non-portable (GHC extensions)
    --
    -- GHC\'s array implementation.
    --
    -----------------------------------------------------------------------------

    module GHC.Arr (
            Ix(..), Array(..), STArray(..),

            indexError, hopelessIndexError,
            arrEleBottom, array, listArray,
            (!), safeRangeSize, negRange, safeIndex, badSafeIndex,
            bounds, numElements, numElementsSTArray, indices, elems,
            assocs, accumArray, adjust, (//), accum,
            amap, ixmap,
            eqArray, cmpArray, cmpIntArray,
            newSTArray, boundsSTArray,
            readSTArray, writeSTArray,
            freezeSTArray, thawSTArray,
            foldlElems, foldlElems', foldl1Elems,
            foldrElems, foldrElems', foldr1Elems,

            -- * Unsafe operations
            fill, done,
            unsafeArray, unsafeArray',
            lessSafeIndex, unsafeAt, unsafeReplace,
            unsafeAccumArray, unsafeAccumArray', unsafeAccum,
            unsafeReadSTArray, unsafeWriteSTArray,
            unsafeFreezeSTArray, unsafeThawSTArray,
        ) where

    import GHC.Enum
    import GHC.Num
    import GHC.ST
    import GHC.Base
    import GHC.List
    import GHC.Real( fromIntegral )
    import GHC.Show

    infixl 9  !, //

    default ()

    -- | The 'Ix' class is used to map a contiguous subrange of values in
    -- a type onto integers.  It is used primarily for array indexing
    -- (see the array package).
    --
    -- The first argument @(l,u)@ of each of these operations is a pair
    -- specifying the lower and upper bounds of a contiguous subrange of values.
    --
    -- An implementation is entitled to assume the following laws about these
    -- operations:
    --
    -- * @'inRange' (l,u) i == 'elem' i ('range' (l,u))@ @ @
    --
    -- * @'range' (l,u) '!!' 'index' (l,u) i == i@, when @'inRange' (l,u) i@
    --
    -- * @'map' ('index' (l,u)) ('range' (l,u))) == [0..'rangeSize' (l,u)-1]@ @ @
    --
    -- * @'rangeSize' (l,u) == 'length' ('range' (l,u))@ @ @
    --
    class (Ord a) => Ix a where
        {-# MINIMAL range, (index | unsafeIndex), inRange #-}

        -- | The list of values in the subrange defined by a bounding pair.
        range               :: (a,a) -> [a]
        -- | The position of a subscript in the subrange.
        index               :: (a,a) -> a -> Int
        -- | Like 'index', but without checking that the value is in range.
        unsafeIndex         :: (a,a) -> a -> Int
        -- | Returns 'True' the given subscript lies in the range defined
        -- the bounding pair.
        inRange             :: (a,a) -> a -> Bool
        -- | The size of the subrange defined by a bounding pair.
        rangeSize           :: (a,a) -> Int
        -- | like 'rangeSize', but without checking that the upper bound is
        -- in range.
        unsafeRangeSize     :: (a,a) -> Int

            -- Must specify one of index, unsafeIndex

            -- 'index' is typically over-ridden in instances, with essentially
            -- the same code, but using indexError instead of hopelessIndexError
            -- Reason: we have 'Show' at the instances
        {-# INLINE index #-}  -- See Note [Inlining index]
        index b i | inRange b i = unsafeIndex b i
                  | otherwise   = hopelessIndexError

        unsafeIndex b i = index b i

        rangeSize b@(_l,h) | inRange b h = unsafeIndex b h + 1
                           | otherwise   = 0        -- This case is only here to
                                                    -- check for an empty range
            -- NB: replacing (inRange b h) by (l <= h) fails for
            --     tuples.  E.g.  (1,2) <= (2,1) but the range is empty

        unsafeRangeSize b@(_l,h) = unsafeIndex b h + 1

    {-
    Note that the following is NOT right
            rangeSize (l,h) | l <= h    = index b h + 1
                            | otherwise = 0

    Because it might be the case that l<h, but the range
    is nevertheless empty.  Consider
            ((1,2),(2,1))
    Here l<h, but the second index ranges from 2..1 and
    hence is empty

    Note [Inlining index]
    ~~~~~~~~~~~~~~~~~~~~~
    We inline the 'index' operation,

     * Partly because it generates much faster code
       (although bigger); see Trac #1216

     * Partly because it exposes the bounds checks to the simplifier which
       might help a big.

    If you make a per-instance index method, you may consider inlining it.

    Note [Double bounds-checking of index values]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    When you index an array, a!x, there are two possible bounds checks we might make:

      (A) Check that (inRange (bounds a) x) holds.

          (A) is checked in the method for 'index'

      (B) Check that (index (bounds a) x) lies in the range 0..n,
          where n is the size of the underlying array

          (B) is checked in the top-level function (!), in safeIndex.

    Of course it *should* be the case that (A) holds iff (B) holds, but that
    is a property of the particular instances of index, bounds, and inRange,
    so GHC cannot guarantee it.

     * If you do (A) and not (B), then you might get a seg-fault,
       by indexing at some bizarre location.  Trac #1610

     * If you do (B) but not (A), you may get no complaint when you index
       an array out of its semantic bounds.  Trac #2120

    At various times we have had (A) and not (B), or (B) and not (A); both
    led to complaints.  So now we implement *both* checks (Trac #2669).

    For 1-d, 2-d, and 3-d arrays of Int we have specialised instances to avoid this.

    Note [Out-of-bounds error messages]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The default method for 'index' generates hoplelessIndexError, because
    Ix doesn't have Show as a superclass.  For particular base types we
    can do better, so we override the default method for index.
    -}

    -- Abstract these errors from the relevant index functions so that
    -- the guts of the function will be small enough to inline.

    {-# NOINLINE indexError #-}
    indexError :: Show a => (a,a) -> a -> String -> b
    indexError rng i tp
      = errorWithoutStackTrace (showString "Ix{" . showString tp . showString "}.index: Index " .
               showParen True (showsPrec 0 i) .
               showString " out of range " $
               showParen True (showsPrec 0 rng) "")

    hopelessIndexError :: Int -- Try to use 'indexError' instead!
    hopelessIndexError = errorWithoutStackTrace "Error in array index"

    ----------------------------------------------------------------------
    -- | @since 2.01
    instance  Ix Char  where
        {-# INLINE range #-}
        range (m,n) = [m..n]

        {-# INLINE unsafeIndex #-}
        unsafeIndex (m,_n) i = fromEnum i - fromEnum m

        {-# INLINE index #-}  -- See Note [Out-of-bounds error messages]
                              -- and Note [Inlining index]
        index b i | inRange b i =  unsafeIndex b i
                  | otherwise   =  indexError b i "Char"

        inRange (m,n) i     =  m <= i && i <= n

    ----------------------------------------------------------------------
    -- | @since 2.01
    instance  Ix Int  where
        {-# INLINE range #-}
            -- The INLINE stops the build in the RHS from getting inlined,
            -- so that callers can fuse with the result of range
        range (m,n) = [m..n]

        {-# INLINE unsafeIndex #-}
        unsafeIndex (m,_n) i = i - m

        {-# INLINE index #-}  -- See Note [Out-of-bounds error messages]
                              -- and Note [Inlining index]
        index b i | inRange b i =  unsafeIndex b i
                  | otherwise   =  indexError b i "Int"

        {-# INLINE inRange #-}
        inRange (I# m,I# n) (I# i) =  isTrue# (m <=# i) && isTrue# (i <=# n)

    -- | @since 4.6.0.0
    instance Ix Word where
        range (m,n)         = [m..n]
        unsafeIndex (m,_) i = fromIntegral (i - m)
        inRange (m,n) i     = m <= i && i <= n

    ----------------------------------------------------------------------
    -- | @since 2.01
    instance  Ix Integer  where
        {-# INLINE range #-}
        range (m,n) = [m..n]

        {-# INLINE unsafeIndex #-}
        unsafeIndex (m,_n) i   = fromInteger (i - m)

        {-# INLINE index #-}  -- See Note [Out-of-bounds error messages]
                              -- and Note [Inlining index]
        index b i | inRange b i =  unsafeIndex b i
                  | otherwise   =  indexError b i "Integer"

        inRange (m,n) i     =  m <= i && i <= n

    ----------------------------------------------------------------------
    -- | @since 2.01
    instance Ix Bool where -- as derived
        {-# INLINE range #-}
        range (m,n) = [m..n]

        {-# INLINE unsafeIndex #-}
        unsafeIndex (l,_) i = fromEnum i - fromEnum l

        {-# INLINE index #-}  -- See Note [Out-of-bounds error messages]
                              -- and Note [Inlining index]
        index b i | inRange b i =  unsafeIndex b i
                  | otherwise   =  indexError b i "Bool"

        inRange (l,u) i = fromEnum i >= fromEnum l && fromEnum i <= fromEnum u

    ----------------------------------------------------------------------
    -- | @since 2.01
    instance Ix Ordering where -- as derived
        {-# INLINE range #-}
        range (m,n) = [m..n]

        {-# INLINE unsafeIndex #-}
        unsafeIndex (l,_) i = fromEnum i - fromEnum l

        {-# INLINE index #-}  -- See Note [Out-of-bounds error messages]
                              -- and Note [Inlining index]
        index b i | inRange b i =  unsafeIndex b i
                  | otherwise   =  indexError b i "Ordering"

        inRange (l,u) i = fromEnum i >= fromEnum l && fromEnum i <= fromEnum u

    ----------------------------------------------------------------------
    -- | @since 2.01
    instance Ix () where
        {-# INLINE range #-}
        range   ((), ())    = [()]
        {-# INLINE unsafeIndex #-}
        unsafeIndex   ((), ()) () = 0
        {-# INLINE inRange #-}
        inRange ((), ()) () = True

        {-# INLINE index #-}  -- See Note [Inlining index]
        index b i = unsafeIndex b i

    ----------------------------------------------------------------------
    -- | @since 2.01
    instance (Ix a, Ix b) => Ix (a, b) where -- as derived
        {-# SPECIALISE instance Ix (Int,Int) #-}

        {-# INLINE range #-}
        range ((l1,l2),(u1,u2)) =
          [ (i1,i2) | i1 <- range (l1,u1), i2 <- range (l2,u2) ]

        {-# INLINE unsafeIndex #-}
        unsafeIndex ((l1,l2),(u1,u2)) (i1,i2) =
          unsafeIndex (l1,u1) i1 * unsafeRangeSize (l2,u2) + unsafeIndex (l2,u2) i2

        {-# INLINE inRange #-}
        inRange ((l1,l2),(u1,u2)) (i1,i2) =
          inRange (l1,u1) i1 && inRange (l2,u2) i2

        -- Default method for index

    ----------------------------------------------------------------------
    -- | @since 2.01
    instance  (Ix a1, Ix a2, Ix a3) => Ix (a1,a2,a3)  where
        {-# SPECIALISE instance Ix (Int,Int,Int) #-}

        range ((l1,l2,l3),(u1,u2,u3)) =
            [(i1,i2,i3) | i1 <- range (l1,u1),
                          i2 <- range (l2,u2),
                          i3 <- range (l3,u3)]

        unsafeIndex ((l1,l2,l3),(u1,u2,u3)) (i1,i2,i3) =
          unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * (
          unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) * (
          unsafeIndex (l1,u1) i1))

        inRange ((l1,l2,l3),(u1,u2,u3)) (i1,i2,i3) =
          inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
          inRange (l3,u3) i3

        -- Default method for index

    ----------------------------------------------------------------------
    -- | @since 2.01
    instance  (Ix a1, Ix a2, Ix a3, Ix a4) => Ix (a1,a2,a3,a4)  where
        range ((l1,l2,l3,l4),(u1,u2,u3,u4)) =
          [(i1,i2,i3,i4) | i1 <- range (l1,u1),
                           i2 <- range (l2,u2),
                           i3 <- range (l3,u3),
                           i4 <- range (l4,u4)]

        unsafeIndex ((l1,l2,l3,l4),(u1,u2,u3,u4)) (i1,i2,i3,i4) =
          unsafeIndex (l4,u4) i4 + unsafeRangeSize (l4,u4) * (
          unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * (
          unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) * (
          unsafeIndex (l1,u1) i1)))

        inRange ((l1,l2,l3,l4),(u1,u2,u3,u4)) (i1,i2,i3,i4) =
          inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
          inRange (l3,u3) i3 && inRange (l4,u4) i4

        -- Default method for index
    -- | @since 2.01
    instance  (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5) => Ix (a1,a2,a3,a4,a5)  where
        range ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) =
          [(i1,i2,i3,i4,i5) | i1 <- range (l1,u1),
                              i2 <- range (l2,u2),
                              i3 <- range (l3,u3),
                              i4 <- range (l4,u4),
                              i5 <- range (l5,u5)]

        unsafeIndex ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) (i1,i2,i3,i4,i5) =
          unsafeIndex (l5,u5) i5 + unsafeRangeSize (l5,u5) * (
          unsafeIndex (l4,u4) i4 + unsafeRangeSize (l4,u4) * (
          unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * (
          unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) * (
          unsafeIndex (l1,u1) i1))))

        inRange ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) (i1,i2,i3,i4,i5) =
          inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
          inRange (l3,u3) i3 && inRange (l4,u4) i4 &&
          inRange (l5,u5) i5

        -- Default method for index

    -- | The type of immutable non-strict (boxed) arrays
    -- with indices in @i@ and elements in @e@.
    data Array i e
       = Array            !i         -- the lower bound, l
                          !i         -- the upper bound, u
           {-# UNPACK #-} !Int       -- A cache of (rangeSize (l,u))
                                     -- used to make sure an index is
                                     -- really in range
                          (Array# e) -- The actual elements

    -- | Mutable, boxed, non-strict arrays in the 'ST' monad.  The type
    -- arguments are as follows:
    --
    --  * @s@: the state variable argument for the 'ST' type
    --
    --  * @i@: the index type of the array (should be an instance of 'Ix')
    --
    --  * @e@: the element type of the array.
    --
    data STArray s i e
      = STArray           !i               -- the lower bound, l
                          !i               -- the upper bound, u
          {-# UNPACK #-}  !Int             -- A cache of (rangeSize (l,u))
                                           -- used to make sure an index is
                                           -- really in range
                       (MutableArray# s e) -- The actual elements
            -- No Ix context for STArray.  They are stupid,
            -- and force an Ix context on the equality instance.

    -- Index types should have nominal role, because of Ix class. See also #9220.
    type role Array nominal representational
    type role STArray nominal nominal representational

    -- Just pointer equality on mutable arrays:
    -- | @since 2.01
    instance Eq (STArray s i e) where
        STArray _ _ _ arr1# == STArray _ _ _ arr2# =
            isTrue# (sameMutableArray# arr1# arr2#)

    ----------------------------------------------------------------------
    -- Operations on immutable arrays

    {-# NOINLINE arrEleBottom #-}
    arrEleBottom :: a
    arrEleBottom = errorWithoutStackTrace "(Array.!): undefined array element"

    -- | Construct an array with the specified bounds and containing values
    -- for given indices within these bounds.
    --
    -- The array is undefined (i.e. bottom) if any index in the list is
    -- out of bounds.  The Haskell 2010 Report further specifies that if any
    -- two associations in the list have the same index, the value at that
    -- index is undefined (i.e. bottom).  However in GHC's implementation,
    -- the value at such an index is the value part of the last association
    -- with that index in the list.
    --
    -- Because the indices must be checked for these errors, 'array' is
    -- strict in the bounds argument and in the indices of the association
    -- list, but non-strict in the values.  Thus, recurrences such as the
    -- following are possible:
    --
    -- > a = array (1,100) ((1,1) : [(i, i * a!(i-1)) | i <- [2..100]])
    --
    -- Not every index within the bounds of the array need appear in the
    -- association list, but the values associated with indices that do not
    -- appear will be undefined (i.e. bottom).
    --
    -- If, in any dimension, the lower bound is greater than the upper bound,
    -- then the array is legal, but empty.  Indexing an empty array always
    -- gives an array-bounds error, but 'bounds' still yields the bounds
    -- with which the array was constructed.
    {-# INLINE array #-}
    array :: Ix i
            => (i,i)        -- ^ a pair of /bounds/, each of the index type
                            -- of the array.  These bounds are the lowest and
                            -- highest indices in the array, in that order.
                            -- For example, a one-origin vector of length
                            -- '10' has bounds '(1,10)', and a one-origin '10'
                            -- by '10' matrix has bounds '((1,1),(10,10))'.
            -> [(i, e)]     -- ^ a list of /associations/ of the form
                            -- (/index/, /value/).  Typically, this list will
                            -- be expressed as a comprehension.  An
                            -- association '(i, x)' defines the value of
                            -- the array at index 'i' to be 'x'.
            -> Array i e
    array (l,u) ies
        = let n = safeRangeSize (l,u)
          in unsafeArray' (l,u) n
                          [(safeIndex (l,u) n i, e) | (i, e) <- ies]

    {-# INLINE unsafeArray #-}
    unsafeArray :: Ix i => (i,i) -> [(Int, e)] -> Array i e
    unsafeArray b ies = unsafeArray' b (rangeSize b) ies

    {-# INLINE unsafeArray' #-}
    unsafeArray' :: (i,i) -> Int -> [(Int, e)] -> Array i e
    unsafeArray' (l,u) n@(I# n#) ies = runST (ST $ \s1# ->
        case newArray# n# arrEleBottom s1# of
            (# s2#, marr# #) ->
                foldr (fill marr#) (done l u n marr#) ies s2#)

    {-# INLINE fill #-}
    fill :: MutableArray# s e -> (Int, e) -> STRep s a -> STRep s a
    -- NB: put the \s after the "=" so that 'fill'
    --     inlines when applied to three args
    fill marr# (I# i#, e) next
     = \s1# -> case writeArray# marr# i# e s1# of
                 s2# -> next s2#

    {-# INLINE done #-}
    done :: i -> i -> Int -> MutableArray# s e -> STRep s (Array i e)
    -- See NB on 'fill'
    -- Make sure it is strict in 'n'
    done l u n@(I# _) marr#
      = \s1# -> case unsafeFreezeArray# marr# s1# of
                  (# s2#, arr# #) -> (# s2#, Array l u n arr# #)

    -- | Construct an array from a pair of bounds and a list of values in
    -- index order.
    {-# INLINE listArray #-}
    listArray :: Ix i => (i,i) -> [e] -> Array i e
    listArray (l,u) es = runST (ST $ \s1# ->
        case safeRangeSize (l,u)            of { n@(I# n#) ->
        case newArray# n# arrEleBottom s1#  of { (# s2#, marr# #) ->
          let
            go y r = \ i# s3# ->
                case writeArray# marr# i# y s3# of
                  s4# -> if (isTrue# (i# ==# n# -# 1#))
                         then s4#
                         else r (i# +# 1#) s4#
          in
            done l u n marr# (
              if n == 0
              then s2#
              else foldr go (\_ s# -> s#) es 0# s2#)}})

    -- | The value at the given index in an array.
    {-# INLINE (!) #-}
    (!) :: Ix i => Array i e -> i -> e
    arr@(Array l u n _) ! i = unsafeAt arr $ safeIndex (l,u) n i

    {-# INLINE safeRangeSize #-}
    safeRangeSize :: Ix i => (i, i) -> Int
    safeRangeSize (l,u) = let r = rangeSize (l, u)
                          in if r < 0 then negRange
                                      else r

    -- Don't inline this error message everywhere!!
    negRange :: Int   -- Uninformative, but Ix does not provide Show
    negRange = errorWithoutStackTrace "Negative range size"

    {-# INLINE[1] safeIndex #-}
    -- See Note [Double bounds-checking of index values]
    -- Inline *after* (!) so the rules can fire
    -- Make sure it is strict in n
    safeIndex :: Ix i => (i, i) -> Int -> i -> Int
    safeIndex (l,u) n@(I# _) i
      | (0 <= i') && (i' < n) = i'
      | otherwise             = badSafeIndex i' n
      where
        i' = index (l,u) i

    -- See Note [Double bounds-checking of index values]
    {-# RULES
    "safeIndex/I"       safeIndex = lessSafeIndex :: (Int,Int) -> Int -> Int -> Int
    "safeIndex/(I,I)"   safeIndex = lessSafeIndex :: ((Int,Int),(Int,Int)) -> Int -> (Int,Int) -> Int
    "safeIndex/(I,I,I)" safeIndex = lessSafeIndex :: ((Int,Int,Int),(Int,Int,Int)) -> Int -> (Int,Int,Int) -> Int
      #-}

    lessSafeIndex :: Ix i => (i, i) -> Int -> i -> Int
    -- See Note [Double bounds-checking of index values]
    -- Do only (A), the semantic check
    lessSafeIndex (l,u) _ i = index (l,u) i

    -- Don't inline this long error message everywhere!!
    badSafeIndex :: Int -> Int -> Int
    badSafeIndex i' n = errorWithoutStackTrace ("Error in array index; " ++ show i' ++
                            " not in range [0.." ++ show n ++ ")")

    {-# INLINE unsafeAt #-}
    unsafeAt :: Array i e -> Int -> e
    unsafeAt (Array _ _ _ arr#) (I# i#) =
        case indexArray# arr# i# of (# e #) -> e

    -- | The bounds with which an array was constructed.
    {-# INLINE bounds #-}
    bounds :: Array i e -> (i,i)
    bounds (Array l u _ _) = (l,u)

    -- | The number of elements in the array.
    {-# INLINE numElements #-}
    numElements :: Array i e -> Int
    numElements (Array _ _ n _) = n

    -- | The list of indices of an array in ascending order.
    {-# INLINE indices #-}
    indices :: Ix i => Array i e -> [i]
    indices (Array l u _ _) = range (l,u)

    -- | The list of elements of an array in index order.
    {-# INLINE elems #-}
    elems :: Array i e -> [e]
    elems arr@(Array _ _ n _) =
        [unsafeAt arr i | i <- [0 .. n - 1]]

    -- | A right fold over the elements
    {-# INLINABLE foldrElems #-}
    foldrElems :: (a -> b -> b) -> b -> Array i a -> b
    foldrElems f b0 = \ arr@(Array _ _ n _) ->
      let
        go i | i == n    = b0
             | otherwise = f (unsafeAt arr i) (go (i+1))
      in go 0

    -- | A left fold over the elements
    {-# INLINABLE foldlElems #-}
    foldlElems :: (b -> a -> b) -> b -> Array i a -> b
    foldlElems f b0 = \ arr@(Array _ _ n _) ->
      let
        go i | i == (-1) = b0
             | otherwise = f (go (i-1)) (unsafeAt arr i)
      in go (n-1)

    -- | A strict right fold over the elements
    {-# INLINABLE foldrElems' #-}
    foldrElems' :: (a -> b -> b) -> b -> Array i a -> b
    foldrElems' f b0 = \ arr@(Array _ _ n _) ->
      let
        go i a | i == (-1) = a
               | otherwise = go (i-1) (f (unsafeAt arr i) $! a)
      in go (n-1) b0

    -- | A strict left fold over the elements
    {-# INLINABLE foldlElems' #-}
    foldlElems' :: (b -> a -> b) -> b -> Array i a -> b
    foldlElems' f b0 = \ arr@(Array _ _ n _) ->
      let
        go i a | i == n    = a
               | otherwise = go (i+1) (a `seq` f a (unsafeAt arr i))
      in go 0 b0

    -- | A left fold over the elements with no starting value
    {-# INLINABLE foldl1Elems #-}
    foldl1Elems :: (a -> a -> a) -> Array i a -> a
    foldl1Elems f = \ arr@(Array _ _ n _) ->
      let
        go i | i == 0    = unsafeAt arr 0
             | otherwise = f (go (i-1)) (unsafeAt arr i)
      in
        if n == 0 then errorWithoutStackTrace "foldl1: empty Array" else go (n-1)

    -- | A right fold over the elements with no starting value
    {-# INLINABLE foldr1Elems #-}
    foldr1Elems :: (a -> a -> a) -> Array i a -> a
    foldr1Elems f = \ arr@(Array _ _ n _) ->
      let
        go i | i == n-1  = unsafeAt arr i
             | otherwise = f (unsafeAt arr i) (go (i + 1))
      in
        if n == 0 then errorWithoutStackTrace "foldr1: empty Array" else go 0

    -- | The list of associations of an array in index order.
    {-# INLINE assocs #-}
    assocs :: Ix i => Array i e -> [(i, e)]
    assocs arr@(Array l u _ _) =
        [(i, arr ! i) | i <- range (l,u)]

    -- | The 'accumArray' function deals with repeated indices in the association
    -- list using an /accumulating function/ which combines the values of
    -- associations with the same index.
    -- For example, given a list of values of some index type, @hist@
    -- produces a histogram of the number of occurrences of each index within
    -- a specified range:
    --
    -- > hist :: (Ix a, Num b) => (a,a) -> [a] -> Array a b
    -- > hist bnds is = accumArray (+) 0 bnds [(i, 1) | i<-is, inRange bnds i]
    --
    -- If the accumulating function is strict, then 'accumArray' is strict in
    -- the values, as well as the indices, in the association list.  Thus,
    -- unlike ordinary arrays built with 'array', accumulated arrays should
    -- not in general be recursive.
    {-# INLINE accumArray #-}
    accumArray :: Ix i
            => (e -> a -> e)        -- ^ accumulating function
            -> e                    -- ^ initial value
            -> (i,i)                -- ^ bounds of the array
            -> [(i, a)]             -- ^ association list
            -> Array i e
    accumArray f initial (l,u) ies =
        let n = safeRangeSize (l,u)
        in unsafeAccumArray' f initial (l,u) n
                             [(safeIndex (l,u) n i, e) | (i, e) <- ies]

    {-# INLINE unsafeAccumArray #-}
    unsafeAccumArray :: Ix i => (e -> a -> e) -> e -> (i,i) -> [(Int, a)] -> Array i e
    unsafeAccumArray f initial b ies = unsafeAccumArray' f initial b (rangeSize b) ies

    {-# INLINE unsafeAccumArray' #-}
    unsafeAccumArray' :: (e -> a -> e) -> e -> (i,i) -> Int -> [(Int, a)] -> Array i e
    unsafeAccumArray' f initial (l,u) n@(I# n#) ies = runST (ST $ \s1# ->
        case newArray# n# initial s1#          of { (# s2#, marr# #) ->
        foldr (adjust f marr#) (done l u n marr#) ies s2# })

    {-# INLINE adjust #-}
    adjust :: (e -> a -> e) -> MutableArray# s e -> (Int, a) -> STRep s b -> STRep s b
    -- See NB on 'fill'
    adjust f marr# (I# i#, new) next
      = \s1# -> case readArray# marr# i# s1# of
                    (# s2#, old #) ->
                        case writeArray# marr# i# (f old new) s2# of
                            s3# -> next s3#

    -- | Constructs an array identical to the first argument except that it has
    -- been updated by the associations in the right argument.
    -- For example, if @m@ is a 1-origin, @n@ by @n@ matrix, then
    --
    -- > m//[((i,i), 0) | i <- [1..n]]
    --
    -- is the same matrix, except with the diagonal zeroed.
    --
    -- Repeated indices in the association list are handled as for 'array':
    -- Haskell 2010 specifies that the resulting array is undefined (i.e. bottom),
    -- but GHC's implementation uses the last association for each index.
    {-# INLINE (//) #-}
    (//) :: Ix i => Array i e -> [(i, e)] -> Array i e
    arr@(Array l u n _) // ies =
        unsafeReplace arr [(safeIndex (l,u) n i, e) | (i, e) <- ies]

    {-# INLINE unsafeReplace #-}
    unsafeReplace :: Array i e -> [(Int, e)] -> Array i e
    unsafeReplace arr ies = runST (do
        STArray l u n marr# <- thawSTArray arr
        ST (foldr (fill marr#) (done l u n marr#) ies))

    -- | @'accum' f@ takes an array and an association list and accumulates
    -- pairs from the list into the array with the accumulating function @f@.
    -- Thus 'accumArray' can be defined using 'accum':
    --
    -- > accumArray f z b = accum f (array b [(i, z) | i <- range b])
    --
    {-# INLINE accum #-}
    accum :: Ix i => (e -> a -> e) -> Array i e -> [(i, a)] -> Array i e
    accum f arr@(Array l u n _) ies =
        unsafeAccum f arr [(safeIndex (l,u) n i, e) | (i, e) <- ies]

    {-# INLINE unsafeAccum #-}
    unsafeAccum :: (e -> a -> e) -> Array i e -> [(Int, a)] -> Array i e
    unsafeAccum f arr ies = runST (do
        STArray l u n marr# <- thawSTArray arr
        ST (foldr (adjust f marr#) (done l u n marr#) ies))

    {-# INLINE [1] amap #-}  -- See Note [amap]
    amap :: (a -> b) -> Array i a -> Array i b
    amap f arr@(Array l u n@(I# n#) _) = runST (ST $ \s1# ->
        case newArray# n# arrEleBottom s1# of
            (# s2#, marr# #) ->
              let go i s#
                    | i == n    = done l u n marr# s#
                    | otherwise = fill marr# (i, f (unsafeAt arr i)) (go (i+1)) s#
              in go 0 s2# )

    {- Note [amap]
    ~~~~~~~~~~~~~~
    amap was originally defined like this:

     amap f arr@(Array l u n _) =
         unsafeArray' (l,u) n [(i, f (unsafeAt arr i)) | i <- [0 .. n - 1]]

    There are two problems:

    1. The enumFromTo implementation produces (spurious) code for the impossible
       case of n<0 that ends up duplicating the array freezing code.

    2. This implementation relies on list fusion for efficiency. In order
       to implement the "amap/coerce" rule, we need to delay inlining amap
       until simplifier phase 1, which is when the eftIntList rule kicks
       in and makes that impossible.  (c.f. Trac #8767)
    -}

    -- See Breitner, Eisenberg, Peyton Jones, and Weirich, "Safe Zero-cost
    -- Coercions for Haskell", section 6.5:
    --   http://research.microsoft.com/en-us/um/people/simonpj/papers/ext-f/coercible.pdf
    {-# RULES
    "amap/coerce" amap coerce = coerce  -- See Note [amap]
     #-}

    -- Second functor law:
    {-# RULES
    "amap/amap" forall f g a . amap f (amap g a) = amap (f . g) a
     #-}

    -- | 'ixmap' allows for transformations on array indices.
    -- It may be thought of as providing function composition on the right
    -- with the mapping that the original array embodies.
    --
    -- A similar transformation of array values may be achieved using 'fmap'
    -- from the 'Array' instance of the 'Functor' class.
    {-# INLINE ixmap #-}
    ixmap :: (Ix i, Ix j) => (i,i) -> (i -> j) -> Array j e -> Array i e
    ixmap (l,u) f arr =
        array (l,u) [(i, arr ! f i) | i <- range (l,u)]

    {-# INLINE eqArray #-}
    eqArray :: (Ix i, Eq e) => Array i e -> Array i e -> Bool
    eqArray arr1@(Array l1 u1 n1 _) arr2@(Array l2 u2 n2 _) =
        if n1 == 0 then n2 == 0 else
        l1 == l2 && u1 == u2 &&
        and [unsafeAt arr1 i == unsafeAt arr2 i | i <- [0 .. n1 - 1]]

    {-# INLINE [1] cmpArray #-}
    cmpArray :: (Ix i, Ord e) => Array i e -> Array i e -> Ordering
    cmpArray arr1 arr2 = compare (assocs arr1) (assocs arr2)

    {-# INLINE cmpIntArray #-}
    cmpIntArray :: Ord e => Array Int e -> Array Int e -> Ordering
    cmpIntArray arr1@(Array l1 u1 n1 _) arr2@(Array l2 u2 n2 _) =
        if n1 == 0 then
            if n2 == 0 then EQ else LT
        else if n2 == 0 then GT
        else case compare l1 l2 of
                 EQ    -> foldr cmp (compare u1 u2) [0 .. (n1 `min` n2) - 1]
                 other -> other
      where
        cmp i rest = case compare (unsafeAt arr1 i) (unsafeAt arr2 i) of
            EQ    -> rest
            other -> other

    {-# RULES "cmpArray/Int" cmpArray = cmpIntArray #-}

    ----------------------------------------------------------------------
    -- Array instances

    -- | @since 2.01
    instance Functor (Array i) where
        fmap = amap

    -- | @since 2.01
    instance (Ix i, Eq e) => Eq (Array i e) where
        (==) = eqArray

    -- | @since 2.01
    instance (Ix i, Ord e) => Ord (Array i e) where
        compare = cmpArray

    -- | @since 2.01
    instance (Ix a, Show a, Show b) => Show (Array a b) where
        showsPrec p a =
            showParen (p > appPrec) $
            showString "array " .
            showsPrec appPrec1 (bounds a) .
            showChar ' ' .
            showsPrec appPrec1 (assocs a)
            -- Precedence of 'array' is the precedence of application

    -- The Read instance is in GHC.Read

    ----------------------------------------------------------------------
    -- Operations on mutable arrays

    {-
    Idle ADR question: What's the tradeoff here between flattening these
    datatypes into @STArray ix ix (MutableArray# s elt)@ and using
    it as is?  As I see it, the former uses slightly less heap and
    provides faster access to the individual parts of the bounds while the
    code used has the benefit of providing a ready-made @(lo, hi)@ pair as
    required by many array-related functions.  Which wins? Is the
    difference significant (probably not).

    Idle AJG answer: When I looked at the outputted code (though it was 2
    years ago) it seems like you often needed the tuple, and we build
    it frequently. Now we've got the overloading specialiser things
    might be different, though.
    -}

    {-# INLINE newSTArray #-}
    newSTArray :: Ix i => (i,i) -> e -> ST s (STArray s i e)
    newSTArray (l,u) initial = ST $ \s1# ->
        case safeRangeSize (l,u)            of { n@(I# n#) ->
        case newArray# n# initial s1#       of { (# s2#, marr# #) ->
        (# s2#, STArray l u n marr# #) }}

    {-# INLINE boundsSTArray #-}
    boundsSTArray :: STArray s i e -> (i,i)
    boundsSTArray (STArray l u _ _) = (l,u)

    {-# INLINE numElementsSTArray #-}
    numElementsSTArray :: STArray s i e -> Int
    numElementsSTArray (STArray _ _ n _) = n

    {-# INLINE readSTArray #-}
    readSTArray :: Ix i => STArray s i e -> i -> ST s e
    readSTArray marr@(STArray l u n _) i =
        unsafeReadSTArray marr (safeIndex (l,u) n i)

    {-# INLINE unsafeReadSTArray #-}
    unsafeReadSTArray :: STArray s i e -> Int -> ST s e
    unsafeReadSTArray (STArray _ _ _ marr#) (I# i#)
        = ST $ \s1# -> readArray# marr# i# s1#

    {-# INLINE writeSTArray #-}
    writeSTArray :: Ix i => STArray s i e -> i -> e -> ST s ()
    writeSTArray marr@(STArray l u n _) i e =
        unsafeWriteSTArray marr (safeIndex (l,u) n i) e

    {-# INLINE unsafeWriteSTArray #-}
    unsafeWriteSTArray :: STArray s i e -> Int -> e -> ST s ()
    unsafeWriteSTArray (STArray _ _ _ marr#) (I# i#) e = ST $ \s1# ->
        case writeArray# marr# i# e s1# of
            s2# -> (# s2#, () #)

    ----------------------------------------------------------------------
    -- Moving between mutable and immutable

    freezeSTArray :: STArray s i e -> ST s (Array i e)
    freezeSTArray (STArray l u n@(I# n#) marr#) = ST $ \s1# ->
        case newArray# n# arrEleBottom s1#  of { (# s2#, marr'# #) ->
        let copy i# s3# | isTrue# (i# ==# n#) = s3#
                        | otherwise =
                case readArray# marr# i# s3# of { (# s4#, e #) ->
                case writeArray# marr'# i# e s4# of { s5# ->
                copy (i# +# 1#) s5# }} in
        case copy 0# s2#                    of { s3# ->
        case unsafeFreezeArray# marr'# s3#  of { (# s4#, arr# #) ->
        (# s4#, Array l u n arr# #) }}}

    {-# INLINE unsafeFreezeSTArray #-}
    unsafeFreezeSTArray :: STArray s i e -> ST s (Array i e)
    unsafeFreezeSTArray (STArray l u n marr#) = ST $ \s1# ->
        case unsafeFreezeArray# marr# s1#   of { (# s2#, arr# #) ->
        (# s2#, Array l u n arr# #) }

    thawSTArray :: Array i e -> ST s (STArray s i e)
    thawSTArray (Array l u n@(I# n#) arr#) = ST $ \s1# ->
        case newArray# n# arrEleBottom s1#  of { (# s2#, marr# #) ->
        let copy i# s3# | isTrue# (i# ==# n#) = s3#
                        | otherwise =
                case indexArray# arr# i#    of { (# e #) ->
                case writeArray# marr# i# e s3# of { s4# ->
                copy (i# +# 1#) s4# }} in
        case copy 0# s2#                    of { s3# ->
        (# s3#, STArray l u n marr# #) }}

    {-# INLINE unsafeThawSTArray #-}
    unsafeThawSTArray :: Array i e -> ST s (STArray s i e)
    unsafeThawSTArray (Array l u n arr#) = ST $ \s1# ->
        case unsafeThawArray# arr# s1#      of { (# s2#, marr# #) ->
        (# s2#, STArray l u n marr# #) }