| Copyright | (c) The University of Glasgow 2001 |
|---|---|
| License | BSD-style (see the file libraries/base/LICENSE) |
| Maintainer | libraries@haskell.org |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Safe |
| Language | Haskell2010 |
GHC.OldList
Description
This legacy module provides access to the list-specialised operations of Data.List. This module may go away again in future GHC versions and is provided as transitional tool to access some of the list-specialised operations that had to be generalised due to the implementation of the Foldable/Traversable-in-Prelude Proposal (FTP).
If the operations needed are available in GHC.List, it's recommended to avoid importing this module and use GHC.List instead for now.
Since: base-4.8.0.0
Synopsis
- (++) :: [a] -> [a] -> [a]
- head :: [a] -> a
- last :: [a] -> a
- tail :: [a] -> [a]
- init :: [a] -> [a]
- uncons :: [a] -> Maybe (a, [a])
- singleton :: a -> [a]
- null :: [a] -> Bool
- length :: [a] -> Int
- map :: (a -> b) -> [a] -> [b]
- reverse :: [a] -> [a]
- intersperse :: a -> [a] -> [a]
- intercalate :: [a] -> [[a]] -> [a]
- transpose :: [[a]] -> [[a]]
- subsequences :: [a] -> [[a]]
- permutations :: [a] -> [[a]]
- foldl :: forall a b. (b -> a -> b) -> b -> [a] -> b
- foldl' :: forall a b. (b -> a -> b) -> b -> [a] -> b
- foldl1 :: (a -> a -> a) -> [a] -> a
- foldl1' :: (a -> a -> a) -> [a] -> a
- foldr :: (a -> b -> b) -> b -> [a] -> b
- foldr1 :: (a -> a -> a) -> [a] -> a
- concat :: [[a]] -> [a]
- concatMap :: (a -> [b]) -> [a] -> [b]
- and :: [Bool] -> Bool
- or :: [Bool] -> Bool
- any :: (a -> Bool) -> [a] -> Bool
- all :: (a -> Bool) -> [a] -> Bool
- sum :: Num a => [a] -> a
- product :: Num a => [a] -> a
- maximum :: Ord a => [a] -> a
- minimum :: Ord a => [a] -> a
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- scanl' :: (b -> a -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
- mapAccumR :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
- iterate :: (a -> a) -> a -> [a]
- iterate' :: (a -> a) -> a -> [a]
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- cycle :: [a] -> [a]
- unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
- take :: Int -> [a] -> [a]
- drop :: Int -> [a] -> [a]
- splitAt :: Int -> [a] -> ([a], [a])
- takeWhile :: (a -> Bool) -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- dropWhileEnd :: (a -> Bool) -> [a] -> [a]
- span :: (a -> Bool) -> [a] -> ([a], [a])
- break :: (a -> Bool) -> [a] -> ([a], [a])
- stripPrefix :: Eq a => [a] -> [a] -> Maybe [a]
- group :: Eq a => [a] -> [[a]]
- inits :: [a] -> [[a]]
- tails :: [a] -> [[a]]
- isPrefixOf :: Eq a => [a] -> [a] -> Bool
- isSuffixOf :: Eq a => [a] -> [a] -> Bool
- isInfixOf :: Eq a => [a] -> [a] -> Bool
- elem :: Eq a => a -> [a] -> Bool
- notElem :: Eq a => a -> [a] -> Bool
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- find :: (a -> Bool) -> [a] -> Maybe a
- filter :: (a -> Bool) -> [a] -> [a]
- partition :: (a -> Bool) -> [a] -> ([a], [a])
- (!!) :: [a] -> Int -> a
- elemIndex :: Eq a => a -> [a] -> Maybe Int
- elemIndices :: Eq a => a -> [a] -> [Int]
- findIndex :: (a -> Bool) -> [a] -> Maybe Int
- findIndices :: (a -> Bool) -> [a] -> [Int]
- zip :: [a] -> [b] -> [(a, b)]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)]
- zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a, b, c, d, e)]
- zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [(a, b, c, d, e, f)]
- zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [(a, b, c, d, e, f, g)]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- zipWith4 :: (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]
- zipWith5 :: (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f]
- zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g]
- zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h]
- unzip :: [(a, b)] -> ([a], [b])
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d])
- unzip5 :: [(a, b, c, d, e)] -> ([a], [b], [c], [d], [e])
- unzip6 :: [(a, b, c, d, e, f)] -> ([a], [b], [c], [d], [e], [f])
- unzip7 :: [(a, b, c, d, e, f, g)] -> ([a], [b], [c], [d], [e], [f], [g])
- lines :: String -> [String]
- words :: String -> [String]
- unlines :: [String] -> String
- unwords :: [String] -> String
- nub :: Eq a => [a] -> [a]
- delete :: Eq a => a -> [a] -> [a]
- (\\) :: Eq a => [a] -> [a] -> [a]
- union :: Eq a => [a] -> [a] -> [a]
- intersect :: Eq a => [a] -> [a] -> [a]
- sort :: Ord a => [a] -> [a]
- sortOn :: Ord b => (a -> b) -> [a] -> [a]
- insert :: Ord a => a -> [a] -> [a]
- nubBy :: (a -> a -> Bool) -> [a] -> [a]
- deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
- deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
- sortBy :: (a -> a -> Ordering) -> [a] -> [a]
- insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
- maximumBy :: (a -> a -> Ordering) -> [a] -> a
- minimumBy :: (a -> a -> Ordering) -> [a] -> a
- genericLength :: Num i => [a] -> i
- genericTake :: Integral i => i -> [a] -> [a]
- genericDrop :: Integral i => i -> [a] -> [a]
- genericSplitAt :: Integral i => i -> [a] -> ([a], [a])
- genericIndex :: Integral i => [a] -> i -> a
- genericReplicate :: Integral i => i -> a -> [a]
Basic functions
(++) :: [a] -> [a] -> [a] infixr 5 #
Append two lists, i.e.,
[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
If the first list is not finite, the result is the first list.
\(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty.
>>>head [1, 2, 3]1>>>head [1..]1>>>head []*** Exception: Prelude.head: empty list
\(\mathcal{O}(n)\). Extract the last element of a list, which must be finite and non-empty.
>>>last [1, 2, 3]3>>>last [1..]* Hangs forever *>>>last []*** Exception: Prelude.last: empty list
\(\mathcal{O}(1)\). Extract the elements after the head of a list, which must be non-empty.
>>>tail [1, 2, 3][2,3]>>>tail [1][]>>>tail []*** Exception: Prelude.tail: empty list
\(\mathcal{O}(n)\). Return all the elements of a list except the last one. The list must be non-empty.
>>>init [1, 2, 3][1,2]>>>init [1][]>>>init []*** Exception: Prelude.init: empty list
\(\mathcal{O}(1)\). Test whether a list is empty.
>>>null []True>>>null [1]False>>>null [1..]False
\(\mathcal{O}(n)\). 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.
>>>length []0>>>length ['a', 'b', 'c']3>>>length [1..]* Hangs forever *
List transformations
map :: (a -> b) -> [a] -> [b] #
\(\mathcal{O}(n)\). map f xs is the list obtained by applying f to
each element of xs, i.e.,
map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]
>>>map (+1) [1, 2, 3][2,3,4]
reverse xs returns the elements of xs in reverse order.
xs must be finite.
>>>reverse [][]>>>reverse [42][42]>>>reverse [2,5,7][7,5,2]>>>reverse [1..]* Hangs forever *
intersperse :: a -> [a] -> [a] #
\(\mathcal{O}(n)\). The intersperse function takes an element and a list
and `intersperses' that element between the elements of the list. For
example,
>>>intersperse ',' "abcde""a,b,c,d,e"
intercalate :: [a] -> [[a]] -> [a] #
intercalate xs xss is equivalent to (.
It inserts the list concat (intersperse xs xss))xs in between the lists in xss and concatenates the
result.
>>>intercalate ", " ["Lorem", "ipsum", "dolor"]"Lorem, ipsum, dolor"
The transpose function transposes the rows and columns of its argument.
For example,
>>>transpose [[1,2,3],[4,5,6]][[1,4],[2,5],[3,6]]
If some of the rows are shorter than the following rows, their elements are skipped:
>>>transpose [[10,11],[20],[],[30,31,32]][[10,20,30],[11,31],[32]]
subsequences :: [a] -> [[a]] #
The subsequences function returns the list of all subsequences of the argument.
>>>subsequences "abc"["","a","b","ab","c","ac","bc","abc"]
permutations :: [a] -> [[a]] #
The permutations function returns the list of all permutations of the argument.
>>>permutations "abc"["abc","bac","cba","bca","cab","acb"]
Reducing lists (folds)
foldl :: forall a b. (b -> a -> b) -> b -> [a] -> b #
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.
>>>foldl (+) 0 [1..4]10>>>foldl (+) 42 []42>>>foldl (-) 100 [1..4]90>>>foldl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']"dcbafoo">>>foldl (+) 0 [1..]* Hangs forever *
foldl1 :: (a -> a -> a) -> [a] -> a #
foldl1 is a variant of foldl that has no starting value argument,
and thus must be applied to non-empty lists. Note that unlike foldl, the accumulated value must be of the same type as the list elements.
>>>foldl1 (+) [1..4]10>>>foldl1 (+) []*** Exception: Prelude.foldl1: empty list>>>foldl1 (-) [1..4]-8>>>foldl1 (&&) [True, False, True, True]False>>>foldl1 (||) [False, False, True, True]True>>>foldl1 (+) [1..]* Hangs forever *
foldr :: (a -> b -> b) -> b -> [a] -> b #
foldr, applied to a binary operator, a starting value (typically
the right-identity of the operator), and a list, reduces the list
using the binary operator, from right to left:
foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
foldr1 :: (a -> a -> a) -> [a] -> a #
foldr1 is a variant of foldr that has no starting value argument,
and thus must be applied to non-empty lists. Note that unlike foldr, the accumulated value must be of the same type as the list elements.
>>>foldr1 (+) [1..4]10>>>foldr1 (+) []*** Exception: Prelude.foldr1: empty list>>>foldr1 (-) [1..4]-2>>>foldr1 (&&) [True, False, True, True]False>>>foldr1 (||) [False, False, True, True]True>>>force $ foldr1 (+) [1..]*** Exception: stack overflow
Special folds
Concatenate a list of lists.
>>>concat [][]>>>concat [[42]][42]>>>concat [[1,2,3], [4,5], [6], []][1,2,3,4,5,6]
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 []True>>>and [True]True>>>and [False]False>>>and [True, True, False]False>>>and (False : repeat True) -- Infinite list [False,True,True,True,True,True,True...False>>>and (repeat True)* Hangs forever *
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 []False>>>or [True]True>>>or [False]False>>>or [True, True, False]True>>>or (True : repeat False) -- Infinite list [True,False,False,False,False,False,False...True>>>or (repeat False)* Hangs forever *
any :: (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 (> 3) []False>>>any (> 3) [1,2]False>>>any (> 3) [1,2,3,4,5]True>>>any (> 3) [1..]True>>>any (> 3) [0, -1..]* Hangs forever *
all :: (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 (> 3) []True>>>all (> 3) [1,2]False>>>all (> 3) [1,2,3,4,5]False>>>all (> 3) [1..]False>>>all (> 3) [4..]* Hangs forever *
The sum function computes the sum of a finite list of numbers.
>>>sum []0>>>sum [42]42>>>sum [1..10]55>>>sum [4.1, 2.0, 1.7]7.8>>>sum [1..]* Hangs forever *
product :: Num a => [a] -> a #
The product function computes the product of a finite list of numbers.
>>>product []1>>>product [42]42>>>product [1..10]3628800>>>product [4.1, 2.0, 1.7]13.939999999999998>>>product [1..]* Hangs forever *
maximum :: Ord a => [a] -> a #
maximum returns the maximum value from a list,
which must be non-empty, finite, and of an ordered type.
It is a special case of maximumBy, which allows the
programmer to supply their own comparison function.
>>>maximum []*** Exception: Prelude.maximum: empty list>>>maximum [42]42>>>maximum [55, -12, 7, 0, -89]55>>>maximum [1..]* Hangs forever *
minimum :: Ord a => [a] -> a #
minimum returns the minimum value from a list,
which must be non-empty, finite, and of an ordered type.
It is a special case of minimumBy, which allows the
programmer to supply their own comparison function.
>>>minimum []*** Exception: Prelude.minimum: empty list>>>minimum [42]42>>>minimum [55, -12, 7, 0, -89]-89>>>minimum [1..]* Hangs forever *
Building lists
Scans
scanl :: (b -> a -> b) -> b -> [a] -> [b] #
\(\mathcal{O}(n)\). 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 (+) 0 [1..4][0,1,3,6,10]>>>scanl (+) 42 [][42]>>>scanl (-) 100 [1..4][100,99,97,94,90]>>>scanl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']["foo","afoo","bafoo","cbafoo","dcbafoo"]>>>scanl (+) 0 [1..]* Hangs forever *
scanl1 :: (a -> a -> a) -> [a] -> [a] #
\(\mathcal{O}(n)\). scanl1 is a variant of scanl that has no starting
value argument:
scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
>>>scanl1 (+) [1..4][1,3,6,10]>>>scanl1 (+) [][]>>>scanl1 (-) [1..4][1,-1,-4,-8]>>>scanl1 (&&) [True, False, True, True][True,False,False,False]>>>scanl1 (||) [False, False, True, True][False,False,True,True]>>>scanl1 (+) [1..]* Hangs forever *
scanr :: (a -> b -> b) -> b -> [a] -> [b] #
\(\mathcal{O}(n)\). scanr is the right-to-left dual of scanl. Note that the order of parameters on the accumulating function are reversed compared to scanl.
Also note that
head (scanr f z xs) == foldr f z xs.
>>>scanr (+) 0 [1..4][10,9,7,4,0]>>>scanr (+) 42 [][42]>>>scanr (-) 100 [1..4][98,-97,99,-96,100]>>>scanr (\nextChar reversedString -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']["abcdfoo","bcdfoo","cdfoo","dfoo","foo"]>>>force $ scanr (+) 0 [1..]*** Exception: stack overflow
scanr1 :: (a -> a -> a) -> [a] -> [a] #
\(\mathcal{O}(n)\). scanr1 is a variant of scanr that has no starting
value argument.
>>>scanr1 (+) [1..4][10,9,7,4]>>>scanr1 (+) [][]>>>scanr1 (-) [1..4][-2,3,-1,4]>>>scanr1 (&&) [True, False, True, True][False,False,True,True]>>>scanr1 (||) [True, True, False, False][True,True,False,False]>>>force $ scanr1 (+) [1..]*** Exception: stack overflow
Accumulating maps
Infinite lists
iterate :: (a -> a) -> a -> [a] #
iterate f x returns an infinite list of repeated applications
of f to x:
iterate f x == [x, f x, f (f x), ...]
Note that iterate is lazy, potentially leading to thunk build-up if
the consumer doesn't force each iterate. See iterate' for a strict
variant of this function.
>>>take 10 $ iterate not True[True,False,True,False...>>>take 10 $ iterate (+3) 42[42,45,48,51,54,57,60,63...
repeat x is an infinite list, with x the value of every element.
>>>take 20 $ repeat 17[17,17,17,17,17,17,17,17,17...
replicate :: Int -> a -> [a] #
replicate n x is a list of length n with x the value of
every element.
It is an instance of the more general genericReplicate,
in which n may be of any integral type.
>>>replicate 0 True[]>>>replicate (-1) True[]>>>replicate 4 True[True,True,True,True]
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 []*** Exception: Prelude.cycle: empty list>>>take 20 $ cycle [42][42,42,42,42,42,42,42,42,42,42...>>>take 20 $ cycle [2, 5, 7][2,5,7,2,5,7,2,5,7,2,5,7...
Unfolding
unfoldr :: (b -> Maybe (a, b)) -> b -> [a] #
The unfoldr function is a `dual' to foldr: while foldr
reduces a list to a summary value, unfoldr builds a list from
a seed value. The function takes the element and returns Nothing
if it is done producing the list or returns Just (a,b), in which
case, a is a prepended to the list and b is used as the next
element in a recursive call. For example,
iterate f == unfoldr (\x -> Just (x, f x))
In some cases, unfoldr can undo a foldr operation:
unfoldr f' (foldr f z xs) == xs
if the following holds:
f' (f x y) = Just (x,y) f' z = Nothing
A simple use of unfoldr:
>>>unfoldr (\b -> if b == 0 then Nothing else Just (b, b-1)) 10[10,9,8,7,6,5,4,3,2,1]
Sublists
Extracting sublists
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 genericTake,
in which n may be of any integral type.
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 genericDrop,
in which n may be of any integral type.
splitAt :: Int -> [a] -> ([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 ( when take n xs, drop n xs)n is not _|_
(splitAt _|_ xs = _|_).
splitAt is an instance of the more general genericSplitAt,
in which n may be of any integral type.
takeWhile :: (a -> Bool) -> [a] -> [a] #
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][]
dropWhileEnd :: (a -> Bool) -> [a] -> [a] #
The dropWhileEnd function drops the largest suffix of a list
in which the given predicate holds for all elements. For example:
>>>dropWhileEnd isSpace "foo\n""foo"
>>>dropWhileEnd isSpace "foo bar""foo bar"
dropWhileEnd isSpace ("foo\n" ++ undefined) == "foo" ++ undefinedSince: base-4.5.0.0
span :: (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])
break :: (a -> Bool) -> [a] -> ([a], [a]) #
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],[])
stripPrefix :: Eq a => [a] -> [a] -> Maybe [a] #
\(\mathcal{O}(\min(m,n))\). The stripPrefix function drops the given
prefix from a list. It returns Nothing if the list did not start with the
prefix given, or Just the list after the prefix, if it does.
>>>stripPrefix "foo" "foobar"Just "bar"
>>>stripPrefix "foo" "foo"Just ""
>>>stripPrefix "foo" "barfoo"Nothing
>>>stripPrefix "foo" "barfoobaz"Nothing
group :: Eq a => [a] -> [[a]] #
The group function takes a list and returns a list of lists such
that the concatenation of the result is equal to the argument. Moreover,
each sublist in the result contains only equal elements. For example,
>>>group "Mississippi"["M","i","ss","i","ss","i","pp","i"]
It is a special case of groupBy, which allows the programmer to supply
their own equality test.
Predicates
isPrefixOf :: Eq a => [a] -> [a] -> Bool #
\(\mathcal{O}(\min(m,n))\). The isPrefixOf function takes two lists and
returns True iff the first list is a prefix of the second.
>>>"Hello" `isPrefixOf` "Hello World!"True
>>>"Hello" `isPrefixOf` "Wello Horld!"False
isSuffixOf :: Eq a => [a] -> [a] -> Bool #
The isSuffixOf function takes two lists and returns True iff
the first list is a suffix of the second. The second list must be
finite.
>>>"ld!" `isSuffixOf` "Hello World!"True
>>>"World" `isSuffixOf` "Hello World!"False
Searching lists
Searching by equality
elem :: Eq a => a -> [a] -> Bool infix 4 #
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.
>>>3 `elem` []False>>>3 `elem` [1,2]False>>>3 `elem` [1,2,3,4,5]True>>>3 `elem` [1..]True>>>3 `elem` [4..]* Hangs forever *
lookup :: Eq a => a -> [(a, b)] -> Maybe b #
\(\mathcal{O}(n)\). lookup key assocs looks up a key in an association
list.
>>>lookup 2 []Nothing>>>lookup 2 [(1, "first")]Nothing>>>lookup 2 [(1, "first"), (2, "second"), (3, "third")]Just "second"
Searching with a predicate
filter :: (a -> Bool) -> [a] -> [a] #
\(\mathcal{O}(n)\). 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 odd [1, 2, 3][1,3]
partition :: (a -> Bool) -> [a] -> ([a], [a]) #
The partition function takes a predicate and a list, and returns
the pair of lists of elements which do and do not satisfy the
predicate, respectively; i.e.,
partition p xs == (filter p xs, filter (not . p) xs)
>>>partition (`elem` "aeiou") "Hello World!"("eoo","Hll Wrld!")
Indexing lists
These functions treat a list xs as a indexed collection,
with indices ranging from 0 to .length xs - 1
(!!) :: [a] -> Int -> a infixl 9 #
List index (subscript) operator, starting from 0.
It is an instance of the more general genericIndex,
which takes an index of any integral type.
>>>['a', 'b', 'c'] !! 0'a'>>>['a', 'b', 'c'] !! 2'c'>>>['a', 'b', 'c'] !! 3*** Exception: Prelude.!!: index too large>>>['a', 'b', 'c'] !! (-1)*** Exception: Prelude.!!: negative index
elemIndices :: Eq a => a -> [a] -> [Int] #
The elemIndices function extends elemIndex, by returning the
indices of all elements equal to the query element, in ascending order.
>>>elemIndices 'o' "Hello World"[4,7]
findIndices :: (a -> Bool) -> [a] -> [Int] #
The findIndices function extends findIndex, by returning the
indices of all elements satisfying the predicate, in ascending order.
>>>findIndices (`elem` "aeiou") "Hello World!"[1,4,7]
Zipping and unzipping lists
zip :: [a] -> [b] -> [(a, b)] #
\(\mathcal{O}(\min(m,n))\). zip takes two lists and returns a list of
corresponding pairs.
>>>zip [1, 2] ['a', 'b'][(1,'a'),(2,'b')]
If one input list is shorter than the other, excess elements of the longer list are discarded, even if one of the lists is infinite:
>>>zip [1] ['a', 'b'][(1,'a')]>>>zip [1, 2] ['a'][(1,'a')]>>>zip [] [1..][]>>>zip [1..] [][]
zip is right-lazy:
>>>zip [] undefined[]>>>zip undefined []*** Exception: Prelude.undefined ...
zip is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] #
\(\mathcal{O}(\min(m,n))\). zipWith generalises zip by zipping with the
function given as the first argument, instead of a tupling function.
zipWith (,) xs ys == zip xs ys zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]
For example, is applied to two lists to produce the list of
corresponding sums:zipWith (+)
>>>zipWith (+) [1, 2, 3] [4, 5, 6][5,7,9]
zipWith is right-lazy:
>>>let f = undefined>>>zipWith f [] undefined[]
zipWith is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] #
The zipWith3 function takes a function which combines three
elements, as well as three lists and returns a list of the function applied
to corresponding elements, analogous to zipWith.
It is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
zipWith3 (,,) xs ys zs == zip3 xs ys zs zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..]
zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h] #
unzip :: [(a, b)] -> ([a], [b]) #
unzip transforms a list of pairs into a list of first components
and a list of second components.
>>>unzip []([],[])>>>unzip [(1, 'a'), (2, 'b')]([1,2],"ab")
Special lists
Functions on strings
lines breaks a string up into a list of strings at newline
characters. The resulting strings do not contain newlines.
Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,
>>>lines ""[]
>>>lines "\n"[""]
>>>lines "one"["one"]
>>>lines "one\n"["one"]
>>>lines "one\n\n"["one",""]
>>>lines "one\ntwo"["one","two"]
>>>lines "one\ntwo\n"["one","two"]
Thus contains at least as many elements as newlines in lines ss.
words breaks a string up into a list of words, which were delimited
by white space.
>>>words "Lorem ipsum\ndolor"["Lorem","ipsum","dolor"]
"Set" operations
\(\mathcal{O}(n^2)\). The nub function removes duplicate elements from a
list. In particular, it keeps only the first occurrence of each element. (The
name nub means `essence'.) It is a special case of nubBy, which allows
the programmer to supply their own equality test.
>>>nub [1,2,3,4,3,2,1,2,4,3,5][1,2,3,4,5]
(\\) :: Eq a => [a] -> [a] -> [a] infix 5 #
The \\ function is list difference (non-associative).
In the result of xs \\ ys, the first occurrence of each element of
ys in turn (if any) has been removed from xs. Thus
(xs ++ ys) \\ xs == ys.
>>>"Hello World!" \\ "ell W""Hoorld!"
It is a special case of deleteFirstsBy, which allows the programmer
to supply their own equality test.
union :: Eq a => [a] -> [a] -> [a] #
The union function returns the list union of the two lists.
For example,
>>>"dog" `union` "cow""dogcw"
Duplicates, and elements of the first list, are removed from the
the second list, but if the first list contains duplicates, so will
the result.
It is a special case of unionBy, which allows the programmer to supply
their own equality test.
intersect :: Eq a => [a] -> [a] -> [a] #
The intersect function takes the list intersection of two lists.
For example,
>>>[1,2,3,4] `intersect` [2,4,6,8][2,4]
If the first list contains duplicates, so will the result.
>>>[1,2,2,3,4] `intersect` [6,4,4,2][2,2,4]
It is a special case of intersectBy, which allows the programmer to
supply their own equality test. If the element is found in both the first
and the second list, the element from the first list will be used.
Ordered lists
sortOn :: Ord b => (a -> b) -> [a] -> [a] #
Sort a list by comparing the results of a key function applied to each
element. sortOn f is equivalent to sortBy (comparing f), but has the
performance advantage of only evaluating f once for each element in the
input list. This is called the decorate-sort-undecorate paradigm, or
Schwartzian transform.
Elements are arranged from lowest to highest, keeping duplicates in the order they appeared in the input.
>>>sortOn fst [(2, "world"), (4, "!"), (1, "Hello")][(1,"Hello"),(2,"world"),(4,"!")]
Since: base-4.8.0.0
insert :: Ord a => a -> [a] -> [a] #
\(\mathcal{O}(n)\). The insert function takes an element and a list and
inserts the element into the list at the first position where it is less than
or equal to the next element. In particular, if the list is sorted before the
call, the result will also be sorted. It is a special case of insertBy,
which allows the programmer to supply their own comparison function.
>>>insert 4 [1,2,3,5,6,7][1,2,3,4,5,6,7]
Generalized functions
The "By" operations
By convention, overloaded functions have a non-overloaded
counterpart whose name is suffixed with `By'.
It is often convenient to use these functions together with
on, for instance .sortBy (compare
`on` fst)
User-supplied equality (replacing an Eq context)
The predicate is assumed to define an equivalence.
deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a] #
The deleteFirstsBy function takes a predicate and two lists and
returns the first list with the first occurrence of each element of
the second list removed.
intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a] #
The intersectBy function is the non-overloaded version of intersect.
User-supplied comparison (replacing an Ord context)
The function is assumed to define a total ordering.
insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a] #
\(\mathcal{O}(n)\). The non-overloaded version of insert.
maximumBy :: (a -> a -> Ordering) -> [a] -> a #
The maximumBy function takes a comparison function and a list
and returns the greatest element of the list by the comparison function.
The list must be finite and non-empty.
We can use this to find the longest entry of a list:
>>>maximumBy (\x y -> compare (length x) (length y)) ["Hello", "World", "!", "Longest", "bar"]"Longest"
minimumBy :: (a -> a -> Ordering) -> [a] -> a #
The minimumBy function takes a comparison function and a list
and returns the least element of the list by the comparison function.
The list must be finite and non-empty.
We can use this to find the shortest entry of a list:
>>>minimumBy (\x y -> compare (length x) (length y)) ["Hello", "World", "!", "Longest", "bar"]"!"
The "generic" operations
The prefix `generic' indicates an overloaded function that
is a generalized version of a Prelude function.
genericLength :: Num i => [a] -> i #
\(\mathcal{O}(n)\). The genericLength function is an overloaded version
of length. In particular, instead of returning an Int, it returns any
type which is an instance of Num. It is, however, less efficient than
length.
>>>genericLength [1, 2, 3] :: Int3>>>genericLength [1, 2, 3] :: Float3.0
genericTake :: Integral i => i -> [a] -> [a] #
The genericTake function is an overloaded version of take, which
accepts any Integral value as the number of elements to take.
genericDrop :: Integral i => i -> [a] -> [a] #
The genericDrop function is an overloaded version of drop, which
accepts any Integral value as the number of elements to drop.
genericSplitAt :: Integral i => i -> [a] -> ([a], [a]) #
The genericSplitAt function is an overloaded version of splitAt, which
accepts any Integral value as the position at which to split.
genericIndex :: Integral i => [a] -> i -> a #
The genericIndex function is an overloaded version of !!, which
accepts any Integral value as the index.
genericReplicate :: Integral i => i -> a -> [a] #
The genericReplicate function is an overloaded version of replicate,
which accepts any Integral value as the number of repetitions to make.