[Haskell-cafe] Lists concatenation being O(n)

[Bas van Dijk]

On 13 October 2011 20:53, Albert Y. C. Lai <trebla at vex.net> wrote:
> The number of new cons cells created in due course is Θ(length xs).

I was actually surprised by this because I expected: length(xs++ys) to
fuse into one efficient loop which doesn't create cons cells at all.

Unfortunately, I was mistaken since length is defined recursively.

length :: [a] -> Int
length l =  len l 0#
  where
    len :: [a] -> Int# -> Int
    len []     a# = I# a#
    len (_:xs) a# = len xs (a# +# 1#)

However, if we would define it as:

length = foldl' (l _ -> l+1) 0

And implemented foldl' using foldr as described here:

http://www.haskell.org/pipermail/libraries/2011-October/016895.html

then fuse = length(xs++ys) where for example xs = replicate 1000000 1
and ys = replicate 5000 (1::Int) would compile to the following
totally fused core:

fuse :: Int
fuse = case $wxs 1000000 0 of ww_srS {
         __DEFAULT -> I# ww_srS
       }

$wxs :: Int# -> Int# -> Int#
$wxs = \ (w_srL :: Int#) (ww_srO :: Int#) ->
    case <=# w_srL 1 of _ {
      False -> $wxs (-# w_srL 1) (+# ww_srO 1);
      True  -> $wxs1_rs8 5000 (+# ww_srO 1)
    }

$wxs1_rs8 :: Int# -> Int# -> Int#
$wxs1_rs8 =
  \ (w_srA :: Int#) (ww_srD :: Int#) ->
    case <=# w_srA 1 of _ {
      False -> $wxs1_rs8 (-# w_srA 1) (+# ww_srD 1);
      True  -> +# ww_srD 1
    }

Bas