utility-ht-0.0.14: Various small helper functions for Lists, Maybes, Tuples, Functions

Safe Haskell | Safe
Language | Haskell98

Data.List.HT

Contents

- Improved standard functions
- Split
- List processing starting at the end
- List processing with Maybe and Either
- Sieve and slice
- Search&replace
- Lists of lists
- Miscellaneous

Synopsis

- 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])
- span :: (a -> Bool) -> [a] -> ([a], [a])
- break :: (a -> Bool) -> [a] -> ([a], [a])
- chop :: (a -> Bool) -> [a] -> [[a]]
- breakAfter :: (a -> Bool) -> [a] -> ([a], [a])
- takeUntil :: (a -> Bool) -> [a] -> [a]
- segmentAfter :: (a -> Bool) -> [a] -> [[a]]
- segmentBefore :: (a -> Bool) -> [a] -> [[a]]
- segmentAfterMaybe :: (a -> Maybe b) -> [a] -> ([([a], b)], [a])
- segmentBeforeMaybe :: (a -> Maybe b) -> [a] -> ([a], [(b, [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
- dropRev :: Int -> [a] -> [a]
- takeRev :: Int -> [a] -> [a]
- splitAtRev :: Int -> [a] -> ([a], [a])
- dropWhileRev :: (a -> Bool) -> [a] -> [a]
- takeWhileRev :: (a -> Bool) -> [a] -> [a]
- maybePrefixOf :: Eq a => [a] -> [a] -> Maybe [a]
- maybeSuffixOf :: Eq a => [a] -> [a] -> Maybe [a]
- partitionMaybe :: (a -> Maybe b) -> [a] -> ([b], [a])
- takeWhileJust :: [Maybe a] -> [a]
- dropWhileNothing :: (a -> Maybe b) -> [a] -> Maybe (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]
- mapAdjacent1 :: (a -> a -> b -> c) -> a -> [(a, b)] -> [c]
- 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]
- lengthAtLeast :: Int -> [a] -> Bool
- lengthAtMost :: Int -> [a] -> Bool

# Improved standard functions

inits :: [a] -> [[a]] #

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`.

tails :: [a] -> [[a]] #

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]] #

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

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

The second ``b`` is compared with the leading ``a``. Thus it is put into the same sublist as ``a``.

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

group :: Eq a => [a] -> [[a]] #

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

Like standard `unzip` but more lazy. It is `Data.List.unzip undefined == undefined`, but `unzip undefined == (undefined, undefined)`.

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

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

span :: (a -> Bool) -> [a] -> ([a], [a]) #

It is `Data.List.span f undefined = undefined`, whereas `span f undefined = (undefined, undefined)`.

break :: (a -> Bool) -> [a] -> ([a], [a]) #

It is `Data.List.span f undefined = undefined`, whereas `span f undefined = (undefined, undefined)`.

# Split

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

Split the list at the occurrences of a separator into sub-lists. Remove the separators. This is somehow a generalization of `lines` and `words`. But note the differences:

    Prelude Data.List.HT> words "a  a"
    ["a","a"]
    Prelude Data.List.HT> chop (' '==) "a  a"
    ["a","","a"]

    Prelude Data.List.HT> lines "a\n\na"
    ["a","","a"]
    Prelude Data.List.HT> chop ('\n'==) "a\n\na"
    ["a","","a"]

    Prelude Data.List.HT> lines "a\n"
    ["a"]
    Prelude Data.List.HT> chop ('\n'==) "a\n"
    ["a",""]

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

Like `break`, but splits after the matching element.

takeUntil :: (a -> Bool) -> [a] -> [a] #

Take all elements until one matches. The matching element is returned, too. This is the key difference to `takeWhile (not . p)`. It holds `takeUntil p xs == fst (breakAfter p xs)`.

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

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. See package `non-empty` for more precise result type.

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

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. See package `non-empty` for more precise result type.

segmentAfterMaybe :: (a -> Maybe b) -> [a] -> ([([a], b)], [a]) #

    Data.List.HT Data.Char> segmentAfterMaybe (\c -> toMaybe (isLetter c) (toUpper c)) "123a5345b---"
    ([("123",'A'),("5345",'B')],"---")

segmentBeforeMaybe :: (a -> Maybe b) -> [a] -> ([a], [(b, [a])]) #

    Data.List.HT Data.Char> segmentBeforeMaybe (\c -> toMaybe (isLetter c) (toUpper c)) "123a5345b---"
    ("123",[('A',"5345"),('B',"---")])

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

`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.

See also the proposal http://www.haskell.org/pipermail/libraries/2008-February/009270.html

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

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

Deprecated: use viewR instead

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.

viewL :: [a] -> Maybe (a, [a]) #

Should be prefered to `head` and `tail`.

viewR :: [a] -> Maybe ([a], a) #

Should be prefered to `init` and `last`.

switchL :: b -> (a -> [a] -> b) -> [a] -> b #

Should be prefered to `head` and `tail`.

switchR :: b -> ([a] -> a -> b) -> [a] -> b #

Should be prefered to `init` and `last`.

# List processing starting at the end

dropRev :: Int -> [a] -> [a] #

`dropRev n` is like `reverse . drop n . reverse` but it is lazy enough to work for infinite lists, too.

takeRev :: Int -> [a] -> [a] #

`takeRev n` is like `reverse . take n . reverse` but it is lazy enough to work for infinite lists, too.

splitAtRev :: Int -> [a] -> ([a], [a]) #

`splitAtRev n xs == (dropRev n xs, takeRev n xs)`. It holds `xs == uncurry (++) (splitAtRev n xs)`

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

Deprecated: Use dropWhile from Data.List.Reverse.StrictElement or Data.List.Reverse.StrictSpine instead

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

Deprecated: Use takeWhile from Data.List.Reverse.StrictElement or Data.List.Reverse.StrictSpine instead

# List processing with Maybe and Either

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

`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`. It is the same as `stripPrefix`.

maybeSuffixOf :: Eq a => [a] -> [a] -> Maybe [a] #

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

Partition a list into elements which evaluate to `Just` or `Nothing` by `f`.

It holds `mapMaybe f == fst . partitionMaybe f` and `partition p == partitionMaybe ( x -> toMaybe (p x) x)`.

takeWhileJust :: [Maybe a] -> [a] #

This is the cousin of `takeWhile` analogously to `catMaybes` being the cousin of `filter`.

Example: Keep the heads of sublists until an empty list occurs.

    takeWhileJust $ map (fmap fst . viewL) xs

For consistency with `takeWhile`, `partitionMaybe` and `dropWhileNothing` it should have been:

    takeWhileJust_ :: (a -> Maybe b) -> a -> [b]

However, both variants are interchangeable:

    takeWhileJust_ f == takeWhileJust . map f
    takeWhileJust == takeWhileJust_ id

dropWhileNothing :: (a -> Maybe b) -> [a] -> Maybe (b, [a]) #

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

# Sieve and slice

sieve :: Int -> [a] -> [a] #

keep every k-th value from the list

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

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

# Search&replace

search :: Eq a => [a] -> [a] -> [Int] #

replace :: Eq a => [a] -> [a] -> [a] -> [a] #

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

# Lists of lists

shear :: [[a]] -> [[a]] #

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]] #

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]] #

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

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

rotate :: Int -> [a] -> [a] #

rotate left

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

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.

allEqual :: Eq a => [a] -> Bool #

isAscending :: Ord a => [a] -> Bool #

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

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

This function combines every pair of neighbour elements in a list with a certain function.

mapAdjacent1 :: (a -> a -> b -> c) -> a -> [(a, b)] -> [c] #

    mapAdjacent f a0 [(a1,b1), (a2,b2), (a3,b3)]
    ==
    [f a0 a1 b1, f a1 a2 b2, f a2 a3 b3]

range :: Num a => Int -> [a] #

Enumerate without Enum context. For Enum equivalent to enumFrom.

padLeft :: a -> Int -> [a] -> [a] #

padRight :: a -> Int -> [a] -> [a] #

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

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] #

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.

lengthAtLeast :: Int -> [a] -> Bool #

lengthAtMost :: Int -> [a] -> Bool #