\begin{code}
-{-# OPTIONS -fno-implicit-prelude #-}
+{-# LANGUAGE CPP, NoImplicitPrelude, MagicHash #-}
+{-# OPTIONS_HADDOCK hide #-}
+
-----------------------------------------------------------------------------
-- |
-- Module : GHC.List
--
-----------------------------------------------------------------------------
+-- #hide
module GHC.List (
- -- [] (..), -- Not Haskell 98; built in syntax
+ -- [] (..), -- Not Haskell 98; built in syntax
map, (++), filter, concat,
- head, last, tail, init, null, length, (!!),
- foldl, foldl1, scanl, scanl1, foldr, foldr1, scanr, scanr1,
+ 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,
- maximum, minimum, concatMap,
+ concatMap,
zip, zip3, zipWith, zipWith3, unzip, unzip3,
-#ifdef USE_REPORT_PRELUDE
-
-#else
+ 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
\end{code}
%*********************************************************
-%* *
+%* *
\subsection{List-manipulation functions}
-%* *
+%* *
%*********************************************************
\begin{code}
--- head and tail extract the first element and remaining elements,
--- respectively, of a list, which must be non-empty. last and init
--- are the dual functions working from the end of a finite list,
--- rather than the beginning.
-
+-- | Extract the first element of a list, which must be non-empty.
head :: [a] -> a
head (x:_) = x
head [] = badHead
+badHead :: a
badHead = errorEmptyList "head"
-- This rule is useful in cases like
--- head [y | (x,y) <- ps, x==t]
+-- 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)
+"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 [] = errorEmptyList "last"
#else
-- eliminate repeated cases
-last [] = errorEmptyList "last"
-last (x:xs) = last' x xs
+last [] = errorEmptyList "last"
+last (x:xs) = last' x xs
where last' y [] = y
- last' _ (y:ys) = last' y ys
+ 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 [] = errorEmptyList "init"
init (x:xs) = init' x xs
where init' _ [] = []
- init' y (z:zs) = y : init' z zs
+ 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 genericLength, the result type of which may be
--- any kind of number.
+-- | /O(n)/. 'length' returns the length of a finite list as an 'Int'.
+-- It is an instance of the more general 'Data.List.genericLength',
+-- the result type of which may be any kind of number.
length :: [a] -> Int
length l = len l 0#
where
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', 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
+ | 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
+ | 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)
+"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.
-- 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
--- foldl1 is a variant that has no starting value argument, and thus must
--- be applied to non-empty lists. 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.
--- scanl1 is similar, again without the starting element:
--- scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
+-- | '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
+foldl f z0 xs0 = lgo z0 xs0
+ where
+ lgo z [] = z
+ lgo z (x:xs) = lgo (f z x) xs
-foldl1 :: (a -> a -> a) -> [a] -> a
-foldl1 f (x:xs) = foldl f x xs
-foldl1 _ [] = errorEmptyList "foldl1"
+-- | '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 :: (a -> a -> a) -> [a] -> [a]
-scanl1 f (x:xs) = scanl f x xs
-scanl1 _ [] = []
+-- | '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
+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), ...]
+-- | '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 :: (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
+"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' @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
+{-# 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
+"repeatFB" [1] repeatFB (:) = repeat
#-}
--- replicate n x is a list of length n with x the value of every element
+-- | '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,
+-- | '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'
+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. dropWhile p xs
--- returns the remaining suffix. Span p xs is equivalent to
--- (takeWhile p xs, dropWhile p xs), while break p uses the negation of p.
+-- | '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 _ [] = []
| 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. drop n xs returns the suffix of xs
--- after the first n elements, or [] if n > length xs. splitAt n xs
--- is equivalent to (take n xs, drop n xs).
-#ifdef USE_REPORT_PRELUDE
+-- | '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)@.
+-- '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 :: Int -> [a] -> [a]
drop n xs | n <= 0 = xs
drop _ [] = []
drop n (_:xs) = drop (n-1) xs
-splitAt :: Int -> [a] -> ([a],[a])
-splitAt n xs = (take n xs, drop n xs)
+splitAt n xs = (take n xs, drop n xs)
#else /* hack away */
-take :: Int -> [b] -> [b]
+{-# 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 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 | 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
| 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 =
+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 :: Int -> [b] -> [b]
drop (I# n#) ls
- | n# <# 0# = []
- | otherwise = drop# n# ls
+ | 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
+ drop# :: Int# -> [a] -> [a]
+ drop# 0# xs = xs
+ drop# _ xs@[] = xs
+ drop# m# (_:xs) = drop# (m# -# 1#) xs
-splitAt :: Int -> [b] -> ([b], [b])
splitAt (I# n#) ls
- | n# <# 0# = ([], ls)
- | otherwise = splitAt# 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
+ 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, break :: (a -> Bool) -> [a] -> ([a],[a])
+-- | '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 _ xs@[] = (xs, xs)
break p xs@(x:xs')
- | p x = ([],xs)
- | otherwise = let (ys,zs) = break p xs' in (x:ys,zs)
+ | 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' @xs@ returns the elements of @xs@ in reverse order.
+-- @xs@ must be finite.
reverse :: [a] -> [a]
#ifdef USE_REPORT_PRELUDE
reverse = foldl (flip (:)) []
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. or is the
--- disjunctive dual of and.
-and, or :: [Bool] -> Bool
+-- | '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
+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
+"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. Similarly, for all.
-any, all :: (a -> Bool) -> [a] -> Bool
+-- | 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
+any _ [] = False
+any p (x:xs) = p x || any p xs
-all _ [] = True
-all p (x:xs) = p x && all 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
+"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. notElem is the negation.
-elem, notElem :: (Eq a) => a -> [a] -> Bool
+-- | '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
+elem _ [] = False
+elem x (y:ys) = x==y || elem x ys
-notElem _ [] = True
+notElem _ [] = True
notElem x (y:ys)= x /= y && notElem x ys
#endif
--- lookup key assocs looks up a key in an association list.
+-- | '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
-
--- maximum and minimum return the maximum or minimum value from a list,
--- which must be non-empty, finite, and of an ordered type.
-{-# SPECIALISE maximum :: [Int] -> Int #-}
-{-# SPECIALISE minimum :: [Int] -> Int #-}
-maximum, minimum :: (Ord a) => [a] -> a
-maximum [] = errorEmptyList "maximum"
-maximum xs = foldl1 max xs
-
-minimum [] = errorEmptyList "minimum"
-minimum xs = foldl1 min xs
-
+-- | 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 (++) []
\begin{code}
--- List index (subscript) operator, 0-origin
+-- | 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"
-- 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
+xs !! (I# n0) | n0 <# 0# = error "Prelude.(!!): negative index\n"
+ | otherwise = sub xs n0
where
- sub :: [a] -> Int# -> a
+ 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#)
+ 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 :: (a -> b -> c -> c) -> c -> [a] -> [b] -> c
+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 :: (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/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
+"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}
I'm going to leave it though.
-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.
-zip3 takes three lists and returns a list of triples. Zips for larger
-tuples are in the List module.
+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
+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
+"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 (,,)
-- The zipWith family generalises the zip family 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.
-
\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 _ _ _ = []
+-- zipWithFB must have arity 2 since it gets two arguments in the "zipWith"
+-- rule; it might not get inlined otherwise
{-# INLINE [0] zipWithFB #-}
-zipWithFB c f x y r = (x `f` y) `c` r
+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
+"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 pair of lists.
+-- | '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))
%*********************************************************
-%* *
+%* *
\subsection{Error code}
-%* *
+%* *
%*********************************************************
Common up near identical calls to `error' to reduce the number
projects / ghc-base.git / blobdiff