|in functional programming languages, tail call elimination is often guaranteed by the language standard, and this guarantee allows using recursion, in particular tail recursion, in place of loops. In such cases, it is not correct (though it may be customary) to refer to it as an optimization. The special case of tail recursive calls, when a function calls itself, may be more amenable to call elimination than general tail calls, when the function may be different.|
|The contrast between the two processes can be seen in another way. In the iterative case, the program variables provide a complete description of the state of the process at any point. If we stopped the computation between steps, all we would need to do to resume the computation is to supply the interpreter with the values of the three program variables. Not so with the recursive process. In this case there is some additional ``hidden'' information, maintained by the interpreter and not contained in the program variables, which indicates ``where the process is'' in negotiating the chain of deferred operations. The longer the chain, the more information must be maintained.30|
In contrasting iteration and recursion, we must be careful not to confuse the notion of a recursive process with the notion of a recursive procedure. When we describe a procedure as recursive, we are referring to the syntactic fact that the procedure definition refers (either directly or indirectly) to the procedure itself. But when we describe a process as following a pattern that is, say, linearly recursive, we are speaking about how the process evolves, not about the syntax of how a procedure is written. It may seem disturbing that we refer to a recursive procedure such as fact-iter as generating an iterative process. However, the process really is iterative: Its state is captured completely by its three state variables, and an interpreter need keep track of only three variables in order to execute the process.
One reason that the distinction between process and procedure may be confusing is that most implementations of common languages (including Ada, Pascal, and C) are designed in such a way that the interpretation of any recursive procedure consumes an amount of memory that grows with the number of procedure calls, even when the process described is, in principle, iterative. As a consequence, these languages can describe iterative processes only by resorting to special-purpose ``looping constructs'' such as do, repeat, until, for, and while. The implementation of Scheme we shall consider in chapter 5 does not share this defect. It will execute an iterative process in constant space, even if the iterative process is described by a recursive procedure. An implementation with this property is called tail-recursive. With a tail-recursive implementation, iteration can be expressed using the ordinary procedure call mechanism, so that special iteration constructs are useful only as syntactic sugar.31
Then there's the cheating, like "the recursive call uses the same call stack and objects as the calling function" but you just told me there were no mutable variables!
|But let's also assume that we have reached a point where we just can't make things smaller and faster anymore - your current computer is as good as it gets.|
|Atomic transistors will keep us right on track in having smaller and faster computers :)|
|I see a problem here. If you loop with recursion, that means you will eventually run out of memory to contain the stack. How do you avoid that?|