Implement 4.35

ex-4_35-xx.scm

@@ -1,4 +1,50 @@
 (load "util.scm")
 
-(display "\nex-4.35\n")
+(define (require p)
+  (if (not p) (amb)))
+
+(define (an-element-of items)
+  (require (not (null? items)))
+  (amb (car items) (an-element-of (cdr items))))
+
+(define (an-integer-starting-from n)
+  (amb n (an-integer-starting-from (+ n 1))))
+
+(display "\nex-4.35 - an-integer-between\n")
+
+(define (an-integer-between a b)
+  (require (<= a b))
+  (amb a (an-integer-between (+ a 1) b)))
+
+(define (a-pythagorean-triple-between low high)
+  (let ((i (an-integer-between low high)))
+    (let ((j (an-integer-between i high)))
+      (let ((k (an-integer-between j high)))
+        (require (= (+ (* i i) (* j j)) (* k k)))
+        (list i j k)))))
+
+(display "[done]\n")
+
+(display "\nex-4.36 - all-pythagorean-triples\n")
+
+; If we replace an-integer-between with an-integer-starting-from the variables
+; i and j will stay at their initial value 1 while k will increment endlessly.
+; Hence, only triplets of the form (1 1 n) will be generated.
+
+(define (all-pythagorean-triples)
+  (let ((i (an-integer-starting-from 1)))
+    (let ((j (an-integer-starting-from i)))
+      (let ((k (an-integer-starting-from j)))
+        (require (= (+ (* i i) (* j j)) (* k k)))
+        (list i j k)))))
+
+; Write a procedure that actually will accomplish this. (That is, write a
+; procedure for which repeatedly typing try-again would in principle eventually
+; generate all Pythagorean triples.) 
+
+; (display "[done]\n")
+
+(display "\nex-4.37\n")
+
+;(display "\nex-4.38\n")