;;
-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 as arguments. Your assignment is to supply comments to the code, to explain what every significant piece is doing.
+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 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.
This code uses Scheme's `cond` construct. That works like this;
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
- * `(lambda () ...)` constructs a thunk
Here is the implementation:
(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)
+
+
+<!--
+ (define (lazy-flatten tree)
+ (letrec ([helper (lambda (tree tailk)
+ (cond
+ [(pair? tree)
(helper (car tree) (lambda () (helper (cdr tree) tailk)))]
- [(null? tree) (tailk)]
[else (cons tree tailk)]))])
(helper tree (lambda () (list)))))
(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)))
+ (define tree1 '(((1 . 2) . (3 . 4)) . (5 . 6)))
+ (define tree2 '(1 . (((2 . 3) . (4 . 5)) . 6)))
(same-fringe? tree1 tree2)
-
-
+-->