List index (subscript) operator, starting from 0. Returns Nothing if the index is out of bounds

This is the total variant of the partial !! operator.

WARNING: This function takes linear time in the index.

Examples

>>> ['a', 'b', 'c'] !? 0
Just 'a'

>>> ['a', 'b', 'c'] !? 2
Just 'c'

>>> ['a', 'b', 'c'] !? 3
Nothing

>>> ['a', 'b', 'c'] !? (-1)
Nothing

The builtin linked list type.

In Haskell, lists are one of the most important data types as they are often used analogous to loops in imperative programming languages. These lists are singly linked, which makes them unsuited for operations that require \(\mathcal{O}(1)\) access. Instead, they are intended to be traversed.

You can use List a or [a] in type signatures:

length :: [a] -> Int

or

length :: List a -> Int

They are fully equivalent, and List a will be normalised to [a].

Usage

Lists are constructed recursively using the right-associative constructor operator (or cons) (:) :: a -> [a] -> [a], which prepends an element to a list, and the empty list [].

(1 : 2 : 3 : []) == (1 : (2 : (3 : []))) == [1, 2, 3]

Lists can also be constructed using list literals of the form [x_1, x_2, ..., x_n] which are syntactic sugar and, unless -XOverloadedLists is enabled, are translated into uses of (:) and []

String literals, like "I 💜 hs", are translated into Lists of characters, ['I', ' ', '💜', ' ', 'h', 's'].

Implementation

╭───┬───┬──╮   ╭───┬───┬──╮   ╭───┬───┬──╮   ╭────╮
│(:)│   │ ─┼──>│(:)│   │ ─┼──>│(:)│   │ ─┼──>│ [] │
╰───┴─┼─┴──╯   ╰───┴─┼─┴──╯   ╰───┴─┼─┴──╯   ╰────╯
      v              v              v
      1              2              3

Examples

>>> ['H', 'a', 's', 'k', 'e', 'l', 'l']
"Haskell"

>>> 1 : [4, 1, 5, 9]
[1,4,1,5,9]

>>> [] : [] : []
[[],[]]

Since: ghc-prim-0.10.0

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

Laziness

>>> take 1 (unfoldr (\x -> Just (x, undefined)) 'a')
"a"

Examples

>>> unfoldr (\b -> if b == 0 then Nothing else Just (b, b-1)) 10
[10,9,8,7,6,5,4,3,2,1]

>>> take 10 $ unfoldr (\(x, y) -> Just (x, (y, x + y))) (0, 1)
[0,1,1,2,3,5,8,13,21,54]

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.

The argument must be finite.

Examples

>>> sortOn fst [(2, "world"), (4, "!"), (1, "Hello")]
[(1,"Hello"),(2,"world"),(4,"!")]

>>> sortOn length ["jim", "creed", "pam", "michael", "dwight", "kevin"]
["jim","pam","creed","kevin","dwight","michael"]

Performance notes

>>> sortBy (comparing fst) [(3, 1), (2, 2), (1, 3)]
[(1,3),(2,2),(3,1)]

>>> (sortBy . comparing) fst [(3, 1), (2, 2), (1, 3)]
[(1,3),(2,2),(3,1)]

The transpose function transposes the rows and columns of its argument.

Laziness

>>> take 1 (transpose ['a' : undefined, 'b' : undefined])
["ab"]

Examples

>>> transpose [[1,2,3],[4,5,6]]
[[1,4],[2,5],[3,6]]

>>> transpose [[10,11],[20],[],[30,31,32]]
[[10,20,30],[11,31],[32]]

>>> transpose (repeat [])
* Hangs forever *

The sortBy function is the non-overloaded version of sort. The argument must be finite.

The supplied comparison relation is supposed to be reflexive and antisymmetric, otherwise, e. g., for _ _ -> GT, the ordered list simply does not exist. The relation is also expected to be transitive: if it is not then sortBy might fail to find an ordered permutation, even if it exists.

Examples

>>> sortBy (\(a,_) (b,_) -> compare a b) [(2, "world"), (4, "!"), (1, "Hello")]
[(1,"Hello"),(2,"world"),(4,"!")]

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.

Examples

>>> cycle []
*** Exception: Prelude.cycle: empty list

>>> take 10 (cycle [42])
[42,42,42,42,42,42,42,42,42,42]

>>> take 10 (cycle [2, 5, 7])
[2,5,7,2,5,7,2,5,7,2]

>>> take 1 (cycle (42 : undefined))
[42]

\(\mathcal{O}(n)\). 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]

Examples

>>> filter odd [1, 2, 3]
[1,3]

>>> filter (\l -> length l > 3) ["Hello", ", ", "World", "!"]
["Hello","World"]

>>> filter (/= 3) [1, 2, 3, 4, 3, 2, 1]
[1,2,4,2,1]

\(\mathcal{O}(\min(m,n))\). zip takes two lists and returns a list of corresponding pairs.

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.

Examples

>>> zip [1, 2, 3] ['a', 'b', 'c']
[(1,'a'),(2,'b'),(3,'c')]

>>> zip [1] ['a', 'b']
[(1,'a')]

>>> zip [1, 2] ['a']
[(1,'a')]

>>> zip [] [1..]
[]

>>> zip [1..] []
[]

\(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty.

To disable the warning about partiality put {-# OPTIONS_GHC -Wno-x-partial -Wno-unrecognised-warning-flags #-} at the top of the file. To disable it throughout a package put the same options into ghc-options section of Cabal file. To disable it in GHCi put :set -Wno-x-partial -Wno-unrecognised-warning-flags into ~/.ghci config file. See also the migration guide.

Examples

>>> head [1, 2, 3]
1

>>> head [1..]
1

>>> head []
*** Exception: Prelude.head: empty list

\(\mathcal{O}(1)\). Decompose a list into its head and tail.

• If the list is empty, returns Nothing.
• If the list is non-empty, returns Just (x, xs), where x is the head of the list and xs its tail.

@since base-4.8.0.0

Examples

>>> uncons []
Nothing

>>> uncons [1]
Just (1,[])

>>> uncons [1, 2, 3]
Just (1,[2,3])

\(\mathcal{O}(n)\). Decompose a list into init and last.

• If the list is empty, returns Nothing.
• If the list is non-empty, returns Just (xs, x), where xs is the initial part of the list and x is its last element.

unsnoc is dual to uncons: for a finite list xs

unsnoc xs = (\(hd, tl) -> (reverse tl, hd)) <$> uncons (reverse xs)

Examples

>>> unsnoc []
Nothing

>>> unsnoc [1]
Just ([],1)

>>> unsnoc [1, 2, 3]
Just ([1,2],3)

Laziness

>>> fst <$> unsnoc [undefined]
Just []

>>> head . fst <$> unsnoc (1 : undefined)
Just *** Exception: Prelude.undefined

>>> head . fst <$> unsnoc (1 : 2 : undefined)
Just 1

\(\mathcal{O}(1)\). Extract the elements after the head of a list, which must be non-empty.

To disable the warning about partiality put {-# OPTIONS_GHC -Wno-x-partial -Wno-unrecognised-warning-flags #-} at the top of the file. To disable it throughout a package put the same options into ghc-options section of Cabal file. To disable it in GHCi put :set -Wno-x-partial -Wno-unrecognised-warning-flags into ~/.ghci config file. See also the migration guide.

Examples

>>> tail [1, 2, 3]
[2,3]

>>> tail [1]
[]

>>> tail []
*** Exception: Prelude.tail: empty list

\(\mathcal{O}(n)\). Extract the last element of a list, which must be finite and non-empty.

WARNING: This function is partial. Consider using unsnoc instead.

Examples

>>> last [1, 2, 3]
3

>>> last [1..]
* Hangs forever *

>>> last []
*** Exception: Prelude.last: empty list

\(\mathcal{O}(n)\). Return all the elements of a list except the last one. The list must be non-empty.

WARNING: This function is partial. Consider using unsnoc instead.

Examples

>>> init [1, 2, 3]
[1,2]

>>> init [1]
[]

>>> init []
*** Exception: Prelude.init: empty list

Test whether the structure is empty. The default implementation is Left-associative and lazy in both the initial element and the accumulator. Thus optimised for structures where the first element can be accessed in constant time. Structures where this is not the case should have a non-default implementation.

Examples

>>> null []
True

>>> null [1]
False

>>> null [1..]
False

Returns the size/length of a finite structure as an Int. The default implementation just counts elements starting with the leftmost. Instances for structures that can compute the element count faster than via element-by-element counting, should provide a specialised implementation.

Examples

>>> length []
0

>>> length ['a', 'b', 'c']
3
>>> length [1..]
* Hangs forever *

A strict version of foldl1.

\(\mathcal{O}(n)\). 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

Examples

>>> 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"]

>>> take 10 (scanl (+) 0 [1..])
[0,1,3,6,10,15,21,28,36,45]

>>> take 1 (scanl undefined 'a' undefined)
"a"

\(\mathcal{O}(n)\). scanl1 is a variant of scanl that has no starting value argument:

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

Examples

>>> 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]

>>> take 10 (scanl1 (+) [1..])
[1,3,6,10,15,21,28,36,45,55]

>>> take 1 (scanl1 undefined ('a' : undefined))
"a"

\(\mathcal{O}(n)\). A strict version of scanl.

\(\mathcal{O}(n)\). 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.

Examples

>>> 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

\(\mathcal{O}(n)\). scanr1 is a variant of scanr that has no starting value argument.

Examples

>>> 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

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

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

Laziness

>>> take 1 $ iterate undefined 42
[42]

Examples

>>> take 10 $ iterate not True
[True,False,True,False,True,False,True,False,True,False]

>>> take 10 $ iterate (+3) 42
[42,45,48,51,54,57,60,63,66,69]

>>> take 10 $ iterate id 1
[1,1,1,1,1,1,1,1,1,1]

iterate' is the strict version of iterate.

It forces the result of each application of the function to weak head normal form (WHNF) before proceeding.

>>> take 1 $ iterate' undefined 42
*** Exception: Prelude.undefined

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

Examples

>>> take 10 $ repeat 17
[17,17,17,17,17,17,17,17,17, 17]

>>> repeat undefined
[*** Exception: Prelude.undefined

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.

Examples

>>> replicate 0 True
[]

>>> replicate (-1) True
[]

>>> replicate 4 True
[True,True,True,True]

takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p.

Laziness

>>> takeWhile (const False) undefined
*** Exception: Prelude.undefined

>>> takeWhile (const False) (undefined : undefined)
[]

>>> take 1 (takeWhile (const True) (1 : undefined))
[1]

Examples

>>> 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 p xs returns the suffix remaining after takeWhile p xs.

Examples

>>> 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]

take n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n >= length xs.

It is an instance of the more general genericTake, in which n may be of any integral type.

Laziness

>>> take 0 undefined
[]
>>> take 2 (1 : 2 : undefined)
[1,2]

Examples

>>> 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]
[]

drop n xs returns the suffix of xs after the first n elements, or [] if n >= length xs.

It is an instance of the more general genericDrop, in which n may be of any integral type.

Examples

>>> 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]

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 is an instance of the more general genericSplitAt, in which n may be of any integral type.

Laziness

>>> fst (splitAt 0 undefined)
[]

>>> take 1 (fst (splitAt 10 (1 : undefined)))
[1]

Examples

>>> 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])

span, applied to a predicate p and a list xs, returns a tuple where first element is the longest prefix (possibly empty) of xs of elements that satisfy p and second element is the remainder of the list:

span p xs is equivalent to (takeWhile p xs, dropWhile p xs), even if p is _|_.

Laziness

>>> span undefined []
([],[])
>>> fst (span (const False) undefined)
*** Exception: Prelude.undefined
>>> fst (span (const False) (undefined : undefined))
[]
>>> take 1 (fst (span (const True) (1 : undefined)))
[1]

>>> take 10 (fst (span (const True) [1..]))
[1,2,3,4,5,6,7,8,9,10]

Examples

>>> 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, 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 p is equivalent to span (not . p) and consequently to (takeWhile (not . p) xs, dropWhile (not . p) xs), even if p is _|_.

Laziness

>>> break undefined []
([],[])

>>> fst (break (const True) undefined)
*** Exception: Prelude.undefined

>>> fst (break (const True) (undefined : undefined))
[]

>>> take 1 (fst (break (const False) (1 : undefined)))
[1]

>>> take 10 (fst (break (const False) [1..]))
[1,2,3,4,5,6,7,8,9,10]

Examples

>>> 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],[])

\(\mathcal{O}(n)\). reverse xs returns the elements of xs in reverse order. xs must be finite.

Laziness

>>> head (reverse [undefined, 1])
1

>>> reverse (1 : 2 : undefined)
*** Exception: Prelude.undefined

Examples

>>> reverse []
[]

>>> reverse [42]
[42]

>>> reverse [2,5,7]
[7,5,2]

>>> reverse [1..]
* Hangs forever *

and returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.

Examples

>>> and []
True

>>> and [True]
True

>>> and [False]
False

>>> and [True, True, False]
False

>>> and (False : repeat True) -- Infinite list [False,True,True,True,...
False

>>> and (repeat True)
* Hangs forever *

or returns the disjunction of a container of Bools. For the result to be False, the container must be finite; True, however, results from a True value finitely far from the left end.

Examples

>>> or []
False

>>> or [True]
True

>>> or [False]
False

>>> or [True, True, False]
True

>>> or (True : repeat False) -- Infinite list [True,False,False,False,...
True

>>> or (repeat False)
* Hangs forever *

Determines whether any element of the structure satisfies the predicate.

Examples

>>> 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 *

Determines whether all elements of the structure satisfy the predicate.

Examples

>>> 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 *

notElem is the negation of elem.

Examples

>>> 3 `notElem` []
True

>>> 3 `notElem` [1,2]
True

>>> 3 `notElem` [1,2,3,4,5]
False

>>> 3 `notElem` [1..]
False

>>> 3 `notElem` ([4..] ++ [3])
* Hangs forever *

\(\mathcal{O}(n)\). lookup key assocs looks up a key in an association list. For the result to be Nothing, the list must be finite.

Examples

>>> lookup 2 []
Nothing

>>> lookup 2 [(1, "first")]
Nothing

>>> lookup 2 [(1, "first"), (2, "second"), (3, "third")]
Just "second"

Map a function over all the elements of a container and concatenate the resulting lists.

Examples

>>> concatMap (take 3) [[1..], [10..], [100..], [1000..]]
[1,2,3,10,11,12,100,101,102,1000,1001,1002]

>>> concatMap (take 3) (Just [1..])
[1,2,3]

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

WARNING: This function is partial, and should only be used if you are sure that the indexing will not fail. Otherwise, use !?.

WARNING: This function takes linear time in the index.

Examples

>>> ['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

zip3 takes three lists and returns a list of triples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

\(\mathcal{O}(\min(m,n))\). 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..]

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.

Examples

>>> zipWith (+) [1, 2, 3] [4, 5, 6]
[5,7,9]

>>> zipWith (++) ["hello ", "foo"] ["world!", "bar"]
["hello world!","foobar"]

\(\mathcal{O}(\min(l,m,n))\). 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..]

Examples

>>> zipWith3 (\x y z -> [x, y, z]) "123" "abc" "xyz"
["1ax","2by","3cz"]

>>> zipWith3 (\x y z -> (x * y) + z) [1, 2, 3] [4, 5, 6] [7, 8, 9]
[11,18,27]

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

Examples

>>> unzip []
([],[])

>>> unzip [(1, 'a'), (2, 'b')]
([1,2],"ab")

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

Examples

>>> unzip3 []
([],[],[])

>>> unzip3 [(1, 'a', True), (2, 'b', False)]
([1,2],"ab",[True,False])

The find function takes a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

Examples

>>> find (> 42) [0, 5..]
Just 45

>>> find (> 12) [1..7]
Nothing

The dropWhileEnd function drops the largest suffix of a list in which the given predicate holds for all elements.

Laziness

>>> take 1 (dropWhileEnd (< 0) (1 : undefined))
[1]

>>> take 1 (reverse $ dropWhile (< 0) $ reverse (1 : undefined))
*** Exception: Prelude.undefined

>>> last (dropWhileEnd (< 0) [undefined, 1])
*** Exception: Prelude.undefined

>>> last (reverse $ dropWhile (< 0) $ reverse [undefined, 1])
1

Examples

>>> dropWhileEnd isSpace "foo\n"
"foo"

>>> dropWhileEnd isSpace "foo bar"
"foo bar"
>>> dropWhileEnd (> 10) [1..20]
[1,2,3,4,5,6,7,8,9,10]

\(\mathcal{O}(\min(m,n))\). 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.

Examples

>>> stripPrefix "foo" "foobar"
Just "bar"

>>> stripPrefix "foo" "foo"
Just ""

>>> stripPrefix "foo" "barfoo"
Nothing

>>> stripPrefix "foo" "barfoobaz"
Nothing

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. For the result to be Nothing, the list must be finite.

Examples

>>> elemIndex 4 [0..]
Just 4

>>> elemIndex 'o' "haskell"
Nothing

>>> elemIndex 0 [1..]
* hangs forever *

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

Examples

>>> elemIndices 'o' "Hello World"
[4,7]

>>> elemIndices 1 [1, 2, 3, 1, 2, 3]
[0,3]

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. For the result to be Nothing, the list must be finite.

Examples

>>> findIndex isSpace "Hello World!"
Just 5

>>> findIndex odd [0, 2, 4, 6]
Nothing

>>> findIndex even [1..]
Just 1

>>> findIndex odd [0, 2 ..]
* hangs forever *

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

Examples

>>> findIndices (`elem` "aeiou") "Hello World!"
[1,4,7]

>>> findIndices (\l -> length l > 3) ["a", "bcde", "fgh", "ijklmnop"]
[1,3]

\(\mathcal{O}(\min(m,n))\). The isPrefixOf function takes two lists and returns True iff the first list is a prefix of the second.

Examples

>>> "Hello" `isPrefixOf` "Hello World!"
True

>>> "Hello" `isPrefixOf` "Wello Horld!"
False

>>> [0..] `isPrefixOf` [1..]
False

>>> [0..] `isPrefixOf` [0..99]
False

>>> [0..99] `isPrefixOf` [0..]
True

>>> [0..] `isPrefixOf` [0..]
* Hangs forever *

>>> isPrefixOf [] undefined
True

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

Examples

>>> "ld!" `isSuffixOf` "Hello World!"
True

>>> "World" `isSuffixOf` "Hello World!"
False

>>> [0..] `isSuffixOf` [0..99]
False

>>> [0..99] `isSuffixOf` [0..]
* Hangs forever *

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

Examples

>>> isInfixOf "Haskell" "I really like Haskell."
True

>>> isInfixOf "Ial" "I really like Haskell."
False

>>> [20..50] `isInfixOf` [0..]
True

>>> [0..] `isInfixOf` [20..50]
False

>>> [0..] `isInfixOf` [0..]
* Hangs forever *

\(\mathcal{O}(n^2)\). 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.

If there exists instance Ord a, it's faster to use nubOrd from the containers package (link to the latest online documentation), which takes only \(\mathcal{O}(n \log d)\) time where d is the number of distinct elements in the list.

Another approach to speed up nub is to use map Data.List.NonEmpty.head . Data.List.NonEmpty.group . sort, which takes \(\mathcal{O}(n \log n)\) time, requires instance Ord a and doesn't preserve the order.

Examples

>>> nub [1,2,3,4,3,2,1,2,4,3,5]
[1,2,3,4,5]

>>> nub "hello, world!"
"helo, wrd!"

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

Examples

>>> nubBy (\x y -> mod x 3 == mod y 3) [1,2,4,5,6]
[1,2,6]

>>> nubBy (/=) [2, 7, 1, 8, 2, 8, 1, 8, 2, 8]
[2,2,2]

>>> nubBy (>) [1, 2, 3, 2, 1, 5, 4, 5, 3, 2]
[1,2,3,5,5]

\(\mathcal{O}(n)\). delete x removes the first occurrence of x from its list argument.

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

Examples

>>> delete 'a' "banana"
"bnana"

>>> delete "not" ["haskell", "is", "not", "awesome"]
["haskell","is","awesome"]

\(\mathcal{O}(n)\). The deleteBy function behaves like delete, but takes a user-supplied equality predicate.

Examples

>>> deleteBy (<=) 4 [1..10]
[1,2,3,5,6,7,8,9,10]

>>> deleteBy (/=) 5 [5, 5, 4, 3, 5, 2]
[5,5,3,5,2]

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.

Examples

>>> "Hello World!" \\ "ell W"
"Hoorld!"

>>> take 5 ([0..] \\ [2..4])
[0,1,5,6,7]

>>> take 5 ([0..] \\ [2..])
* Hangs forever *

The union function returns the list union of the two lists. It is a special case of unionBy, which allows the programmer to supply their own equality test.

Examples

>>> "dog" `union` "cow"
"dogcw"

>>> import Data.Semigroup(Arg(..))
>>> union [Arg () "dog"] [Arg () "cow"]
[Arg () "dog"]
>>> union [] [Arg () "dog", Arg () "cow"]
[Arg () "dog"]

>>> "coot" `union` "duck"
"cootduk"
>>> "duck" `union` "coot"
"duckot"

>>> [0, 2 ..] `union` [1, 3 ..]
[0,2,4,6,8,10,12..

The unionBy function is the non-overloaded version of union. Both arguments may be infinite.

Examples

>>> unionBy (>) [3, 4, 5] [1, 2, 3, 4, 5, 6]
[3,4,5,4,5,6]

>>> import Data.Semigroup (Arg(..))
>>> unionBy (/=) [Arg () "Saul"] [Arg () "Kim"]
[Arg () "Saul", Arg () "Kim"]

The intersect function takes the list intersection of two lists. It is a special case of intersectBy, which allows the programmer to supply their own equality test.

Examples

>>> [1,2,3,4] `intersect` [2,4,6,8]
[2,4]

>>> import Data.Semigroup
>>> intersect [Arg () "dog"] [Arg () "cow", Arg () "cat"]
[Arg () "dog"]

>>> "coot" `intersect` "heron"
"oo"
>>> "heron" `intersect` "coot"
"o"

>>> intersect [100..] [0..]
[100,101,102,103...
>>> intersect [0] [1..]
* Hangs forever *
>>> intersect [1..] [0]
* Hangs forever *
>>> intersect (cycle [1..3]) [2]
[2,2,2,2...

The intersectBy function is the non-overloaded version of intersect. It is productive for infinite arguments only if the first one is a subset of the second.

\(\mathcal{O}(n)\). The intersperse function takes an element and a list and `intersperses' that element between the elements of the list.

Laziness

>>> take 1 (intersperse undefined ('a' : undefined))
"a"

>>> take 2 (intersperse ',' ('a' : undefined))
"a*** Exception: Prelude.undefined

Examples

>>> intersperse ',' "abcde"
"a,b,c,d,e"

>>> intersperse 1 [3, 4, 5]
[3,1,4,1,5]

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)

Examples

>>> partition (`elem` "aeiou") "Hello World!"
("eoo","Hll Wrld!")

>>> partition even [1..10]
([2,4,6,8,10],[1,3,5,7,9])

>>> partition (< 5) [1..10]
([1,2,3,4],[5,6,7,8,9,10])

\(\mathcal{O}(n)\). 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.

Examples

>>> insert (-1) [1, 2, 3]
[-1,1,2,3]

>>> insert 'd' "abcefg"
"abcdefg"

>>> insert 4 [1, 2, 3, 5, 6, 7]
[1,2,3,4,5,6,7]

\(\mathcal{O}(n)\). The non-overloaded version of insert.

Examples

>>> insertBy (\x y -> compare (length x) (length y)) [1, 2] [[1], [1, 2, 3], [1, 2, 3, 4]]
[[1],[1,2],[1,2,3],[1,2,3,4]]

\(\mathcal{O}(n)\). 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.

Examples

>>> genericLength [1, 2, 3] :: Int
3
>>> genericLength [1, 2, 3] :: Float
3.0

>>> genericLength [1..200] :: Int8
-56

The genericTake function is an overloaded version of take, which accepts any Integral value as the number of elements to take.

The genericDrop function is an overloaded version of drop, which accepts any Integral value as the number of elements to drop.

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

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

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

The zip4 function takes four lists and returns a list of quadruples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

The zip5 function takes five lists and returns a list of five-tuples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

The zip6 function takes six lists and returns a list of six-tuples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

The zip7 function takes seven lists and returns a list of seven-tuples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

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. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

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. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

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. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

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. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

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

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

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

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

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. This is the non-overloaded version of (\\).

(\\) == deleteFirstsBy (==)

The second list must be finite, but the first may be infinite.

Examples

>>> deleteFirstsBy (>) [1..10] [3, 4, 5]
[4,5,6,7,8,9,10]

>>> deleteFirstsBy (/=) [1..10] [1, 3, 5]
[4,5,6,7,8,9,10]

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 is non-empty, all elements are equal to the first one, and consecutive equal elements of the input end up in the same element of the output list.

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

It's often preferable to use Data.List.NonEmpty.group, which provides type-level guarantees of non-emptiness of inner lists. A common idiom to squash repeating elements map head . group is better served by map Data.List.NonEmpty.head . Data.List.NonEmpty.group because it avoids partial functions.

Examples

>>> group "Mississippi"
["M","i","ss","i","ss","i","pp","i"]

>>> group [1, 1, 1, 2, 2, 3, 4, 5, 5]
[[1,1,1],[2,2],[3],[4],[5,5]]

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

When a supplied relation is not transitive, it is important to remember that equality is checked against the first element in the group, not against the nearest neighbour:

>>> groupBy (\a b -> b - a < 5) [0..19]
[[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14],[15,16,17,18,19]]

It's often preferable to use Data.List.NonEmpty.groupBy, which provides type-level guarantees of non-emptiness of inner lists.

Examples

>>> groupBy (/=) [1, 1, 1, 2, 3, 1, 4, 4, 5]
[[1],[1],[1,2,3],[1,4,4,5]]

>>> groupBy (>) [1, 3, 5, 1, 4, 2, 6, 5, 4]
[[1],[3],[5,1,4,2],[6,5,4]]

>>> groupBy (const not) [True, False, True, False, False, False, True]
[[True,False],[True,False,False,False],[True]]

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

inits is semantically equivalent to map reverse . scanl (flip (:)) [], but under the hood uses a queue to amortize costs of reverse.

Laziness

Examples

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

>>> inits []
[[]]

>>> take 5 $ inits [1..]
[[],[1],[1,2],[1,2,3],[1,2,3,4]]

\(\mathcal{O}(n)\). The tails function returns all final segments of the argument, longest first.

Laziness

>>> tails undefined
[*** Exception: Prelude.undefined

>>> drop 1 (tails [undefined, 1, 2])
[[1, 2], [2], []]

Examples

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

>>> tails [1, 2, 3]
[[1,2,3],[2,3],[3],[]]

>>> tails []
[[]]

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

Laziness

>>> take 1 (subsequences undefined)
[[]]
>>> take 2 (subsequences ('a' : undefined))
["","a"]

Examples

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

>>> take 8 $ subsequences ['a'..]
["","a","b","ab","c","ac","bc","abc"]

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

Note that the order of permutations is not lexicographic. It satisfies the following property:

map (take n) (take (product [1..n]) (permutations ([1..n] ++ undefined))) == permutations [1..n]

Laziness

Examples

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

>>> permutations [1, 2]
[[1,2],[2,1]]

>>> permutations []
[[]]

>>> take 6 $ map (take 3) $ permutations ['a'..]
["abc","bac","cba","bca","cab","acb"]

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.

Elements are arranged from lowest to highest, keeping duplicates in the order they appeared in the input.

The argument must be finite.

Examples

>>> sort [1,6,4,3,2,5]
[1,2,3,4,5,6]

>>> sort "haskell"
"aehklls"

>>> import Data.Semigroup(Arg(..))
>>> sort [Arg ":)" 0, Arg ":D" 0, Arg ":)" 1, Arg ":3" 0, Arg ":D" 1]
[Arg ":)" 0,Arg ":)" 1,Arg ":3" 0,Arg ":D" 0,Arg ":D" 1]

Construct a list from a single element.

Examples

>>> singleton True
[True]

>>> singleton [1, 2, 3]
[[1,2,3]]

>>> singleton 'c'
"c"

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

Examples

>>> mapAccumL (\a b -> (a + b, a)) 0 [1..10]
(55,[0,1,3,6,10,15,21,28,36,45])

>>> mapAccumL (\a b -> (a <> show b, a)) "0" [1..5]
("012345",["0","01","012","0123","01234"])

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

Examples

>>> mapAccumR (\a b -> (a + b, a)) 0 [1..10]
(55,[54,52,49,45,40,34,27,19,10,0])

>>> mapAccumR (\a b -> (a <> show b, a)) "0" [1..5]
("054321",["05432","0543","054","05","0"])

The isSubsequenceOf function takes two lists and returns True if all the elements of the first list occur, in order, in the second. The elements do not have to occur consecutively.

isSubsequenceOf x y is equivalent to x `elem` (subsequences y).

Note: isSubsequenceOf is often used in infix form.

@since base-4.8.0.0

Examples

>>> "GHC" `isSubsequenceOf` "The Glorious Haskell Compiler"
True

>>> ['a','d'..'z'] `isSubsequenceOf` ['a'..'z']
True

>>> [1..10] `isSubsequenceOf` [10,9..0]
False

>>> [0,2..10] `isSubsequenceOf` [0..]
True

>>> [0..] `isSubsequenceOf` [0,2..10]
False

>>> [0,2..] `isSubsequenceOf` [0..]
* Hangs forever*

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following:

Left identity

return a >>= k = k a

Right identity

m >>= return = m

Associativity

m >>= (\x -> k x >>= h) = (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

• pure = return

• m1 <*> m2 = m1 >>= (\x1 -> m2 >>= (\x2 -> return (x1 x2)))

The above laws imply:

• fmap f xs  =  xs >>= return . f

• (>>) = (*>)

and that pure and (<*>) satisfy the applicative functor laws.

The instances of Monad for List, Maybe and IO defined in the Prelude satisfy these laws.

A type f is a Functor if it provides a function fmap which, given any types a and b lets you apply any function from (a -> b) to turn an f a into an f b, preserving the structure of f. Furthermore f needs to adhere to the following:

Identity

fmap id == id

Composition

fmap (f . g) == fmap f . fmap g

Note, that the second law follows from the free theorem of the type fmap and the first law, so you need only check that the former condition holds. See these articles by School of Haskell or David Luposchainsky for an explanation.