- unfold-right p f g seed #!optional tailprocedure
unfold-right constructs a list with the following loop:
(let lp ((seed seed) (lis tail)) (if (p seed) lis (lp (g seed) (cons (f seed) lis))))
- Determines when to stop unfolding.
- Maps each seed value to the corresponding list element.
- Maps each seed value to next seed value.
- The "state" value for the unfold.
- list terminator; defaults to '().
In other words, we use G to generate a sequence of seed values
SEED, G(SEED), G^2(SEED), G^3(SEED), ...
These seed values are mapped to list elements by F, producing the elements of the result list in a right-to-left order. P says when to stop.
unfold-right is the fundamental iterative list constructor, just as fold is the fundamental iterative list consumer. While unfold-right may seem a bit abstract to novice functional programmers, it can be used in a number of ways:
;; List of squares: 1^2 ... 10^2 (unfold-right zero? (lambda (x) (* x x)) (lambda (x) (- x 1)) 10) ;; Reverse a proper list. (unfold-right null-list? car cdr lis) ;; Read current input port into a list of values. (unfold-right eof-object? values (lambda (x) (read)) (read)) ;; (append-reverse rev-head tail) (unfold-right null-list? car cdr rev-head tail)
Interested functional programmers may enjoy noting that fold and unfold-right are in some sense inverses. That is, given operations KNULL?, KAR, KDR, KONS, and KNIL satisfying
(KONS (KAR X) (KDR X)) = x and (KNULL? KNIL) = #t
(fold KONS KNIL (unfold-right KNULL? KAR KDR X)) = X
(unfold-right KNULL? KAR KDR (fold KONS KNIL X)) = X.
This combinator presumably has some pretentious mathematical name; interested readers are invited to communicate it to the author.