1 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.
3 type 'a tree = Leaf of 'a | Node of ('a tree * 'a tree)
5 type 'a starred_level = Root | Starring_Left of 'a starred_nonroot | Starring_Right of 'a starred_nonroot
6 and 'a starred_nonroot = { parent : 'a starred_level; sibling: 'a tree };;
8 type 'a zipper = { level : 'a starred_level; filler: 'a tree };;
10 let rec move_botleft (z : 'a zipper) : 'a zipper =
11 (* returns z if the targetted node in z has no children *)
12 (* else returns move_botleft (zipper which results from moving down from z to the leftmost child) *)
14 (* YOU SUPPLY THE DEFINITION *)
17 let rec move_right_or_up (z : 'a zipper) : 'a zipper option =
18 (* if it's possible to move right in z, returns Some (the result of doing so) *)
19 (* else if it's not possible to move any further up in z, returns None *)
20 (* else returns move_right_or_up (result of moving up in z) *)
22 (* YOU SUPPLY THE DEFINITION *)
25 let new_zipper (t : 'a tree) : 'a zipper =
26 {level = Root; filler = t}
31 let make_fringe_enumerator (t: 'a tree) =
32 (* create a zipper targetting the botleft of t *)
33 let zbotleft = move_botleft (new_zipper t)
34 (* create a refcell initially pointing to zbotleft *)
35 in let zcell = ref (Some zbotleft)
36 (* construct the next_leaf function *)
37 in let next_leaf () : 'a option =
40 (* extract label of currently-targetted leaf *)
41 let Leaf current = z.filler
42 (* update zcell to point to next leaf, if there is one *)
43 in let () = zcell := match move_right_or_up z with
45 | Some z' -> Some (move_botleft z')
46 (* return saved label *)
49 | None -> (* we've finished enumerating the fringe *)
51 (* return the next_leaf function *)
55 let same_fringe (t1 : 'a tree) (t2 : 'a tree) : bool =
56 let next1 = make_fringe_enumerator t1
57 in let next2 = make_fringe_enumerator t2
58 in let rec loop () : bool =
59 match next1 (), next2 () with
60 | Some a, Some b when a = b -> loop ()
67 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 "the rest of the enumeration of the fringe" as a thunk argument (`tail-thunk` below). 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.
69 This code uses Scheme's `cond` construct. That works like this;
72 ((test1 argument argument) result1)
73 ((test2 argument argument) result2)
74 ((test3 argument argument) result3)
79 (if (test1 argument argument)
83 (if (test2 argument argument)
87 (if (test3 argument argument)
93 Some other Scheme details:
95 * `#t` is true and `#f` is false
96 * `(lambda () ...)` constructs a thunk
97 * there is no difference in meaning between `[...]` and `(...)`; we just sometimes use the square brackets for clarity
98 * `'(1 . 2)` and `(cons 1 2)` are pairs (the same pair)
99 * `(list)` and `'()` both evaluate to the empty list
100 * `(null? lst)` tests whether `lst` is the empty list
101 * non-empty lists are implemented as pairs whose second member is a list
102 * `'()` `'(1)` `'(1 2)` `'(1 2 3)` are all lists
103 * `(list)` `(list 1)` `(list 1 2)` `(list 1 2 3)` are the same lists as the preceding
104 * `'(1 2 3)` and `(cons 1 '(2 3))` are both pairs and lists (the same list)
105 * `(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
106 * `(car lst)` extracts the first member of a pair / head of a list
107 * `(cdr lst)` extracts the second member of a pair / tail of a list
109 Here is the implementation:
111 (define (lazy-flatten tree)
112 (letrec ([helper (lambda (tree tail-thunk)
115 (helper (car tree) (lambda () (helper _____ tail-thunk)))]
116 [else (cons tree tail-thunk)]))])
117 (helper tree (lambda () _____))))
119 (define (stream-equal? stream1 stream2)
121 [(and (null? stream1) (null? stream2)) _____]
122 [(and (pair? stream1) (pair? stream2))
123 (and (equal? (car stream1) (car stream2))
127 (define (same-fringe? tree1 tree2)
128 (stream-equal? (lazy-flatten tree1) (lazy-flatten tree2)))
130 (define tree1 '(((1 . 2) . (3 . 4)) . (5 . 6)))
131 (define tree2 '(1 . (((2 . 3) . (4 . 5)) . 6)))
133 (same-fringe? tree1 tree2)