Anonymous recursion

Anonymous recursion is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

While implementing a recursive function, it often happens that we must resort to a separate "helper function" to handle the actual recursion.

This is usually the case when directly calling the current function would waste too many resources (stack space, execution time), cause unwanted side-effects, and/or the function doesn't have the right arguments and/and return values.

So we end up inventing some silly name like "foo2" or "foo_helper". I have always found it painful to come up with a proper name, and see a quite some disadvantages:

• You have to think up a name, which then pollutes the namespace
• A function is created which is called from nowhere else
• The program flow in the source code is interrupted

Some languages allow you to embed recursion directly in-place. This might work via a label, a local gosub instruction, or some special keyword.

Anonymous recursion can also be accomplished using the Y combinator.

If possible, demonstrate this by writing the recursive version of the fibonacci function (see Fibonacci sequence) which checks for a negative argument before doing the actual recursion.

J

Copied directly from the fibonacci sequence task, which in turn copied from one of several implementations in an essay on the J Wiki: <lang j> fibN=: (-&2 +&$: -&1)^:(1&<) M."0</lang>

Note that this is an identity function for arguments less than 1 (and 1 (and 5)).

Examples: <lang j> fibN 12 144

  fibN  i.31

0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040</lang>

(This implementation is doubly recursive except that results are cached across function calls.)

$: is an anonymous reference to the largest containing verb in the sentence.

JavaScript

<lang javascript>function fibo(n) {

 if (n < 0)
   throw "Argument cannot be negative";
 else
   return (function(x) {
     if (n < 2)
       return 1;
     else
       return arguments.callee(n-1) + arguments.callee(n-2);
   })(n);

}</lang>

PicoLisp

<lang PicoLisp>(de fibo (N)

  (if (lt0 N)
     (quit "Illegal argument" N) )
  (recur (N)
     (if (> 2 N)
        1
        (+ (recurse (dec N)) (recurse (- N 2))) ) ) )</lang>