Implement till 3.56

ex-3_50-xx.scm

@@ -106,3 +106,85 @@
 
 (display "\nex-3.53\n")
 
+(define (add-streams s1 s2)
+  (stream-map + s1 s2))
+
+(define ones (cons-stream 1 ones))
+
+(define integers (cons-stream 1 (add-streams ones integers)))
+
+(define (take n xs)
+  (if (= n 0)
+    '()
+    (cons (stream-car xs)
+          (take (- n 1) (stream-cdr xs)))))
+
+(assert (take 3 integers)
+        '(1 2 3))
+
+(define fibs
+  (cons-stream 0
+               (cons-stream 1
+                            (add-streams (stream-cdr fibs)
+                                         fibs))))
+
+(assert (take 7 fibs)
+        '(0 1 1 2 3 5 8))
+
+(define (scale-stream stream factor)
+  (stream-map (lambda (x) (* x factor)) stream))
+
+(define double (cons-stream 1 (scale-stream double 2)))
+
+(assert (take 3 double)
+        '(1 2 4))
+
+(define s (cons-stream 1 (add-streams s s)))
+(assert (take 5 s)
+        '(1 2 4 8 16))
+
+(display "\nex-3.54 - factorials\n")
+
+(define (mul-streams s1 s2)
+  (stream-map * s1 s2))
+
+(define factorials (cons-stream 1 (mul-streams (stream-cdr integers) factorials)))
+
+(assert (take 5 factorials)
+        '(1 2 6 24 120))
+
+(display "\nex-3.55 - partial-sums\n")
+
+(define (partial-sums xs)
+  (cons-stream (stream-car xs)
+               (add-streams (partial-sums xs)
+                            (stream-cdr xs))))
+
+(assert (take 5 (partial-sums integers))
+        '(1 3 6 10 15))
+
+(display "\nex-3.56 - enumerate multiplies of 2, 3, 5\n")
+
+(define (merge s1 s2)
+  (cond ((stream-null? s1) s2)
+        ((stream-null? s2) s1)
+        (else
+         (let ((s1car (stream-car s1))
+               (s2car (stream-car s2)))
+           (cond ((< s1car s2car)
+                  (cons-stream s1car (merge (stream-cdr s1) s2)))
+                 ((> s1car s2car)
+                  (cons-stream s2car (merge s1 (stream-cdr s2))))
+                 (else
+                  (cons-stream s1car
+                               (merge (stream-cdr s1)
+                                      (stream-cdr s2)))))))))
+
+(define S (cons-stream 1 (merge (merge (scale-stream S 2) (scale-stream S 3))
+                                (scale-stream S 5))))
+
+(assert (take 10 S)
+        '(1 2 3 4 5 6 8 9 10 12))
+
+(display "\nex-3.57\n")
+