unfold function in scheme

Question

Goal: implement unfold function using only two arguments.

The arguments:

• the first argument is f which takes an initial value of some type I and returns nil or a cons pair of two elements (the first of these two is the next element that goes in the list of some type A and the next initial value again of some type I).
• The second argument is an initial value of some type I and the return is a list of items of type A.

This is what I have so far and I am not sure why it is not working:

(define (descending i)
  (if (= i 0)
    (list)
    (cons i (- i 1))))

(define nil (list))

(define (unfold f init)
  (if (eq? (f init) '())
    (list)
    (cons init (unfold f (f init)))))

(unfold (descending 5))

should evaluate to

'(5 4 3 2 1)

This should be the result but isn't. What am I doing wrong?

Answer 1

First, it should be (unfold descending 5). Then f would produce a pair and you would use both components of it,

(define (unfold f init)
  (if (eq? (f init) '())
      (list)
      (cons (car (f init)) (unfold f (cdr (f init))))))

But this has awful computational complexity as it calls (f init) three times per iteration. A humble let binding remedies this.

(define (unfold f init)
  (let ((r (f init)))
    (if (empty? r) ;; instead of (eq? r '())
        (list)
        (cons (car r) (unfold f (cdr r))))))

And a tail recursive form using named let

(define (unfold f init)
  (let loop ((acc empty)
             (state (f init)))
    (if (empty? state)
        (reverse acc)
        (loop (cons (car state) acc)
              (f (cdr state))))))

And using match.

(define (unfold f init)
  (let loop ((acc empty)
             (state (f init)))
    (match state
      ((cons x next)
       (loop (cons x acc)
             (f next)))
      (empty
       (reverse acc)))))