Implement till 3.69

ex-3_63-xx.scm

@@ -138,5 +138,55 @@
 ; The explanations on Schemewiki are good, though:
 ; http://community.schemewiki.org/?sicp-ex-3.66
 
-(display "\nex-3.67\n")
+(display "\nex-3.67 - all-pairs\n")
 
+(define (all-pairs s t)
+  (cons-stream
+   (list (stream-car s) (stream-car t))
+   (interleave
+     (interleave
+       (stream-map (lambda (x) (list (stream-car s) x))
+                   (stream-cdr t))
+       (stream-map (lambda (x) (list x (stream-car t)))
+                   (stream-cdr s)))
+       (all-pairs (stream-cdr s) (stream-cdr t)))))
+
+(define int-pairs (all-pairs integers integers))
+
+(assert (stream-ref int-pairs 10) '(3 4))
+
+(display "\nex-3.68 - non-lazy pairs\n")
+(display "[answered]\n")
+
+(define (bad-pairs s t)
+  (interleave
+   (stream-map (lambda (x) (list (stream-car s) x))
+               t)
+   (pairs (stream-cdr s) (stream-cdr t))))
+
+; MIT-Scheme uses applicative-order evluation. Hence, pairs gets evaluated
+; recursively. Since there is no delay this implementation results in an
+; endless loop.
+
+(display "\nex-3.69 - triples\n")
+
+(define (triples a b c)
+  (cons-stream
+    (list (stream-car a) (stream-car b) (stream-car c))
+    (interleave
+      (stream-map (lambda (pairs) (cons (stream-car a) pairs))
+                  (pairs b (stream-cdr c)))
+      (triples (stream-cdr a) (stream-cdr b) (stream-cdr c)))))
+
+(define (pythagorean? a b c)
+    (= (+ (* a a) (* b b)) (* c c)))
+
+(define pythagorean-triples
+  (stream-filter (lambda (ts) (apply pythagorean? ts))
+                 (triples integers integers integers)))
+
+(assert (stream-ref pythagorean-triples 1) '(6 8 10))
+
+(display "\nex-3.70\n")
+
+; (display "\nex-3.71\n")