- inits :: [a] -> [[a]]
- tails :: [a] -> [[a]]
- groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
- group :: Eq a => [a] -> [[a]]
- unzip :: [(a, b)] -> ([a], [b])
- partition :: (a -> Bool) -> [a] -> ([a], [a])
- chop :: (a -> Bool) -> [a] -> [[a]]
- breakAfter :: (a -> Bool) -> [a] -> ([a], [a])
- segmentAfter :: (a -> Bool) -> [a] -> [[a]]
- segmentBefore :: (a -> Bool) -> [a] -> [[a]]
- removeEach :: [a] -> [(a, [a])]
- splitEverywhere :: [a] -> [([a], a, [a])]
- splitLast :: [a] -> ([a], a)
- viewL :: [a] -> Maybe (a, [a])
- viewR :: [a] -> Maybe ([a], a)
- switchL :: b -> (a -> [a] -> b) -> [a] -> b
- switchR :: b -> ([a] -> a -> b) -> [a] -> b
- dropWhileRev :: (a -> Bool) -> [a] -> [a]
- takeWhileRev :: (a -> Bool) -> [a] -> [a]
- maybePrefixOf :: Eq a => [a] -> [a] -> Maybe [a]
- partitionMaybe :: (a -> Maybe b) -> [a] -> ([b], [a])
- unzipEithers :: [Either a b] -> ([a], [b])
- sieve :: Int -> [a] -> [a]
- sliceHorizontal :: Int -> [a] -> [[a]]
- sliceVertical :: Int -> [a] -> [[a]]
- search :: Eq a => [a] -> [a] -> [Int]
- replace :: Eq a => [a] -> [a] -> [a] -> [a]
- multiReplace :: Eq a => [([a], [a])] -> [a] -> [a]
- shear :: [[a]] -> [[a]]
- shearTranspose :: [[a]] -> [[a]]
- outerProduct :: (a -> b -> c) -> [a] -> [b] -> [[c]]
- takeWhileMulti :: [a -> Bool] -> [a] -> [a]
- rotate :: Int -> [a] -> [a]
- mergeBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- allEqual :: Eq a => [a] -> Bool
- isAscending :: Ord a => [a] -> Bool
- isAscendingLazy :: Ord a => [a] -> [Bool]
- mapAdjacent :: (a -> a -> b) -> [a] -> [b]
- range :: Num a => Int -> [a]
- padLeft :: a -> Int -> [a] -> [a]
- padRight :: a -> Int -> [a] -> [a]
- iterateAssociative :: (a -> a -> a) -> a -> [a]
- iterateLeaky :: (a -> a -> a) -> a -> [a]

# Improved standard functions

This function is lazier than the one suggested in the Haskell 98 report.
It is `inits undefined = [] : undefined`

,
in contrast to `Data.List.inits undefined = undefined`

.

This function is lazier than the one suggested in the Haskell 98 report.
It is `tails undefined = ([] : undefined) : undefined`

,
in contrast to `Data.List.tails undefined = undefined`

.

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

This function compares adjacent elements of a list. If two adjacent elements satisfy a relation then they are put into the same sublist. Example:

groupBy (<) "abcdebcdef" == ["abcde","bcdef"]

In contrast to that `Data.List.groupBy`

compares
the head of each sublist with each candidate for this sublist.
This yields

List.groupBy (<) "abcdebcdef" == ["abcdebcdef"]

The second

is compared with the leading `b`

.
Thus it is put into the same sublist as `a`

.
`a`

The sublists are never empty.
Thus the more precise result type would be `[(a,[a])]`

.

unzip :: [(a, b)] -> ([a], [b])Source

Like standard `unzip`

but more lazy.
It is `Data.List.unzip undefined == undefined`

,
but `unzip undefined == (undefined, undefined)`

.

partition :: (a -> Bool) -> [a] -> ([a], [a])Source

`Data.List.partition`

of GHC 6.2.1 fails on infinite lists.
But this one does not.

# Split

chop :: (a -> Bool) -> [a] -> [[a]]Source

Split the list at the occurrences of a separator into sub-lists.
Remove the separators.
This is a generalization of `words`

.

breakAfter :: (a -> Bool) -> [a] -> ([a], [a])Source

Like `break`

, but splits after the matching element.

segmentAfter :: (a -> Bool) -> [a] -> [[a]]Source

Split the list after each occurence of a terminator. Keep the terminator. There is always a list for the part after the last terminator. It may be empty.

segmentBefore :: (a -> Bool) -> [a] -> [[a]]Source

Split the list before each occurence of a leading character. Keep these characters. There is always a list for the part before the first leading character. It may be empty.

removeEach :: [a] -> [(a, [a])]Source

`removeEach xs`

represents a list of sublists of `xs`

,
where each element of `xs`

is removed and
the removed element is separated.
It seems to be much simpler to achieve with
`zip xs (map (flip List.delete xs) xs)`

,
but the implementation of `removeEach`

does not need the `Eq`

instance
and thus can also be used for lists of functions.

splitEverywhere :: [a] -> [([a], a, [a])]Source

splitLast :: [a] -> ([a], a)Source

It holds `splitLast xs == (init xs, last xs)`

,
but `splitLast`

is more efficient
if the last element is accessed after the initial ones,
because it avoids memoizing list.

# List processing starting at the end

dropWhileRev :: (a -> Bool) -> [a] -> [a]Source

Remove the longest suffix of elements satisfying p.
In contrast to `reverse . dropWhile p . reverse`

this works for infinite lists, too.

takeWhileRev :: (a -> Bool) -> [a] -> [a]Source

Alternative version of `reverse . takeWhile p . reverse`

.

# List processing with Maybe and Either

maybePrefixOf :: Eq a => [a] -> [a] -> Maybe [a]Source

`maybePrefixOf xs ys`

is `Just zs`

if `xs`

is a prefix of `ys`

,
where `zs`

is `ys`

without the prefix `xs`

.
Otherwise it is `Nothing`

.

partitionMaybe :: (a -> Maybe b) -> [a] -> ([b], [a])Source

Partition a list into elements which evaluate to `Just`

or `Nothing`

by `f`

.

unzipEithers :: [Either a b] -> ([a], [b])Source

# Sieve and slice

sliceHorizontal :: Int -> [a] -> [[a]]Source

sliceVertical :: Int -> [a] -> [[a]]Source

# Search&replace

multiReplace :: Eq a => [([a], [a])] -> [a] -> [a]Source

# Lists of lists

Transform

[[00,01,02,...], [[00], [10,11,12,...], --> [10,01], [20,21,22,...], [20,11,02], ...] ...]

With `concat . shear`

you can perform a Cantor diagonalization,
that is an enumeration of all elements of the sub-lists
where each element is reachable within a finite number of steps.
It is also useful for polynomial multiplication (convolution).

shearTranspose :: [[a]] -> [[a]]Source

Transform

[[00,01,02,...], [[00], [10,11,12,...], --> [01,10], [20,21,22,...], [02,11,20], ...] ...]

It's like `shear`

but the order of elements in the sub list is reversed.
Its implementation seems to be more efficient than that of `shear`

.
If the order does not matter, better choose `shearTranspose`

.

outerProduct :: (a -> b -> c) -> [a] -> [b] -> [[c]]Source

Operate on each combination of elements of the first and the second list.
In contrast to the list instance of `Monad.liftM2`

in holds the results in a list of lists.
It holds
`concat (outerProduct f xs ys) == liftM2 f xs ys`

# Miscellaneous

takeWhileMulti :: [a -> Bool] -> [a] -> [a]Source

Take while first predicate holds, then continue taking while second predicate holds, and so on.

mergeBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]Source

Given two lists that are ordered
(i.e. `p x y`

holds for subsequent `x`

and `y`

)
`mergeBy`

them into a list that is ordered, again.

isAscending :: Ord a => [a] -> BoolSource

isAscendingLazy :: Ord a => [a] -> [Bool]Source

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

iterateAssociative :: (a -> a -> a) -> a -> [a]Source

For an associative operation `op`

this computes
`iterateAssociative op a = iterate (op a) a`

but it is even faster than `map (powerAssociative op a a) [0..]`

since it shares temporary results.

The idea is:
From the list `map (powerAssociative op a a) [0,(2*n)..]`

we compute the list `map (powerAssociative op a a) [0,n..]`

,
and iterate that until `n==1`

.

iterateLeaky :: (a -> a -> a) -> a -> [a]Source

This is equal to `iterateAssociative`

.
The idea is the following:
The list we search is the fixpoint of the function:
Square all elements of the list,
then spread it and fill the holes with successive numbers
of their left neighbour.
This also preserves log n applications per value.
However it has a space leak,
because for the value with index `n`

all elements starting at `div n 2`

must be kept.