\begin{code}
{-# OPTIONS -fno-implicit-prelude #-}
-----------------------------------------------------------------------------
-- |
-- 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 (
-- [] (..), -- Not Haskell 98; built in syntax
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 {-# SOURCE #-} GHC.Err ( error )
import Data.Tuple
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
badHead = errorEmptyList "head"
-- This rule is useful in cases like
-- head [y | (x,y) <- ps, x==t]
{-# RULES
"head/build" forall (g::forall b.(Bool->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 finite and 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
-- | '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 :: [a] -> Int
length l = len l 0#
where
len :: [a] -> Int# -> Int
len [] a# = I# a#
len (_:xs) a# = len xs (a# +# 1#)
-- | '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 :: (a -> Bool) -> [a] -> [a]
filter _pred [] = []
filter pred (x:xs)
| pred x = x : filter pred xs
| otherwise = filter pred xs
{-# NOINLINE [0] filterFB #-}
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 :: (a -> b -> a) -> a -> [b] -> a
foldl f z xs = lgo z xs
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 :: (a -> b -> a) -> a -> [b] -> [a]
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 f [] = []
scanr1 f [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), ...]
iterate :: (a -> a) -> a -> [a]
iterate f x = x : iterate f (f x)
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 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.
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 :: (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 :: (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@.
-- 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@.
-- 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@ is equivalent to @('take' n xs, 'drop' n xs)@.
-- It 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 */
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
| 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
| 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
| n# <# 0# = []
| 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
| 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' @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' @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
{-# 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.
any :: (a -> Bool) -> [a] -> Bool
-- | Applied to a predicate and a list, 'all' determines if all elements
-- of the list satisfy the predicate.
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
{-# 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@.
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 (++) []
{-# 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# n) | n <# 0# = error "Prelude.(!!): negative index\n"
| otherwise = sub xs n
where
sub :: [a] -> Int# -> a
sub [] _ = error "Prelude.(!!): index too large\n"
sub (y:ys) n = if n ==# 0#
then y
else sub ys (n -# 1#)
#endif
\end{code}
%*********************************************************
%* *
\subsection{The zip family}
%* *
%*********************************************************
\begin{code}
foldr2 _k z [] _ys = z
foldr2 _k z _xs [] = z
foldr2 k z (x:xs) (y:ys) = k x y (foldr2 k z xs ys)
foldr2_left _k z _x _r [] = z
foldr2_left k _z x r (y:ys) = k x y (r ys)
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.
zip :: [a] -> [b] -> [(a,b)]
zip (a:as) (b:bs) = (a,b) : zip as bs
zip _ _ = []
{-# INLINE [0] zipFB #-}
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.
zipWith :: (a->b->c) -> [a]->[b]->[c]
zipWith f (a:as) (b:bs) = f a b : zipWith f as bs
zipWith _ _ _ = []
{-# INLINE [0] zipWithFB #-}
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}