Comment by javcasas

> For example, you need to manage a stack to do iteration on your binary tree

Recursion around trees can get you into trouble with the stack. Consider:

    def traverse(node):
      do_work(node.payload)
      traverse(node.left)
      traverse(node.right)

The second recursive call to traverse is in tail position and is a candidate for elimination, but the first one isn't and will _always_ eat stack space. This is fine if you know what you're doing, but can bite you in the arse if you're expecting TCO to save you.

What's a plain old data structure?

Linked lists are recursive, but you can use loops just fine to deal with them.

Similarly, it depends on what you do with your trees. If you want to go down a single path (eg to find an element in a search tree), loops aren't too bad.

And arrays don't necessarily ask for loops. Eg implementing quicksort or heap sort with loops is possible (and depending on your language, compiler and target machine might have performance benefits), but I'd hardly call it ergonomical.

Despite all my criticism you are hinting at a good point though: it's often useful to define your data structures together with combinators that work on them. So eg you want to define various tree traversals together with your tree. (Most people are familiar with the combinators 'map' and 'filter' for lists but that's a very small pool.)

Whether those combinators are implemented with recursion or loops is an implementation detail that the user of the combinator doesn't need to worry about too much.

This is overly simplistic.

Is a binary tree recursive from the perspective of a type declaration? Yes.

Is it recursive from the point of view of search? Depends. If you're doing depth-first search, then you need a stack and a recursive algorithm seems natural. If you're doing breadth-first search, then you need a queue and the algorithm is less obviously recursive.

In either case the program could be expressed recursively or as an explicit loop. When a stack is needed, the underlying hardware always provides automatic stack management so recursion feels natural in that case.

When a queue is needed it's more of a tossup since hardware and programming languages don't generally provide automatic queue management, so you're going to need to manage that data structure manually anyway. In which case whether you choose to use recursion or not is more of a personal preference.