base-4.5.1.0: Basic libraries

Portabilityportable
Stabilitystable
Maintainer[email protected]
Safe HaskellTrustworthy

Data.List

Contents

Description

Operations on lists.

Synopsis

Basic functions

(++) :: [a] -> [a] -> [a]Source

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.

head :: [a] -> aSource

Extract the first element of a list, which must be non-empty.

last :: [a] -> aSource

Extract the last element of a list, which must be finite and non-empty.

tail :: [a] -> [a]Source

Extract the elements after the head of a list, which must be non-empty.

init :: [a] -> [a]Source

Return all the elements of a list except the last one. The list must be non-empty.

null :: [a] -> BoolSource

Test whether a list is empty.

length :: [a] -> IntSource

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.

List transformations

map :: (a -> b) -> [a] -> [b]Source

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, ...]

reverse :: [a] -> [a]Source

reverse xs returns the elements of xs in reverse order. xs must be finite.

intersperse :: a -> [a] -> [a]Source

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]Source

intercalate xs xss is equivalent to (concat (intersperse xs xss)). It inserts the list xs in between the lists in xss and concatenates the result.

transpose :: [[a]] -> [[a]]Source

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]]

subsequences :: [a] -> [[a]]Source

The subsequences function returns the list of all subsequences of the argument.

 subsequences "abc" == ["","a","b","ab","c","ac","bc","abc"]

permutations :: [a] -> [[a]]Source

The permutations function returns the list of all permutations of the argument.

 permutations "abc" == ["abc","bac","cba","bca","cab","acb"]

Reducing lists (folds)

foldl :: (a -> b -> a) -> a -> [b] -> aSource

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' :: (a -> b -> a) -> a -> [b] -> aSource

A strict version of foldl.

foldl1 :: (a -> a -> a) -> [a] -> aSource

foldl1 is a variant of foldl that has no starting value argument, and thus must be applied to non-empty lists.

foldl1' :: (a -> a -> a) -> [a] -> aSource

A strict version of foldl1

foldr :: (a -> b -> b) -> b -> [a] -> bSource

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] -> aSource

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

Special folds

concat :: [[a]] -> [a]Source

Concatenate a list of lists.

concatMap :: (a -> [b]) -> [a] -> [b]Source

Map a function over a list and concatenate the results.

and :: [Bool] -> BoolSource

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 :: [Bool] -> BoolSource

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.

any :: (a -> Bool) -> [a] -> BoolSource

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.

all :: (a -> Bool) -> [a] -> BoolSource

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.

sum :: Num a => [a] -> aSource

The sum function computes the sum of a finite list of numbers.

product :: Num a => [a] -> aSource

The product function computes the product of a finite list of numbers.

maximum :: Ord a => [a] -> aSource

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.

minimum :: Ord a => [a] -> aSource

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.

Building lists

Scans

scanl :: (a -> b -> a) -> a -> [b] -> [a]Source

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 :: (a -> a -> a) -> [a] -> [a]Source

scanl1 is a variant of scanl that has no starting value argument:

 scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]

scanr :: (a -> b -> b) -> b -> [a] -> [b]Source

scanr is the right-to-left dual of scanl. Note that

 head (scanr f z xs) == foldr f z xs.

scanr1 :: (a -> a -> a) -> [a] -> [a]Source

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

Accumulating maps

mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])Source

The mapAccumL function behaves like a combination of map and foldl; it applies a function to each element of a list, passing an accumulating parameter from left to right, and returning a final value of this accumulator together with the new list.

mapAccumR :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])Source

The mapAccumR function behaves like a combination of map and foldr; it applies a function to each element of a list, passing an accumulating parameter from right to left, and returning a final value of this accumulator together with the new list.

Infinite lists

iterate :: (a -> a) -> a -> [a]Source

iterate f x returns an infinite list of repeated applications of f to x:

 iterate f x == [x, f x, f (f x), ...]

repeat :: a -> [a]Source

repeat x is an infinite list, with x the value of every element.

replicate :: Int -> a -> [a]Source

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.

cycle :: [a] -> [a]Source

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.

Unfolding

unfoldr :: (b -> Maybe (a, b)) -> b -> [a]Source

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 :: Int -> [a] -> [a]Source

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 :: Int -> [a] -> [a]Source

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])Source

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 genericSplitAt, in which n may be of any integral type.

takeWhile :: (a -> Bool) -> [a] -> [a]Source

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] == []

dropWhile :: (a -> Bool) -> [a] -> [a]Source

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]

dropWhileEnd :: (a -> Bool) -> [a] -> [a]Source

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" ++ undefined

span :: (a -> Bool) -> [a] -> ([a], [a])Source

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)

break :: (a -> Bool) -> [a] -> ([a], [a])Source

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).

stripPrefix :: Eq a => [a] -> [a] -> Maybe [a]Source

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]]Source

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.

inits :: [a] -> [[a]]Source

The inits function returns all initial segments of the argument, shortest first. For example,

 inits "abc" == ["","a","ab","abc"]

Note that inits has the following strictness property: inits _|_ = [] : _|_

tails :: [a] -> [[a]]Source

The tails function returns all final segments of the argument, longest first. For example,

 tails "abc" == ["abc", "bc", "c",""]

Note that tails has the following strictness property: tails _|_ = _|_ : _|_

Predicates

isPrefixOf :: Eq a => [a] -> [a] -> BoolSource

The isPrefixOf function takes two lists and returns True iff the first list is a prefix of the second.

isSuffixOf :: Eq a => [a] -> [a] -> BoolSource

The isSuffixOf function takes two lists and returns True iff the first list is a suffix of the second. Both lists must be finite.

isInfixOf :: Eq a => [a] -> [a] -> BoolSource

The isInfixOf function takes two lists and returns True iff the first list is contained, wholly and intact, anywhere within the second.

Example:

isInfixOf "Haskell" "I really like Haskell." == True
isInfixOf "Ial" "I really like Haskell." == False

Searching lists

Searching by equality

elem :: Eq a => a -> [a] -> BoolSource

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.

notElem :: Eq a => a -> [a] -> BoolSource

notElem is the negation of elem.

lookup :: Eq a => a -> [(a, b)] -> Maybe bSource

lookup key assocs looks up a key in an association list.

Searching with a predicate

find :: (a -> Bool) -> [a] -> Maybe aSource

The find function takes a predicate and a list and returns the first element in the list matching the predicate, or Nothing if there is no such element.

filter :: (a -> Bool) -> [a] -> [a]Source

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]

partition :: (a -> Bool) -> [a] -> ([a], [a])Source

The partition function takes a predicate 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)

Indexing lists

These functions treat a list xs as a indexed collection, with indices ranging from 0 to length xs - 1.

(!!) :: [a] -> Int -> aSource

List index (subscript) operator, starting from 0. It is an instance of the more general genericIndex, which takes an index of any integral type.

elemIndex :: Eq a => a -> [a] -> Maybe IntSource

The elemIndex function returns the index of the first element in the given list which is equal (by ==) to the query element, or Nothing if there is no such element.

elemIndices :: Eq a => a -> [a] -> [Int]Source

The elemIndices function extends elemIndex, by returning the indices of all elements equal to the query element, in ascending order.

findIndex :: (a -> Bool) -> [a] -> Maybe IntSource

The findIndex function takes a predicate and a list and returns the index of the first element in the list satisfying the predicate, or Nothing if there is no such element.

findIndices :: (a -> Bool) -> [a] -> [Int]Source

The findIndices function extends findIndex, by returning the indices of all elements satisfying the predicate, in ascending order.

Zipping and unzipping lists

zip :: [a] -> [b] -> [(a, b)]Source

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 :: [a] -> [b] -> [c] -> [(a, b, c)]Source

zip3 takes three lists and returns a list of triples, analogous to zip.

zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)]Source

The zip4 function takes four lists and returns a list of quadruples, analogous to zip.

zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a, b, c, d, e)]Source

The zip5 function takes five lists and returns a list of five-tuples, analogous to zip.

zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [(a, b, c, d, e, f)]Source

The zip6 function takes six lists and returns a list of six-tuples, analogous to zip.

zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [(a, b, c, d, e, f, g)]Source

The zip7 function takes seven lists and returns a list of seven-tuples, analogous to zip.

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]Source

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.

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]Source

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.

zipWith4 :: (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]Source

The zipWith4 function takes a function which combines four elements, as well as four lists and returns a list of their point-wise combination, analogous to zipWith.

zipWith5 :: (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f]Source

The zipWith5 function takes a function which combines five elements, as well as five lists and returns a list of their point-wise combination, analogous to zipWith.

zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g]Source

The zipWith6 function takes a function which combines six elements, as well as six lists and returns a list of their point-wise combination, analogous to zipWith.

zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h]Source

The zipWith7 function takes a function which combines seven elements, as well as seven lists and returns a list of their point-wise combination, analogous to zipWith.

unzip :: [(a, b)] -> ([a], [b])Source

unzip transforms a list of pairs into a list of first components and a list of second components.

unzip3 :: [(a, b, c)] -> ([a], [b], [c])Source

The unzip3 function takes a list of triples and returns three lists, analogous to unzip.

unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d])Source

The unzip4 function takes a list of quadruples and returns four lists, analogous to unzip.

unzip5 :: [(a, b, c, d, e)] -> ([a], [b], [c], [d], [e])Source

The unzip5 function takes a list of five-tuples and returns five lists, analogous to unzip.

unzip6 :: [(a, b, c, d, e, f)] -> ([a], [b], [c], [d], [e], [f])Source

The unzip6 function takes a list of six-tuples and returns six lists, analogous to unzip.

unzip7 :: [(a, b, c, d, e, f, g)] -> ([a], [b], [c], [d], [e], [f], [g])Source

The unzip7 function takes a list of seven-tuples and returns seven lists, analogous to unzip.

Special lists

Functions on strings

lines :: String -> [String]Source

lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

words :: String -> [String]Source

words breaks a string up into a list of words, which were delimited by white space.

unlines :: [String] -> StringSource

unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.

unwords :: [String] -> StringSource

unwords is an inverse operation to words. It joins words with separating spaces.

"Set" operations

nub :: Eq a => [a] -> [a]Source

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.

delete :: Eq a => a -> [a] -> [a]Source

delete x removes the first occurrence of x from its list argument. For example,

 delete 'a' "banana" == "bnana"

It is a special case of deleteBy, which allows the programmer to supply their own equality test.

(\\) :: Eq a => [a] -> [a] -> [a]Source

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.

It is a special case of deleteFirstsBy, which allows the programmer to supply their own equality test.

union :: Eq a => [a] -> [a] -> [a]Source

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]Source

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.

Ordered lists

sort :: Ord a => [a] -> [a]Source

The sort function implements a stable sorting algorithm. It is a special case of sortBy, which allows the programmer to supply their own comparison function.

insert :: Ord a => a -> [a] -> [a]Source

The insert function takes an element and a list and inserts the element into the list at the last position where it is still 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.

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.

nubBy :: (a -> a -> Bool) -> [a] -> [a]Source

The nubBy function behaves just like nub, except it uses a user-supplied equality predicate instead of the overloaded == function.

deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]Source

The deleteBy function behaves like delete, but takes a user-supplied equality predicate.

deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]Source

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.

unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]Source

The unionBy function is the non-overloaded version of union.

intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]Source

The intersectBy function is the non-overloaded version of intersect.

groupBy :: (a -> a -> Bool) -> [a] -> [[a]]Source

The groupBy function is the non-overloaded version of group.

User-supplied comparison (replacing an Ord context)

The function is assumed to define a total ordering.

sortBy :: (a -> a -> Ordering) -> [a] -> [a]Source

The sortBy function is the non-overloaded version of sort.

insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]Source

The non-overloaded version of insert.

maximumBy :: (a -> a -> Ordering) -> [a] -> aSource

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.

minimumBy :: (a -> a -> Ordering) -> [a] -> aSource

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.

The "generic" operations

The prefix `generic' indicates an overloaded function that is a generalized version of a Prelude function.

genericLength :: Num i => [b] -> iSource

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.

genericTake :: Integral i => i -> [a] -> [a]Source

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]Source

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 -> [b] -> ([b], [b])Source

The genericSplitAt function is an overloaded version of splitAt, which accepts any Integral value as the position at which to split.

genericIndex :: Integral a => [b] -> a -> bSource

The genericIndex function is an overloaded version of !!, which accepts any Integral value as the index.

genericReplicate :: Integral i => i -> a -> [a]Source

The genericReplicate function is an overloaded version of replicate, which accepts any Integral value as the number of repetitions to make.