base-4.6.0.1: Basic libraries

Portability | portable
Stability | stable
Maintainer | libraries@haskell.org
Safe Haskell | Trustworthy

Data.List

Contents

- Basic functions
- List transformations
- Reducing lists (folds)
  - Special folds
- Building lists
  - Scans
  - Accumulating maps
  - Infinite lists
  - Unfolding
- Sublists
  - Extracting sublists
  - Predicates
- Searching lists
  - Searching by equality
  - Searching with a predicate
- Indexing lists
- Zipping and unzipping lists
- Special lists
  - Functions on strings
  - "Set" operations
  - Ordered lists
- Generalized functions
  - The "`By`" operations
    - User-supplied equality (replacing an `Eq` context)
    - User-supplied comparison (replacing an `Ord` context)
  - The "`generic`" operations

Description

Operations on lists.

Synopsis

- (++) :: [a] -> [a] -> [a]
- head :: [a] -> a
- last :: [a] -> a
- tail :: [a] -> [a]
- init :: [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 :: (a -> b -> a) -> a -> [b] -> a
- foldl' :: (a -> b -> a) -> a -> [b] -> a
- 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 :: (a -> b -> a) -> a -> [b] -> [a]
- 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]
- 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]
- 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 => [b] -> i
- genericTake :: Integral i => i -> [a] -> [a]
- genericDrop :: Integral i => i -> [a] -> [a]
- genericSplitAt :: Integral i => i -> [b] -> ([b], [b])
- genericIndex :: Integral a => [b] -> a -> b
- genericReplicate :: Integral i => i -> a -> [a]

# Basic functions

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

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] -> a

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

last :: [a] -> a

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

tail :: [a] -> [a]

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

init :: [a] -> [a]

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

null :: [a] -> Bool

Test whether a list is empty.

length :: [a] -> Int

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]

`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]

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

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

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 `(`concat` (`intersperse` xs xss))`. It inserts the list `xs` in between the lists in `xss` and concatenates the result.

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

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]]

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

`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] -> a

A strict version of `foldl`.

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.

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

A strict version of `foldl1`

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.

## Special folds

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

Concatenate a list of lists.

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

Map a function over a list and concatenate the results.

and :: [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.

or :: [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.

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.

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.

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

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

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

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

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.

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.

# Building lists

## Scans

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

`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]

`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]

`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]

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

## Accumulating maps

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

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])

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]

`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]

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

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.

cycle :: [a] -> [a]

`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]

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]

`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]

`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 `(`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]

`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]

`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]

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])

`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])

`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]

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.

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

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]]

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] -> Bool

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

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. Both lists must be finite.

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

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] -> 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.

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

`notElem` is the negation of `elem`.

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

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

## Searching with a predicate

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

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]

`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])

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 -> a

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 Int

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]

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 Int

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]

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)]

`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)]

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

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

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)]

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)]

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)]

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

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

`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]

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]

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]

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]

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]

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])

`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])

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

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

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])

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])

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])

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

# Special lists

## Functions on strings

lines :: String -> [String]

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

words :: String -> [String]

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

unlines :: [String] -> String

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

unwords :: [String] -> String

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

## "Set" operations

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

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]

`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]

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]

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

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

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]

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.

# 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]

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]

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

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.

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

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

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

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

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

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]

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

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

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.

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.

## The "`generic`" operations

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

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

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]

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

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 -> b

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.