General recursion to tail-recursion

Question

Is it theoretically possible to transform every kind of general-recursion into tail-recursion? Are they equivalent for example from a lambda-calculus point of view? That's a debate between me and an acquaintance.

My view is that it's not possible everytime. For example if you have a function which calls itself recursively twice or three times, then you can't make all the recursive calls into tail-calls, right? Or is there always a way to reduce the number of recursive calls to one single recursive call?

Answer 1

No. If you cannot rewrite your algorithm to have only tail calls, like in tree traversal, at least one call will not be in tail position.

Some may say loop + explicit stack is iterative, but IMO it's still recursion and a tree traversal will grow the stack just as general recursion.