{-# 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}