Data.List.Split

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A theoretical module which contains implementations/combinators for implementing every possible method of list-splitting known to man. This way no one has to argue about what the correct interface for split is, we can just have them all.

Some possible ways to split a list, to get your creative juices flowing:

  • what to split on?
    • single-element separator
    • sublist separator
    • use a list of possible separators instead of just one
    • use a predicate on elements or sublists instead of giving explicit separators
    • use approximate matching?
    • chunks of fixed length
  • how to split?
    • discard the separators
    • keep the separators with the preceding or following splits
    • keep the separators as their own separate pieces of the result list
    • what to do with separators at the beginning/end? create a blank split before/after, or not?
    • keep blank splits between consecutive delimiters, or merge multiple consecutive delimiters into one delimiter?

An important caveat: we should strive to keep things flexible yet SIMPLE. The more complicated things get, the closer this gets to just being a general parsing or regex library. So the right balance needs to be struck.

Add your implementations below! Once we converge on something good we can upload it to hackage.

{-# LANGUAGE ViewPatterns #-}

import Data.List (unfoldr)


-- intercalate :: [a] -> [[a]] -> [a]
-- intercalate x [a,b,c,x,y,z] = [a,x,b,x,c,x,x,y,x,z,x]

-- unintercalate :: [a] -> [a] -> [[a]]
-- unintercalate x [a,x,b,x,c,x,x,y,x,z,x] = [a,b,c,[],y,z]

-- unintercalate is the "inverse" of intercalate

match [] string = Just string
match (_:_) [] = Nothing
match (p:ps) (q:qs) | p == q = match ps qs
match (_:_)  (_:_)  | otherwise = Nothing

chopWith delimiter (match delimiter -> Just tail) = return ([], tail)
chopWith delimiter (c:cs) = chopWith delimiter cs >>= \(head, tail) ->
                              return (c:head, tail)
chopWith delimiter [] = Nothing
-- note: chopWith could be make 'more efficient' i.e. remove the >>=\-> bit
--       by adding an accumulator


unintercalate delimiter = unfoldr (chopWith delimiter)

-- > unintercalate "x" "axbxcxxyxzx"
-- ["a","b","c","","y","z"]

splitOn :: (a -> Bool) -> [a] -> [[a]]
splitOn _ [] = []
splitOn f l@(x:xs)
  | f x = splitOn f xs
  | otherwise = let (h,t) = break f l in h:(splitOn f t)

-- take the element who make predict true as delimiter
-- > splitOn even [1,3,5,6,7,3,3,2,1,1,1]
-- [[1,3,5],[7,3,3],[1,1,1]]

-- | like String split, except for any element that obeys Eq
splitEq :: Eq a => a -> [a] -> [[a]]
splitEq e = splitOn (==e)

-- | split at regular intervals
chunk :: Int -> [a] -> [[a]]
chunk _ [] = [[]]
chunk n xs = y1 : chunk n y2
  where
    (y1, y2) = splitAt n xs

-- another version (CPS) of chunk
chunk n list = case list of { [] -> [] ; (y:ys) -> ch' ys (n-1) (y:) } where
 ch' [] _ k = k [] : []
 ch' (y:ys) 0 k = k [] : ch' ys (n-1) (y:)
 ch' (y:ys) (c+1) k = ch' ys c (k . (y:))

A combinator approach?

Here are some initial thoughts on a combinator approach. The trick is to find nice implementations of the declarations below. Please add your own thoughts, other combinators, etc.

data Splitter a

split :: Splitter a -> [a] -> [[a]]

onElts :: [a] -> Splitter a     -- split on any of these elements
onSublist :: [a] -> Splitter a  -- split on this exact subsequence
whenElt :: (a -> Bool) -> Splitter a
keepingDelims :: Splitter a -> Splitter a
collapsingNulls :: Splitter a -> Splitter a
-- other basic combinators?

-- now you can write things like
--
--   split (collapsingNulls $ onElts " ,") "abc,def   , gh"
--
-- which should evaluate to ["abc", "def", "gh"]. 

-- some convenience functions can be provided, such as...

splitOn   = split . onElts
splitWhen = split . whenElt

Splits of known lengths

I frequently require two types of splits, splitting into blocks of fixed length and splitting into lists of sizes of increasing powers of 2. My implementation was designed to be fold/builded as much as possible, so here goes:

splitEvery :: Int -> [e] -> [[e]]
splitEvery i l = map (take i) (build (splitter l)) where
  splitter [] _ n = n
  splitter l c n  = l `c` splitter (drop i l) c n

For more general splits with foreknown lengths,
splitPlaces :: [Int] -> [e] -> [[e]]
splitPlaces ls xs = build (splitPlacer ls xs) where
  splitPlacer [] _ _ n      = n
  splitPlacer _ [] _ n      = n
  splitPlacer (l:ls) xs c n = let (x1, x2) = splitAt l xs in x1 `c` splitPlacer ls x2 c n

splitPowersOf2 :: [e] -> [[e]]
splitPowersOf2 = splitPlaces (iterate (*2) 1)

To be sure, neither is a good consumer, but I don't think that's avoidable, given that drop isn't a good consumer either.

Here splitEvery is equivalent to "chunks" above, but it is a much better producer, I think. (It is also intended to be mapped on, given that the (map (take i)) makes every element of the list into a producer.

Break on Nothing

import Data.Maybe
import Data.Either
import Data.List (find, isPrefixOf)

breaks :: [Maybe a] -> [[a]]
breaks xs = (if null cur then id else ((map fromJust cur):))
            (if null rem then [] else breaks (tail rem))
    where (cur, rem) = break isNothing xs

replaces :: (Eq a) => [([a], [b])] -> (a -> b) -> [a] -> [b]
replaces reps f = process
  where process [] = []
        process xs = case find ((`isPrefixOf` xs).fst) reps of
                         Nothing -> f (head xs) : process (tail xs)
                         Just (pat, rep) -> rep ++ (process $ drop (length pat) xs)

split :: (Eq a) => [([a], [Maybe a])] -> [a] -> [[a]]
split reps = breaks . replaces reps Just

onSeq, onSeqKeep :: (Eq a) => [a] -> ([a], [Maybe a])
onSeq xs = (xs, [Nothing])
onSeqKeep xs = (xs, Nothing : (map Just xs ++ [Nothing]))

onElt, onEltKeep :: (Eq a) => a -> ([a], [Maybe a])
onElt x = onSeq [x]
onEltKeep x = onSeqKeep [x]

insertAfter :: [Int] -> a -> [a] -> [a]
insertAfter [] _ xs = xs
insertAfter (i:_) _ [] | i > 0 = []
insertAfter (i:is) x xs = pre ++ [x] ++ insertAfter is x post
  where (pre, post) = splitAt i xs

splitEvery :: Int -> [a] -> [[a]]
splitEvery i = splitPlaces (repeat i)

splitPlaces :: [Int] -> [a] -> [[a]]
splitPlaces is xs = breaks $ insertAfter is Nothing $ map Just xs

splitPowersOf2 = splitPlaces (iterate (*2) 1)

Implements all of the above ideas (except predicate matching). In order to split up an arithmetic expression, for example:

split (onElt ' ' : map onEltKeep "+-/*^()")