[Haskell-cafe] generalized, tail-recursive left fold that can finish tne computation prematurely

[Roman Cheplyaka]

* Petr Pudlák <petr.mvd at 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