Question

How can I flatten a nested list like this:

[1, 2, 3, 4] == flatten [[[1,2],[3]],[[4]]]

Answer 1

Since nobody else has given this, it is possible to define a function which will flatten lists of an arbitrary depth by using MultiParamTypeClasses. I haven’t actually found it useful, but hopefully it could be considered an interesting hack. I got the idea from Oleg’s polyvariadic function implementation.

{-# LANGUAGE MultiParamTypeClasses, OverlappingInstances, FlexibleInstances #-}

module Flatten where

class Flatten i o where
  flatten :: [i] -> [o]

instance Flatten a a where
  flatten = id

instance Flatten i o => Flatten [i] o where 
  flatten = concatMap flatten

Now if you load it and run in ghci:

*Flatten> let g = [1..5]
*Flatten> flatten g :: [Integer]
[1,2,3,4,5]
*Flatten> let h = [[1,2,3],[4,5]]
*Flatten> flatten h :: [Integer]
[1,2,3,4,5]
*Flatten> let i = [[[1,2],[3]],[],[[4,5],[6]]]
*Flatten> :t i
i :: [[[Integer]]]
*Flatten> flatten i :: [Integer]
[1,2,3,4,5,6]

Note that it’s usually necessary to provide the result type annotation, because otherwise ghc can’t figure out where to stop recursively applying the flatten class method. If you use a function with a monomorphic type that’s sufficient however.

*Flatten> :t sum
sum :: Num a => [a] -> a
*Flatten> sum $ flatten g

<interactive>:1:7:
    No instance for (Flatten Integer a0)
      arising from a use of `flatten'
    Possible fix: add an instance declaration for (Flatten Integer a0)
    In the second argument of `($)', namely `flatten g'
    In the expression: sum $ flatten g
    In an equation for `it': it = sum $ flatten g
*Flatten> let sumInt = sum :: [Integer] -> Integer
*Flatten> sumInt $ flatten g
15
*Flatten> sumInt $ flatten h
15