Thanks Roman and Andres for the tip. I knew the trick with accumulating a function, but I had never imagined it could work so efficiently. I thought the problem with using foldr would be that the function would be neither tail recursive nor efficient and so I hadn't even tried. Apparently that was wrong. After your suggestion I checked its performance and how it compiles to core and to my surprise GHC optimizes the whole thing into a most-efficient tail recursive function!

  Best regards,
  Petr


2013/2/18 Roman Cheplyaka <roma@ro-che.info>
* Petr Pudlįk <petr.mvd@gmail.com> [2013-02-18 17:10:26+0100]
> Dear Haskellers,
>
> while playing with folds and trying to implement `!!` by folding, I came to
> the conclusion that:
>
> - `foldr` is unsuitable because it counts the elements from the end, while
> `!!` needs counting from the start (and it's not tail recursive).
> - `foldl` is also unsuitable, because it always traverses the whole list.

Every structurally-recursive function is definable through foldr,
because foldr *is* the structural recursion (aka catamorphism) operation
for lists.

Here the trick is to make the accumulator a function. This way you can
pass a value from left to right.

Something like

  foldr (\x rest n -> ...) id list 0

I'll leave filling in the dots as an exercise.

Roman