(++) :: [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.
Extract the first element of a list, which must be non-empty.
Extract the last element of a list, which must be finite and non-empty.
Extract the elements after the head of a list, which must be non-empty.
Return all the elements of a list except the last one. The list must be non-empty.
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.
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 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"
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.
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.
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.
concatMap :: (a -> [b]) -> [a] -> [b]Source
Map a function over a list and concatenate the results.
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 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.
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.
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.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.
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), ...]
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.
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 ( 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]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.
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 _|_ = [] : _|_
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 _|_ = _|_ : _|_
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." == FalseSearching 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.
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
List index (subscript) operator, starting from 0. It is an instance of the more general genericIndex, which takes an index of any integral type.
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.
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 (+)
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.
lines :: String -> [String]Source
lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.
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.
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.
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)
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.
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.
Ord context)
The function is assumed to define a total ordering.
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.
generic" operations
The prefix `generic' indicates an overloaded function that is a generalized version of a Prelude function.
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