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I wrote a function, doSkip.

For an N-sized list, an element at index 0 consists of the entire input. Index 1 consists of every other element, i.e. the odd elements. Then, indexes 2 to N consist of the respective index of the input.

doSkip :: [a] -> [[a]]
doSkip []            = []
doSkip [x]           = [[x]]
doSkip xxs@(_:_:[])  = [xxs]  
doSkip xxs@(_:_:xs)  = xxs : everyOther : (rest xs)
    where everyOther  = (map (\(_, y) -> y) . filter (\(x, _) -> odd x) . zip [0..]) xxs
          rest []     = []
          rest (y:ys) = [y] : rest ys

Testing

ghci> doSkip"FOOBAR"
["FOOBAR","OBR","O","B","A","R"]
ghci> doSkip"bippy"
["bippy","ip","p","p","y"]

Please critique. I think it's a bit long, but I'm not sure how to shorten it.

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First up, that has to be one of the most niche functions I've ever seen :) Is there a real use case? Is this homework?

The prefix do seems strange. You obviously can't call it skip, and the definition of the function is so odd to me that I can't think of another name right now, but I would recommend thinking hard about the name.

I would recommend installing hlint. It will give you suggestions on keeping code clean, and using standard functions. For instance,

map (\(_, y) -> y)

is just map snd.

rest []     = []
rest (y:ys) = [y] : rest ys

can be written as rest = map (: []).

As for the actual code, let's break it down. First we want the entire input:

doSkip xs = xs : ???

Now we want every other element

doSkip xs = xs : everyOther xs : ???

Then we want elements 2...

doSkip xs = xs : everyOther xs : [ [x] | x <- drop 2 xs ]

Great, so all that is left is our definition of everyOther

everyOther (x:y:xs) = y : everyOther xs
everyOther _ = []

And finally base cases, just as you had them

doSkip [] = []
doSkip [x] = [[x]]
doSkip xs = xs : everyOther xs : [ [x] | x <- drop 2 xs ]
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  • \$\begingroup\$ Technically, it is homework. However, I'm not in the class - I'm taking a class taught in 2013 for my own learning. I'm not in school anymore. Also, I re-named the function in case future students try to look up the real name. Wouldn't want them to cheat. \$\endgroup\$ Commented Sep 24, 2014 at 1:12
  • \$\begingroup\$ @KevinMeredith respect for the self-learning. I'm also taking an online course, and there just aren't enough hours in the day. \$\endgroup\$ Commented Sep 24, 2014 at 1:35

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