Add exercise 4.36 Pythagorean triples

mceval/amb-pythagorean-triples.rkt

@@ -28,8 +28,29 @@
 
 ;; To generate all pythagorean triples, it is not sufficient to
 ;; replace an-integer-between with an-integer-starting-from because
-;; this would attempt to search through all i, then all j and then all
-;; k.  As such, we'd never get to the second value of j or k.
+;; this would attempt to search through all k, then all j and then all
+;; i.  As such, we'd never get to the second value of j or i.
 ;; Instead, we need to visit the values of i, j and k diagonally to
 ;; ensure that they are visited in order.
 
+(define (a-pythagorean-triple)
+  (let ((t (a-triple-with-sum-from 3)))
+    (let ((i (car t))
+          (j (car (cdr t)))
+          (k (car (cdr (cdr t)))))
+      (require (= (+ (* i i) (* j j))
+                 (* k k)))
+      (list i j k))))
+
+(define (a-triple-with-sum-between low high)
+  (let ((i (an-integer-between 1 high)))
+    (let ((j (an-integer-between i (max 1 (- high i)))))
+      (let ((k (an-integer-between j (max 1 (- high j i)))))
+        (let ((sum (+ i j k)))
+          (require (>= sum low))
+          (require (< sum high))
+          (list i j k))))))
+
+(define (a-triple-with-sum-from n)
+  (amb (a-triple-with-sum-between n (+ n 1))
+       (a-triple-with-sum-from (+ n 1))))

mceval/environment.rkt

@@ -177,6 +177,7 @@
         (list '>= >=)
         (list '<= <=)
         (list 'abs abs)
+        (list 'max max)
         (list 'remainder remainder)
         (list 'integer? integer?)
         (list 'sqrt sqrt)