GHC.OldList

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]]

(++) 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

This function takes linear time in the number of elements of the first list. Thus it is better to associate repeated applications of (++) to the right (which is the default behaviour): xs ++ (ys ++ zs) or simply xs ++ ys ++ zs, but not (xs ++ ys) ++ zs. For the same reason GHC.Internal.Data.List.concat = GHC.Internal.Data.List.foldr (++) [] has linear performance, while GHC.Internal.Data.List.foldl (++) [] is prone to quadratic slowdown

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]

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)...)

\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]

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

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'] !? 0Just 'a'

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

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

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

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 *

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 *

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 *

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]

break produces the first component of the tuple lazily:

>>> 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],[])

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]

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]

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]

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]

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 *

\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]

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 *

A strict version of foldl1.

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

\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). 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

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

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

Laziness

Note that iterate is lazy, potentially leading to thunk build-up if the consumer doesn't force each iterate. See iterate' for a strict variant of this function.

>>> 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]

iterate id == repeat:

>>> 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

\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). 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 *

\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"

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 GHC.Internal.Data.List.maximumBy, which allows the programmer to supply their own comparison function.

>>> 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. It is a special case of GHC.Internal.Data.List.minimumBy, which allows the programmer to supply their own comparison function.

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

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

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

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 *

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 *

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]

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

Laziness

reverse is lazy in its elements.

>>> 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}(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). A strict version of scanl.

\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). 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

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]

span produces the first component of the tuple lazily:

>>> 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])

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

It is equivalent to (take n xs, drop n xs) unless n is _|_: splitAt _|_ xs = _|_, not (_|_, _|_)).

The first component of the tuple is produced lazily:

>>> 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])

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 *

\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

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][]

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][]

\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])

\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

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])

\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')]

If one input list is shorter than the other, excess elements of the longer list are discarded, even if one of the lists is infinite:

>>> 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 (+) can be applied to two lists to produce the list of corresponding sums:

>>> 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]

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!"

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

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

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

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

Laziness

transpose is lazy in its elements

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

Examples

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

If some of the rows are shorter than the following rows, their elements are skipped:

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

For this reason the outer list must be finite; otherwise transpose hangs:

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

\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] :: Int3>>> genericLength [1, 2, 3] :: Float3.0

Users should take care to pick a return type that is wide enough to contain the full length of the list. If the width is insufficient, the overflow behaviour will depend on the (+) implementation in the selected Num instance. The following example overflows because the actual list length of 200 lies outside of the Int8 range of -128..127.

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

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.

mapAccumL does not force accumulator if it is unused:

>>> take 1 (snd (mapAccumL (\_ x -> (undefined, x)) undefined ('a' : undefined)))"a"

unwords joins words with separating spaces (U+0020 SPACE).

unwords is neither left nor right inverse of words:

>>> words (unwords [" "])[]>>> unwords (words "foo\nbar")"foo bar"

Examples

>>> unwords ["Lorem", "ipsum", "dolor"]"Lorem ipsum dolor"

>>> unwords ["foo", "bar", "", "baz"]"foo bar  baz"

words breaks a string up into a list of words, which were delimited by white space (as defined by isSpace). This function trims any white spaces at the beginning and at the end.

Examples

>>> words "Lorem ipsum\ndolor"["Lorem","ipsum","dolor"]

>>> words " foo bar "["foo","bar"]

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.

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

Laziness

This function is lazy in spine, but strict in elements, which makes it different from reverse . dropWhile p . reverse, which is strict in spine, but lazy in elements. For instance:

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

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

but on the other hand

>>> 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]

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

Examples

>>> find (> 4) [1..]Just 5

>>> find (< 0) [1..10]Nothing

>>> find ('a' `elem`) ["john", "marcus", "paul"]Just "marcus"

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]

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

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

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

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

Note that inits has the following strictness property: inits (xs ++ _|_) = inits xs ++ _|_

In particular, inits _|_ = [] : _|_

Examples

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

>>> inits [][[]]

inits is productive on infinite lists:

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

\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]]

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.

Laziness

intercalate has the following properties:

>>> take 5 (intercalate undefined ("Lorem" : undefined))"Lorem"

>>> take 6 (intercalate ", " ("Lorem" : undefined))"Lorem*** Exception: Prelude.undefined

Examples

>>> intercalate ", " ["Lorem", "ipsum", "dolor"]"Lorem, ipsum, dolor"

>>> intercalate [0, 1] [[2, 3], [4, 5, 6], []][2,3,0,1,4,5,6,0,1]

>>> intercalate [1, 2, 3] [[], []][1,2,3]

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]

If equal elements are present in both lists, an element from the first list will be used, and all duplicates from the second list quashed:

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

However if the first list contains duplicates, so will the result.

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

If the second list is infinite, intersect either hangs or returns its first argument in full. Otherwise if the first list is infinite, intersect might be productive:

>>> 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

intersperse has the following properties

>>> 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 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

For the result to be True, the first list must be finite; for the result to be False, the second list must be finite:

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

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

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

\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

For the result to be True, the first list must be finite; False, however, results from any mismatch:

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

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

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

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

isPrefixOf shortcuts when the first argument is empty:

>>> isPrefixOf [] undefinedTrue

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

The second list must be finite; however the first list may be infinite:

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

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

Splits the argument into a list of lines stripped of their terminating \n characters. The \n terminator is optional in a final non-empty line of the argument string.

When the argument string is empty, or ends in a \n character, it can be recovered by passing the result of lines to the unlines function. Otherwise, unlines appends the missing terminating \n. This makes unlines . lines idempotent:

(unlines . lines) . (unlines . lines) = (unlines . lines)

Examples

>>> lines ""           -- empty input contains no lines[]

>>> lines "\n"         -- single empty line[""]

>>> lines "one"        -- single unterminated line["one"]

>>> lines "one\n"      -- single non-empty line["one"]

>>> lines "one\n\n"    -- second line is empty["one",""]

>>> lines "one\ntwo"   -- second line is unterminated["one","two"]

>>> lines "one\ntwo\n" -- two non-empty lines["one","two"]

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.

The maximumBy function is the non-overloaded version of maximum, which 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.

Examples

We can use this to find the longest entry of a list:

>>> maximumBy (\x y -> compare (length x) (length y)) ["Hello", "World", "!", "Longest", "bar"]"Longest"

>>> minimumBy (\(a, b) (c, d) -> compare (abs (a - b)) (abs (c - d))) [(10, 15), (1, 2), (3, 5)](10, 15)

The minimumBy function is the non-overloaded version of minimum, which 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.

Examples

We can use this to find the shortest entry of a list:

>>> minimumBy (\x y -> compare (length x) (length y)) ["Hello", "World", "!", "Longest", "bar"]"!"

>>> minimumBy (\(a, b) (c, d) -> compare (abs (a - b)) (abs (c - d))) [(10, 15), (1, 2), (3, 5)](1, 2)

\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]

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])

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

The permutations function is maximally lazy: for each n, the value of permutations xs starts with those permutations that permute take n xs and keep drop n xs.

Examples

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

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

>>> permutations [][[]]

This function is productive on infinite inputs:

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

Construct a list from a single element.

Examples

>>> singleton True[True]

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

>>> singleton 'c'"c"

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]

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,"!")]

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

This function minimises the projections performed, by materialising the projections in an intermediate list.

For trivial projections, you should prefer using sortBy with comparing, for example:

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

Or, for the exact same API as sortOn, you can use `sortBy . comparing`:

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

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

Laziness

subsequences does not look ahead unless it must:

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

Examples

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

This function is productive on infinite inputs:

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

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

Laziness

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

>>> 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 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]

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"

If equal elements are present in both lists, an element from the first list will be used. If the second list contains equal elements, only the first one will be retained:

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

However if the first list contains duplicates, so will the result:

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

union is productive even if both arguments are infinite.

>>> [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"]

Appends a \n character to each input string, then concatenates the results. Equivalent to foldMap (s -> s ++ "\n").

Examples

>>> unlines ["Hello", "World", "!"]"Hello\nWorld\n!\n"

Note that unlines . lines /= id when the input is not \n-terminated:

>>> unlines . lines $ "foo\nbar""foo\nbar\n"

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 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.