Answer 3.66

ex-3_63-xx.scm

@@ -101,4 +101,42 @@
 
 (display "\nex-3.66\n")
 
-; (display "\nex-3.67\n")
+(define (pairs s t)
+  (cons-stream
+   (list (stream-car s) (stream-car t))
+   (interleave
+       (stream-map (lambda (x) (list (stream-car s) x))
+                   (stream-cdr t))
+       (pairs (stream-cdr s) (stream-cdr t)))))
+
+(define int-pairs (pairs integers integers))
+
+(define prime-pairs
+  (stream-filter
+    (lambda (pair) (prime? (+ (car pair) (cadr pair))))
+    int-pairs))
+
+(define (stream-append s1 s2)
+  (if (stream-null? s1)
+      s2
+      (cons-stream (stream-car s1)
+                   (stream-append (stream-cdr s1) s2))))
+
+(define (interleave s1 s2)
+  (if (stream-null? s1)
+      s2
+      (cons-stream (stream-car s1)
+                   (interleave s2 (stream-cdr s1)))))
+
+(assert (find (list 2 5) prime-pairs) 6)
+(assert (find (list 3 3) int-pairs) 6)
+(assert (find (list 1 100) int-pairs) 197)
+;(assert (find (list 99 100) int-pairs) 1000)
+;(assert (find (list 100 100) int-pairs) 10)
+
+; I haven't been able to figure out the relationship by myself.
+; The explanations on Schemewiki are good, though:
+; http://community.schemewiki.org/?sicp-ex-3.66
+
+(display "\nex-3.67\n")
+

util.scm

@@ -74,6 +74,13 @@
     (cons (stream-car xs)
           (take (- n 1) (stream-cdr xs)))))
 
+(define (find item stream)
+  (define (iter n stream)
+    (if (equal? (stream-car stream) item)
+      n
+      (iter (+ n 1) (stream-cdr stream))))
+  (iter 0 stream))
+
 (define (display-stream s)
   (stream-for-each display-line s))
 
@@ -97,4 +104,8 @@
 (define (add-streams s1 s2)
   (stream-map + s1 s2))
 
+(define ones (cons-stream 1 ones))
+
+(define integers (cons-stream 1 (add-streams ones integers)))
+
 'util-loaded