-1. Complete the definitions of `move_botleft` and `move_right_or_up` from the same-fringe solution in the [[week11]] notes. Test your attempts against some example trees to see if the resulting `make_fringe_enumerator` and `same_fringe` functions work as expected.
+1. Complete the definitions of `move_botleft` and `move_right_or_up` from the same-fringe solution in the [[week11]] notes. **Test your attempts** against some example trees to see if the resulting `make_fringe_enumerator` and `same_fringe` functions work as expected. Show us some of your tests.
type 'a tree = Leaf of 'a | Node of ('a tree * 'a tree)
- type 'a starred_tree = Root | Starring_Left of 'a starred_pair | Starring_Right of 'a starred_pair
- and 'a starred_pair = { parent : 'a starred_tree; sibling: 'a tree }
- and 'a zipper = { tree : 'a starred_tree; filler: 'a tree };;
+ type 'a starred_level = Root | Starring_Left of 'a starred_nonroot | Starring_Right of 'a starred_nonroot
+ and 'a starred_nonroot = { parent : 'a starred_level; sibling: 'a tree };;
+
+ type 'a zipper = { tree : 'a starred_level; filler: 'a tree };;
let rec move_botleft (z : 'a zipper) : 'a zipper =
(* returns z if the targetted node in z has no children *)
- (* else returns move_botleft (zipper which results from moving down and left in z) *)
- YOU SUPPLY THE DEFINITION
+ (* else returns move_botleft (zipper which results from moving down from z to the leftmost child) *)
+ _____
+ (* YOU SUPPLY THE DEFINITION *)
let rec move_right_or_up (z : 'a zipper) : 'a zipper option =
(* if it's possible to move right in z, returns Some (the result of doing so) *)
(* else if it's not possible to move any further up in z, returns None *)
(* else returns move_right_or_up (result of moving up in z) *)
- YOU SUPPLY THE DEFINITION
+ _____
+ (* YOU SUPPLY THE DEFINITION *)
let new_zipper (t : 'a tree) : 'a zipper =
{tree = Root; filler = t}
;;
+
+
let make_fringe_enumerator (t: 'a tree) =
(* create a zipper targetting the root of t *)
let zstart = new_zipper t
in loop ()
;;
+
+2. Here's another implementation of the same-fringe function, in Scheme. It's taken from <http://c2.com/cgi/wiki?SameFringeProblem>. It uses thunks to delay the evaluation of code that computes the tail of a list of a tree's fringe. It also involves passing continuations (`tailk`s) as arguments. Your assignment is to fill in the blanks in the code, **and also to supply comments to the code,** to explain what every significant piece is doing. Don't forget to supply the comments, this is an important part of the assignment.
+
+ This code uses Scheme's `cond` construct. That works like this;
+
+ (cond
+ ((test1 argument argument) result1)
+ ((test2 argument argument) result2)
+ ((test3 argument argument) result3)
+ (else result4))
+
+ is equivalent to:
+
+ (if (test1 argument argument)
+ ; then
+ result1
+ ; else
+ (if (test2 argument argument)
+ ; then
+ result2
+ ; else
+ (if (test3 argument argument)
+ ; then
+ result3
+ ; else
+ result4)))
+
+ Some other Scheme details:
+
+ * `#t` is true and `#f` is false
+ * `(lambda () ...)` constructs a thunk
+ * there is no difference in meaning between `[...]` and `(...)`; we just sometimes use the square brackets for clarity
+ * `'(1 . 2)` and `(cons 1 2)` are pairs (the same pair)
+ * `(list)` and `'()` both evaluate to the empty list
+ * `(null? lst)` tests whether `lst` is the empty list
+ * non-empty lists are implemented as pairs whose second member is a list
+ * `'()` `'(1)` `'(1 2)` `'(1 2 3)` are all lists
+ * `(list)` `(list 1)` `(list 1 2)` `(list 1 2 3)` are the same lists as the preceding
+ * `'(1 2 3)` and `(cons 1 '(2 3))` are both pairs and lists (the same list)
+ * `(pair? lst)` tests whether `lst` is a pair; if `lst` is a non-empty list, it will also pass this test; if `lst` fails this test, it may be because `lst` is the empty list, or because it's not a list or pair at all
+ * `(car lst)` extracts the first member of a pair / head of a list
+ * `(cdr lst)` extracts the second member of a pair / tail of a list
+
+ Here is the implementation:
+
+ (define (lazy-flatten tree)
+ (letrec ([helper (lambda (tree tailk)
+ (cond
+ [(pair? tree)
+ (helper (car tree) (lambda () (helper _____ tailk)))]
+ [else (cons tree tailk)]))])
+ (helper tree (lambda () _____))))
+
+ (define (stream-equal? stream1 stream2)
+ (cond
+ [(and (null? stream1) (null? stream2)) _____]
+ [(and (pair? stream1) (pair? stream2))
+ (and (equal? (car stream1) (car stream2))
+ _____)]
+ [else #f]))
+
+ (define (same-fringe? tree1 tree2)
+ (stream-equal? (lazy-flatten tree1) (lazy-flatten tree2)))
+
+ (define tree1 '(((1 . 2) . (3 . 4)) . (5 . 6)))
+ (define tree2 '(1 . (((2 . 3) . (4 . 5)) . 6)))
+
+ (same-fringe? tree1 tree2)
+
+