X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment8.mdwn;h=fe9a87c4f6031021e3bd7415af5e5bbe69e5f910;hp=547db8eda795b39b81e253edbc6a7da571a866ce;hb=aeec785e1d00c613973b4912d4b0f510954491ec;hpb=b7801991967a3ca88aaa238169eec3a63d916bcb

diff --git a/assignment8.mdwn b/assignment8.mdwn
index 547db8ed..fe9a87c4 100644
--- a/assignment8.mdwn
+++ b/assignment8.mdwn
@@ -59,3 +59,66 @@
 			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 as arguments. Your assignment is 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;
+
+		(cond
+			((test1 argument argument) result1)
+			((test2 argument argument) result2)
+			((test3 argument argument) result3)
+			(else result4))
+
+	is equivalent to:
+
+		(if (test1 argument argument)
+			result1
+			(if (test2 argument argument)
+				result2
+				(if (test3 argument argument)
+					result3
+					result4)))
+
+	Some other Scheme details:
+
+	*	`#t` is true and `#f` is false
+	*	`'(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)` `(list1)` `(list 1 2)` `(list 1 2 3)` are the same lists
+	*	`'(1 2 3)` and `(cons 1 '(2 3))` are pairs that are also 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:
+
+		(define (lazy-flatten tree)
+		  (letrec ([helper (lambda (tree tailk)
+		                  (cond
+		                    [(pair? tree)
+		                      (helper (car tree) (lambda () (helper (cdr tree) tailk)))]
+		                    [else (cons tree tailk)]))])
+		    (helper tree (lambda () (list)))))
+		
+		(define (stream-equal? stream1 stream2)
+		  (cond
+		    [(and (null? stream1) (null? stream2)) #t]
+		    [(and (pair? stream1) (pair? stream2))
+		     (and (equal? (car stream1) (car stream2))
+		          (stream-equal? ((cdr stream1)) ((cdr 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)
+
+