GHC/List.lhs

\begin{code}

    {-# LANGUAGE Trustworthy #-}
    {-# LANGUAGE CPP, NoImplicitPrelude, MagicHash #-}
    {-# OPTIONS_HADDOCK hide #-}

    -----------------------------------------------------------------------------
    -- |
    -- 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 (
       -- [] (..),          -- built-in syntax; can't be used in export list

       map, (++), filter, concat,
       head, last, tail, init, null, length, (!!),
       foldl, scanl, scanl1, foldr, foldr1, scanr, scanr1,
       iterate, repeat, replicate, cycle,
       take, drop, splitAt, takeWhile, dropWhile, span, break,
       reverse, and, or,
       any, all, elem, notElem, lookup,
       concatMap,
       zip, zip3, zipWith, zipWith3, unzip, unzip3,
       errorEmptyList,

    #ifndef USE_REPORT_PRELUDE
       -- non-standard, but hidden when creating the Prelude
       -- export list.
       takeUInt_append
    #endif

     ) where

    import Data.Maybe
    import GHC.Base

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

\end{code} %********************************************************* %* * \subsection{List-manipulation functions} %* * %********************************************************* \begin{code}

    -- | Extract the first element of a list, which must be non-empty.
    head                    :: [a] -> a
    head (x:_)              =  x
    head []                 =  badHead
    {-# NOINLINE [1] head #-}

    badHead :: a
    badHead = errorEmptyList "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)
     #-}

    -- | Extract the elements after the head of a list, which must be non-empty.
    tail                    :: [a] -> [a]
    tail (_:xs)             =  xs
    tail []                 =  errorEmptyList "tail"

    -- | Extract the last element of a list, which must be finite and non-empty.
    last                    :: [a] -> a
    #ifdef USE_REPORT_PRELUDE
    last [x]                =  x
    last (_:xs)             =  last xs
    last []                 =  errorEmptyList "last"
    #else
    -- eliminate repeated cases
    last []                 =  errorEmptyList "last"
    last (x:xs)             =  last' x xs
      where last' y []     = y
            last' _ (y:ys) = last' y ys
    #endif

    -- | Return all the elements of a list except the last one.
    -- The list must be non-empty.
    init                    :: [a] -> [a]
    #ifdef USE_REPORT_PRELUDE
    init [x]                =  []
    init (x:xs)             =  x : init xs
    init []                 =  errorEmptyList "init"
    #else
    -- eliminate repeated cases
    init []                 =  errorEmptyList "init"
    init (x:xs)             =  init' x xs
      where init' _ []     = []
            init' y (z:zs) = y : init' z zs
    #endif

    -- | Test whether a list is empty.
    null                    :: [a] -> Bool
    null []                 =  True
    null (_:_)              =  False

    -- | /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.
    {-# NOINLINE [1] length #-}
    length                  :: [a] -> Int
    length l                =  lenAcc l 0#

    lenAcc :: [a] -> Int# -> Int
    lenAcc []     a# = I# a#
    lenAcc (_:xs) a# = lenAcc xs (a# +# 1#)

    incLen :: a -> (Int# -> Int) -> Int# -> Int
    incLen _ g x = g (x +# 1#)

    -- These rules make length into a good consumer
    -- Note that we use a higher-order-style use of foldr, so that
    -- the accumulating parameter can be evaluated strictly
    -- See Trac #876 for what goes wrong otherwise
    {-# RULES
    "length"     [~1] forall xs. length xs = foldr incLen I# xs 0#
    "lengthList" [1]  foldr incLen I# = lenAcc
     #-}

    -- | '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]

    {-# NOINLINE [1] filter #-}
    filter :: (a -> Bool) -> [a] -> [a]
    filter _pred []    = []
    filter pred (x:xs)
      | pred x         = x : filter pred xs
      | otherwise      = filter pred xs

    {-# NOINLINE [0] filterFB #-}
    filterFB :: (a -> b -> b) -> (a -> Bool) -> a -> b -> b
    filterFB c p x r | p x       = x `c` r
                     | otherwise = 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.

    -- We write foldl as a non-recursive thing, so that it
    -- can be inlined, and then (often) strictness-analysed,
    -- and hence the classic space leak on foldl (+) 0 xs

    foldl        :: (b -> a -> b) -> b -> [a] -> b
    foldl f z0 xs0 = lgo z0 xs0
                 where
                    lgo z []     =  z
                    lgo z (x:xs) = lgo (f z x) xs

    -- | '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                   :: (b -> a -> b) -> b -> [a] -> [b]
    scanl f q ls            =  q : (case ls of
                                    []   -> []
                                    x:xs -> scanl f (f q x) xs)

    -- | 'scanl1' is a variant of 'scanl' that has no starting value argument:
    --
    -- > scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]

    scanl1                  :: (a -> a -> a) -> [a] -> [a]
    scanl1 f (x:xs)         =  scanl f x xs
    scanl1 _ []             =  []

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

    -- | 'foldr1' is a variant of 'foldr' that has no starting value argument,
    -- and thus must be applied to non-empty lists.

    foldr1                  :: (a -> a -> a) -> [a] -> a
    foldr1 _ [x]            =  x
    foldr1 f (x:xs)         =  f x (foldr1 f xs)
    foldr1 _ []             =  errorEmptyList "foldr1"

    -- | 'scanr' is the right-to-left dual of 'scanl'.
    -- Note that
    --
    -- > head (scanr f z xs) == foldr f z xs.

    scanr                   :: (a -> b -> b) -> b -> [a] -> [b]
    scanr _ q0 []           =  [q0]
    scanr f q0 (x:xs)       =  f x q : qs
                               where qs@(q:_) = scanr f q0 xs

    -- | 'scanr1' is a variant of 'scanr' that has no starting value argument.

    scanr1                  :: (a -> a -> a) -> [a] -> [a]
    scanr1 _ []             =  []
    scanr1 _ [x]            =  [x]
    scanr1 f (x:xs)         =  f x q : qs
                               where qs@(q:_) = scanr1 f xs

    -- | 'iterate' @f x@ returns an infinite list of repeated applications
    -- of @f@ to @x@:
    --
    -- > iterate f x == [x, f x, f (f x), ...]

    {-# NOINLINE [1] iterate #-}
    iterate :: (a -> a) -> a -> [a]
    iterate f x =  x : iterate f (f x)

    {-# NOINLINE [0] iterateFB #-}
    iterateFB :: (a -> b -> b) -> (a -> a) -> a -> b
    iterateFB c f x = x `c` iterateFB c f (f x)

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

    -- | 'repeat' @x@ is an infinite list, with @x@ the value of every element.
    repeat :: a -> [a]
    {-# INLINE [0] repeat #-}
    -- The pragma just gives the rules more chance to fire
    repeat x = xs where xs = x : xs

    {-# INLINE [0] repeatFB #-}     -- ditto
    repeatFB :: (a -> b -> b) -> a -> b
    repeatFB c x = xs where xs = x `c` 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.
    {-# INLINE replicate #-}
    replicate               :: Int -> a -> [a]
    replicate n x           =  take n (repeat 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                   :: [a] -> [a]
    cycle []                = error "Prelude.cycle: empty list"
    cycle xs                = xs' where xs' = xs ++ 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] == []
    --

    takeWhile               :: (a -> Bool) -> [a] -> [a]
    takeWhile _ []          =  []
    takeWhile p (x:xs)
                | p x       =  x : takeWhile p xs
                | otherwise =  []

    -- | '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 _ []          =  []
    dropWhile p xs@(x:xs')
                | p x       =  dropWhile p xs'
                | otherwise =  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]

    -- | '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]

    -- | '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])

    #ifdef USE_REPORT_PRELUDE
    take n _      | n <= 0 =  []
    take _ []              =  []
    take n (x:xs)          =  x : take (n-1) xs

    drop n xs     | n <= 0 =  xs
    drop _ []              =  []
    drop n (_:xs)          =  drop (n-1) xs

    splitAt n xs           =  (take n xs, drop n xs)

    #else /* hack away */
    {-# RULES
    "take"     [~1] forall n xs . take n xs = takeFoldr n xs
    "takeList"  [1] forall n xs . foldr (takeFB (:) []) (takeConst []) xs n = takeUInt n xs
     #-}

    {-# INLINE takeFoldr #-}
    takeFoldr :: Int -> [a] -> [a]
    takeFoldr (I# n#) xs
      = build (\c nil -> if isTrue# (n# <=# 0#) then nil else
                         foldr (takeFB c nil) (takeConst nil) xs n#)

    {-# NOINLINE [0] takeConst #-}
    -- just a version of const that doesn't get inlined too early, so we
    -- can spot it in rules.  Also we need a type sig due to the unboxed Int#.
    takeConst :: a -> Int# -> a
    takeConst x _ = x

    {-# NOINLINE [0] takeFB #-}
    takeFB :: (a -> b -> b) -> b -> a -> (Int# -> b) -> Int# -> b
    takeFB c n x xs m | isTrue# (m <=# 1#) = x `c` n
                      | otherwise          = x `c` xs (m -# 1#)

    {-# INLINE [0] take #-}
    take (I# n#) xs = takeUInt n# xs

    -- The general code for take, below, checks n <= maxInt
    -- No need to check for maxInt overflow when specialised
    -- at type Int or Int# since the Int must be <= maxInt

    takeUInt :: Int# -> [b] -> [b]
    takeUInt n xs
      | isTrue# (n >=# 0#) = take_unsafe_UInt n xs
      | otherwise          = []

    take_unsafe_UInt :: Int# -> [b] -> [b]
    take_unsafe_UInt 0#  _  = []
    take_unsafe_UInt m   ls =
      case ls of
        []     -> []
        (x:xs) -> x : take_unsafe_UInt (m -# 1#) xs

    takeUInt_append :: Int# -> [b] -> [b] -> [b]
    takeUInt_append n xs rs
      | isTrue# (n >=# 0#) = take_unsafe_UInt_append n xs rs
      | otherwise          = []

    take_unsafe_UInt_append :: Int# -> [b] -> [b] -> [b]
    take_unsafe_UInt_append 0#  _ rs  = rs
    take_unsafe_UInt_append m  ls rs  =
      case ls of
        []     -> rs
        (x:xs) -> x : take_unsafe_UInt_append (m -# 1#) xs rs

    drop (I# n#) ls
      | isTrue# (n# <# 0#) = ls
      | otherwise          = drop# n# ls
        where
            drop# :: Int# -> [a] -> [a]
            drop# 0# xs      = xs
            drop# _  xs@[]   = xs
            drop# m# (_:xs)  = drop# (m# -# 1#) xs

    splitAt (I# n#) ls
      | isTrue# (n# <# 0#) = ([], ls)
      | otherwise          = splitAt# n# ls
        where
            splitAt# :: Int# -> [a] -> ([a], [a])
            splitAt# 0# xs     = ([], xs)
            splitAt# _  xs@[]  = (xs, xs)
            splitAt# m# (x:xs) = (x:xs', xs'')
              where
                (xs', xs'') = splitAt# (m# -# 1#) 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 _ xs@[]            =  (xs, xs)
    span p xs@(x:xs')
             | p x          =  let (ys,zs) = span p xs' in (x:ys,zs)
             | otherwise    =  ([],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])
    #ifdef USE_REPORT_PRELUDE
    break p                 =  span (not . p)
    #else
    -- HBC version (stolen)
    break _ xs@[]           =  (xs, xs)
    break p xs@(x:xs')
               | p x        =  ([],xs)
               | otherwise  =  let (ys,zs) = break p xs' in (x:ys,zs)
    #endif

    -- | 'reverse' @xs@ returns the elements of @xs@ in reverse order.
    -- @xs@ must be finite.
    reverse                 :: [a] -> [a]
    #ifdef USE_REPORT_PRELUDE
    reverse                 =  foldl (flip (:)) []
    #else
    reverse l =  rev l []
      where
        rev []     a = a
        rev (x:xs) a = rev xs (x: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                     :: [Bool] -> Bool

    -- | '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                      :: [Bool] -> Bool
    #ifdef USE_REPORT_PRELUDE
    and                     =  foldr (&&) True
    or                      =  foldr (||) False
    #else
    and []          =  True
    and (x:xs)      =  x && and xs
    or []           =  False
    or (x:xs)       =  x || or xs

    {-# NOINLINE [1] and #-}
    {-# NOINLINE [1] or #-}

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

    -- | 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                     :: (a -> Bool) -> [a] -> Bool
    #ifdef USE_REPORT_PRELUDE
    any p                   =  or . map p
    all p                   =  and . map p
    #else
    any _ []        = False
    any p (x:xs)    = p x || any p xs

    all _ []        =  True
    all p (x:xs)    =  p x && all p xs

    {-# NOINLINE [1] any #-}
    {-# NOINLINE [1] all #-}

    {-# RULES
    "any/build"     forall p (g::forall b.(a->b->b)->b->b) .
                    any p (build g) = g ((||) . p) False
    "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.
    elem                    :: (Eq a) => a -> [a] -> Bool

    -- | 'notElem' is the negation of 'elem'.
    notElem                 :: (Eq a) => a -> [a] -> Bool
    #ifdef USE_REPORT_PRELUDE
    elem x                  =  any (== x)
    notElem x               =  all (/= x)
    #else
    elem _ []       = False
    elem x (y:ys)   = x==y || elem x ys

    notElem _ []    =  True
    notElem x (y:ys)=  x /= y && notElem x ys
    #endif

    -- | 'lookup' @key assocs@ looks up a key in an association list.
    lookup                  :: (Eq a) => a -> [(a,b)] -> Maybe b
    lookup _key []          =  Nothing
    lookup  key ((x,y):xys)
        | key == x          =  Just y
        | otherwise         =  lookup key xys

    -- | Map a function over a list and concatenate the results.
    concatMap               :: (a -> [b]) -> [a] -> [b]
    concatMap f             =  foldr ((++) . f) []

    -- | Concatenate a list of lists.
    concat :: [[a]] -> [a]
    concat = foldr (++) []

    {-# 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
     #-}

\end{code} \begin{code}

    -- | 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] -> Int -> a
    #ifdef USE_REPORT_PRELUDE
    xs     !! n | n < 0 =  error "Prelude.!!: negative index"
    []     !! _         =  error "Prelude.!!: index too large"
    (x:_)  !! 0         =  x
    (_:xs) !! n         =  xs !! (n-1)
    #else
    -- HBC version (stolen), then unboxified
    -- The semantics is not quite the same for error conditions
    -- in the more efficient version.
    --
    xs !! (I# n0) | isTrue# (n0 <# 0#) =  error "Prelude.(!!): negative index\n"
                  | otherwise          =  sub xs n0
                             where
                                sub :: [a] -> Int# -> a
                                sub []     _ = error "Prelude.(!!): index too large\n"
                                sub (y:ys) n = if isTrue# (n ==# 0#)
                                               then y
                                               else sub ys (n -# 1#)
    #endif

\end{code} %********************************************************* %* * \subsection{The zip family} %* * %********************************************************* \begin{code}

    foldr2 :: (a -> b -> c -> c) -> c -> [a] -> [b] -> c
    foldr2 k z = go
      where
    	go []    _ys     = z
    	go _xs   []      = z
    	go (x:xs) (y:ys) = k x y (go xs ys)
    {-# INLINE [0] foldr2 #-}

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

    foldr2_right :: (a -> b -> c -> d) -> d -> b -> ([a] -> c) -> [a] -> d
    foldr2_right _k z  _y _r []     = z
    foldr2_right  k _z  y  r (x:xs) = k x y (r xs)

    -- foldr2 k z xs ys = foldr (foldr2_left k z)  (\_ -> z) xs ys
    -- foldr2 k z xs ys = foldr (foldr2_right k z) (\_ -> z) ys xs
    {-# RULES
    "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

    "foldr2/right"  forall k z xs (g::forall b.(a->b->b)->b->b) .
                      foldr2 k z xs (build g) = g (foldr2_right k z) (\_ -> z) xs
     #-}

\end{code} The foldr2/right rule isn't exactly right, because it changes the strictness of foldr2 (and thereby zip) E.g. main = print (null (zip nonobviousNil (build undefined))) where nonobviousNil = f 3 f n = if n == 0 then [] else f (n-1) I'm going to leave it though. Zips for larger tuples are in the List module. \begin{code}

    ----------------------------------------------
    -- | 'zip' takes two lists and returns a list of corresponding pairs.
    -- If one input list is short, excess elements of the longer list are
    -- discarded.
    {-# NOINLINE [1] zip #-}
    zip :: [a] -> [b] -> [(a,b)]
    zip (a:as) (b:bs) = (a,b) : zip as bs
    zip _      _      = []

    {-# INLINE [0] zipFB #-}
    zipFB :: ((a, b) -> c -> d) -> a -> b -> c -> d
    zipFB c = \x y r -> (x,y) `c` r

    {-# RULES
    "zip"      [~1] forall xs ys. zip xs ys = build (\c n -> foldr2 (zipFB c) n xs ys)
    "zipList"  [1]  foldr2 (zipFB (:)) []   = zip
     #-}

\end{code} \begin{code}

    ----------------------------------------------
    -- | 'zip3' takes three lists and returns a list of triples, analogous to
    -- 'zip'.
    zip3 :: [a] -> [b] -> [c] -> [(a,b,c)]
    -- Specification
    -- zip3 =  zipWith3 (,,)
    zip3 (a:as) (b:bs) (c:cs) = (a,b,c) : zip3 as bs cs
    zip3 _      _      _      = []

\end{code} -- The zipWith family generalises the zip family by zipping with the -- function given as the first argument, instead of a tupling function. \begin{code}

    ----------------------------------------------
    -- | 'zipWith' generalises 'zip' by zipping with the function given
    -- as the first argument, instead of a tupling function.
    -- For example, @'zipWith' (+)@ is applied to two lists to produce the
    -- list of corresponding sums.
    {-# NOINLINE [1] zipWith #-}
    zipWith :: (a->b->c) -> [a]->[b]->[c]
    zipWith f (a:as) (b:bs) = f a b : zipWith f as bs
    zipWith _ _      _      = []

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

    {-# RULES
    "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
      #-}

\end{code} \begin{code}

    -- | The 'zipWith3' function takes a function which combines three
    -- elements, as well as three lists and returns a list of their point-wise
    -- combination, analogous to 'zipWith'.
    zipWith3                :: (a->b->c->d) -> [a]->[b]->[c]->[d]
    zipWith3 z (a:as) (b:bs) (c:cs)
                            =  z a b c : zipWith3 z as bs cs
    zipWith3 _ _ _ _        =  []

    -- | 'unzip' transforms a list of pairs into a list of first components
    -- and a list of second components.
    unzip    :: [(a,b)] -> ([a],[b])
    {-# INLINE unzip #-}
    unzip    =  foldr (\(a,b) ~(as,bs) -> (a:as,b:bs)) ([],[])

    -- | The 'unzip3' function takes a list of triples and returns three
    -- lists, analogous to 'unzip'.
    unzip3   :: [(a,b,c)] -> ([a],[b],[c])
    {-# INLINE unzip3 #-}
    unzip3   =  foldr (\(a,b,c) ~(as,bs,cs) -> (a:as,b:bs,c:cs))
                      ([],[],[])

\end{code} %********************************************************* %* * \subsection{Error code} %* * %********************************************************* Common up near identical calls to `error' to reduce the number constant strings created when compiled: \begin{code}

    errorEmptyList :: String -> a
    errorEmptyList fun =
      error (prel_list_str ++ fun ++ ": empty list")

    prel_list_str :: String
    prel_list_str = "Prelude."

\end{code}