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

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)...)

foldr' is a variant of foldr that begins list reduction from the last element and evaluates the accumulator strictly as it unwinds the stack back to the beginning of the list. The input list must be finite, otherwise foldr' runs out of space (diverges).

Note that if the function that combines the accumulated value with each element is strict in the accumulator, other than a possible improvement in the constant factor, you get the same \(\mathcal{O}(n)\) space cost as with just foldr.

If you want a strict right fold in constant space, you need a structure that supports faster than \(\mathcal{O}(n)\) access to the right-most element, such as Seq from the containers package.

Use of this function is a hint that the [] structure may be a poor fit for the task at hand. If the order in which the elements are combined is not important, use foldl' instead.

>>> foldr' (+) [1..4]  -- Use foldl' instead!
10
>>> foldr' (&&) [True, False, True, True] -- Use foldr instead!
False
>>> foldr' (||) [False, False, True, True] -- Use foldr instead!
True

foldr1 is a variant of foldr that has no starting value argument, and thus must be applied to non-empty lists. Note that unlike foldr, the accumulated value must be of the same type as the list elements.

>>> foldr1 (+) [1..4]
10
>>> foldr1 (+) []
*** Exception: Prelude.foldr1: empty list
>>> foldr1 (-) [1..4]
-2
>>> foldr1 (&&) [True, False, True, True]
False
>>> foldr1 (||) [False, False, True, True]
True
>>> force $ foldr1 (+) [1..]
*** Exception: stack overflow

foldl, applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn

The list must be finite.

>>> foldl (+) 0 [1..4]
10
>>> foldl (+) 42 []
42
>>> foldl (-) 100 [1..4]
90
>>> foldl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
"dcbafoo"
>>> foldl (+) 0 [1..]
* Hangs forever *

A strict version of foldl.

foldl1 is a variant of foldl that has no starting value argument, and thus must be applied to non-empty lists. Note that unlike foldl, the accumulated value must be of the same type as the list elements.

>>> foldl1 (+) [1..4]
10
>>> foldl1 (+) []
*** Exception: Prelude.foldl1: empty list
>>> foldl1 (-) [1..4]
-8
>>> foldl1 (&&) [True, False, True, True]
False
>>> foldl1 (||) [False, False, True, True]
True
>>> foldl1 (+) [1..]
* Hangs forever *

\(\mathcal{O}(1)\). Test whether a list is empty.

>>> null []
True
>>> null [1]
False
>>> null [1..]
False

\(\mathcal{O}(n)\). length returns the length of a finite list as an Int. It is an instance of the more general genericLength, the result type of which may be any kind of number.

>>> length []
0
>>> length ['a', 'b', 'c']
3
>>> length [1..]
* Hangs forever *

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.

Examples

>>> 3 `elem` []
False

>>> 3 `elem` [1,2]
False

>>> 3 `elem` [1,2,3,4,5]
True

>>> 3 `elem` [1..]
True

>>> 3 `elem` [4..]
* Hangs forever *

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..]
* Hangs forever *

maximum returns the maximum value from a list, which must be non-empty, finite, and of an ordered type. This function is equivalent to foldr1 max, and its behavior on lists with multiple maxima depends on the relevant implementation of max. For the default implementation of max, list order is used as a tie-breaker: if there are multiple maxima, the rightmost of them is chosen (this is equivalent to maximumBy compare).

>>> maximum []
*** Exception: Prelude.maximum: empty list
>>> maximum [42]
42
>>> maximum [55, -12, 7, 0, -89]
55
>>> maximum [1..]
* Hangs forever *

minimum returns the minimum value from a list, which must be non-empty, finite, and of an ordered type. This function is equivalent to foldr1 min, and its behavior on lists with multiple minima depends on the relevant implementation of min. For the default implementation of min, list order is used as a tie-breaker: if there are multiple minima, the leftmost of them is chosen (this is equivalent to minimumBy compare).

>>> minimum []
*** Exception: Prelude.minimum: empty list
>>> minimum [42]
42
>>> minimum [55, -12, 7, 0, -89]
-89
>>> minimum [1..]
* Hangs forever *

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

>>> sum []
0
>>> sum [42]
42
>>> sum [1..10]
55
>>> sum [4.1, 2.0, 1.7]
7.8
>>> sum [1..]
* Hangs forever *

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

>>> product []
1
>>> product [42]
42
>>> product [1..10]
3628800
>>> product [4.1, 2.0, 1.7]
13.939999999999998
>>> product [1..]
* Hangs forever *

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.

Examples

>>> and []
True

>>> and [True]
True

>>> and [False]
False

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

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

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

or returns the disjunction of a Boolean list. For the result to be False, the list must be finite; True, however, results from a True value at a finite index of a finite or infinite list.

Examples

>>> or []
False

>>> or [True]
True

>>> or [False]
False

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

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

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

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.

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 *

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.

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 *

A strict version of foldl1.

Concatenate a list of lists.

Examples

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

>>> concat []
[]

>>> concat [[42]]
[42]

Map a function returning a list over a list and concatenate the results. concatMap can be seen as the composition of concat and map.

concatMap f xs == (concat . map f) xs

Examples

>>> concatMap (\i -> [-i,i]) []
[]

>>> concatMap (\i -> [-i, i]) [1, 2, 3]
[-1,1,-2,2,-3,3]

>>> concatMap ('replicate' 3) [0, 2, 4]
[0,0,0,2,2,2,4,4,4]

\(\mathcal{O}(n)\). map f xs is the list obtained by applying f to each element of xs, i.e.,

map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
map f [x1, x2, ...] == [f x1, f x2, ...]

this means that map id == id

Examples

>>> map (+1) [1, 2, 3]
[2,3,4]

>>> map id [1, 2, 3]
[1,2,3]

>>> map (\n -> 3 * n + 1) [1, 2, 3]
[4,7,10]

(++) appends 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.

Performance considerations

Examples

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

>>> [] ++ [1, 2, 3]
[1,2,3]

>>> [3, 2, 1] ++ []
[3,2,1]

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

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

\(\mathcal{O}(1)\). 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

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

\(\mathcal{O}(1)\). 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

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

\(\mathcal{O}(1)\). 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.

Examples

>>> uncons []
Nothing

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

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

Since: base-4.8.0.0

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

Since: base-4.19.0.0

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

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

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

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]

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])

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]

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 *

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

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])

A list producer that can be fused with foldr. This function is merely

   augment g xs = g (:) xs

but GHC's simplifier will transform an expression of the form foldr k z (augment g xs), which may arise after inlining, to g k (foldr k z xs), which avoids producing an intermediate list.

A list producer that can be fused with foldr. This function is merely

   build g = g (:) []

but GHC's simplifier will transform an expression of the form foldr k z (build g), which may arise after inlining, to g k z, which avoids producing an intermediate list.