Permuting output of a tree of closures

Question

This a conceptual question on how one would implement the following in Lisp (assuming Common Lisp in my case, but any dialect would work). Assume you have a function that creates closures that sequentially iterate over an arbitrary collection (or otherwise return different values) of data and returns nil when exhausted, i.e.

(defun make-counter (up-to)
  (let ((cnt 0))
    (lambda ()
       (if (< cnt up-to)
           (incf cnt)
           nil))))

CL-USER> (defvar gen (make-counter 3))
GEN
CL-USER> (funcall gen)
1
CL-USER> (funcall gen)
2
CL-USER> (funcall gen)
3
CL-USER> (funcall gen)
NIL
CL-USER> (funcall gen)
NIL

Now, assume you are trying to permute a combinations of one or more of these closures. How would you implement a function that returns a new closure that subsequently creates a permutation of all closures contained within it? i.e.:

(defun permute-closures (counters)
  ......)

such that the following holds true:

CL-USER> (defvar collection (permute-closures (list 
                                                 (make-counter 3)
                                                 (make-counter 3))))
CL-USER> (funcall collection)
(1 1)
CL-USER> (funcall collection)
(1 2)
CL-USER> (funcall collection)
(1 3)
CL-USER> (funcall collection)
(2 1)
...

and so on.

The way I had it designed originally was to add a 'pause' parameter to the initial counting lambda such that when iterating you can still call it and receive the old cached value if passed ":pause t", in hopes of making the permutation slightly cleaner. Also, while the example above is a simple list of two identical closures, the list can be an arbitrarily-complicated tree (which can be permuted in depth-first order, and the resulting permutation set would have the shape of the tree.).

I had this implemented, but my solution wasn't very clean and am trying to poll how others would approach the problem.

Thanks in advance.

---

edit Thank you for all the answers. What I ended up doing was adding a 'continue' argument to the generator and flattening my structure by replacing any nested list with a closure that permuted that list. The generators did not advance and always returned the last cached value unless 'continue' was passed. Then I just recursively called each generator until I got to the either the last cdr or a nil. If i got to the last cdr, I just bumped it. If I got to a NIL, I bumped the one before it, and reset every closure following it.

Answer 1

You'll clearly need some way of using each value returned by a generator more than once.

In addition to Rainer Joswig's suggestions, three approaches come to mind.

Caching values

permute-closures could, of course, remember every value returned by each generator by storing it in a list, and reuse that over and over. This approach obviously implies some memory overhead, and it won't work very well if the generated sequences can be infinite.

Creating new generators on each iteration

In this approach, you would change the signature of permute-closures to take as arguments not ready-to-use generators but thunks that create them. Your example would then look like this:

(permute-closures (list (lambda () (make-counter 3))
                        (lambda () (make-counter 3))))

This way, permute-closures is able to reset a generator by simply recreating it.

Making generator states copyable

You could provide a way of making copies of generators along with their states. This is kind of like approach #2 in that permute-closures would reset the generators as needed except the resetting would be done by reverting to a copy of the original state. Also, you would be able to do partial resets (i.e., backtrack to an arbitrary point rather than just the beginning), which may or may not make the code of permute-closures significantly simpler.

Copying generator states might be a bit easier in a language with first-class continuations (like Scheme), but if all generators follow some predefined structure, abstracting it away with a define-generator macro or some such should be possible in Common Lisp as well.