Why should recursion be preferred over iteration?

Question

Iteration is more performant than recursion, right?

Not necessarily. This conception comes from many C-like languages, where calling a function, recursive or not, had a large overhead and created a new stackframe for every call.

For many languages this is not the case, and recursion is equally or more performant than an iterative version. These days, even some C compilers rewrite some recursive constructs to an iterative version, or reuse the stack frame for a tail recursive call.

Try implementing depth-first search recursively and iteratively and tell me which one gave you an easier time of it. Or merge sort. For a lot of problems it comes down to explicitly maintaining your own stack vs. leaving your data on the function stack.

I can't speak to Haskell as I've never used it, but this is to address the more general part of the question posed in your title.

Haskell do not allow iteration because iteration involves mutable state (the index).

As others have stated, there's nothing intrinsically less performant about recursion. There are some languages where it will be slower, but it's not a universal rule.

That being said, to me recursion is a tool, to be used when it makes sense. There are some algorithms that are better represented as recursion (just as some are better via iteration).

Case in point:

fib 0 = 0
fib 1 = 1
fib n = fib(n-1) + fib(n-2)

I can't imagine an iterative solution that could possibly make the intent clearer than that.

Here is some information on the pros & cons of recursion & iteration in c:

http://www.stanford.edu/~blp/writings/clc/recursion-vs-iteration.html

Mostly for me Recursion is sometimes easier to understand than iteration.

Iteration is just a special form of recursion.