Add exercise 4.53

mceval/amb-implementation.rkt

@@ -139,3 +139,52 @@ try-again
 7
 (if-fail (let ((x (an-element-of (quote (1 3 5 8))))) (require (even? x)) x) (quote all-odd))
 
+
+;; Exercise 4.53
+
+(define (square x) (* x x))
+
+(define (smallest-divisor n)
+  (find-divisor n 2))
+
+(define (find-divisor n test-divisor)
+  (cond ((> (square test-divisor) n) n)
+        ((divides? test-divisor n) test-divisor)
+        (else (find-divisor n (+ test-divisor 1)))))
+
+(define (divides? a b)
+  (= (remainder b a) 0))
+
+(define (prime? n)
+  (= n (smallest-divisor n)))
+
+(define (prime-sum-pair list1 list2)
+  (let ((a (an-element-of list1))
+        (b (an-element-of list2)))
+    (require (prime? (+ a b)))
+    (list a b)))
+
+
+;;; Amb-Eval input:
+(let ((pairs '()))
+  (if-fail (let ((p (prime-sum-pair '(1 3 5 8) '(20 35 110))))
+             (permanent-set! pairs (cons p pairs))
+             (amb))
+           pairs))
+
+;;; Starting a new problem 
+
+
+;;; Amb-Eval value:
+0
+((8 35) (3 110) (3 20))
+
+;; The call to prime-sum-pair succeeds for each of the pairs that
+;; satisfy the condition.  On success, the let body is entered, which
+;; conses the current result onto pairs.  Then the (amb) call forces
+;; back tracking to the next solution.  For each of these, pairs is
+;; augmented with the candidate solution, until there are no more
+;; solutions.  At this point, the let expression fails, and if-fail
+;; causes pairs to be evaluated.
+
+