GHC.Internal.Data.OldList

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]

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 *

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 *

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 *

\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

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"

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

iterate 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

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]

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]

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

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])

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]

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]

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])

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],[])

\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 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 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 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 [][[]]

\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 *

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 *

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 *

\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"

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"

\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]

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])

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"]

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"]

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"

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"

\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.Data.List.NonEmpty.head . Data.List.NonEmpty.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!"

\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"]

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 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 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 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]

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}(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]

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). 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 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 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.

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 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,"!")]

\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]]

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). 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 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.