X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment8.mdwn;h=7e358a8eb248f1f0a3f65720ccf8ddf2918a0427;hp=547db8eda795b39b81e253edbc6a7da571a866ce;hb=d7222c3a02d8dd06a06377ee4d305bc4fbeab5f4;hpb=b7801991967a3ca88aaa238169eec3a63d916bcb diff --git a/assignment8.mdwn b/assignment8.mdwn index 547db8ed..7e358a8e 100644 --- a/assignment8.mdwn +++ b/assignment8.mdwn @@ -59,3 +59,62 @@ in loop () ;; + +2. Here's another implementation of the same-fringe function, in Scheme. It's taken from . 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 + * `(list)` and `'()` both evaluate to the empty list + * `(null? lst)` tests whether `lst` is the empty 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)))] + [(null? 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) + +