refactor chapter 2

1.01.scm

@@ -1,32 +1,32 @@
-10 ; 10
-
-(+ 5 3 4) ; 12
-
-(- 9 1) ; 8
-
-(/ 6 2) ; 3
-
-(+ (* 2 4) (- 4 6)) ; 6
-
-(define a 3) ; a
-
-(define b (+ a 1)) ; b
-
-(+ a b (* a b)) ; 19
-
-(= a b) ; #f
-
-(if (and (> b a) (< b (* a b)))
-    b
-    a) ; 4
-
-(cond ((= a 4) 6)
-      ((= b 4) (+ 6 7 a))
-      (else 25)) ; 16
-
-(+ 2 (if (> b a) b a)) ; 6
-
-(* (cond ((> a b) a)
-         ((< a b) b)
-         (else -1))
+10 ; 10
+
+(+ 5 3 4) ; 12
+
+(- 9 1) ; 8
+
+(/ 6 2) ; 3
+
+(+ (* 2 4) (- 4 6)) ; 6
+
+(define a 3) ; a
+
+(define b (+ a 1)) ; b
+
+(+ a b (* a b)) ; 19
+
+(= a b) ; #f
+
+(if (and (> b a) (< b (* a b)))
+    b
+    a) ; 4
+
+(cond ((= a 4) 6)
+      ((= b 4) (+ 6 7 a))
+      (else 25)) ; 16
+
+(+ 2 (if (> b a) b a)) ; 6
+
+(* (cond ((> a b) a)
+         ((< a b) b)
+         (else -1))
    (+ a 1)) ; 16

1.03.scm

@@ -1,8 +1,8 @@
-(define (>= a b)
-  (or (> a b) (= a b)))
-
-(define (sum-larger-numbers a b c)
-  (cond
-    ((and (>= a c) (>= b c)) (+ a b))
-    ((and (>= b a) (>= c a)) (+ b c))
+(define (>= a b)
+  (or (> a b) (= a b)))
+
+(define (sum-larger-numbers a b c)
+  (cond
+    ((and (>= a c) (>= b c)) (+ a b))
+    ((and (>= b a) (>= c a)) (+ b c))
     ((and (>= a b) (>= c b)) (+ a c))))

1.04.scm

@@ -1,2 +1,2 @@
-(define (a-plus-abs-b a b)
+(define (a-plus-abs-b a b)
   ((if (> b 0) + -) a b))

1.05.scm

@@ -1,8 +1,8 @@
-(define (p) (p))
-
-(define (test x y)
-  (if (= x 0)
-      0
-      y))
-
+(define (p) (p))
+
+(define (test x y)
+  (if (= x 0)
+      0
+      y))
+
 (test 0 (p))

1.06.scm

@@ -1,3 +1,3 @@
-(define (new-if predicate then-clause else-clause)
-  (cond (predicate then-clause)
+(define (new-if predicate then-clause else-clause)
+  (cond (predicate then-clause)
         (else else-clause)))

1.07.scm

@@ -1,27 +1,27 @@
-(define (sqrt-iter guess x)
-  (if (good-enough? guess x)
-      guess
-      (sqrt-iter (improve guess x)
-                 x)))
-
-(define (improve guess x)
-  (average guess (/ x guess)))
-
-(define (average x y)
-  (/ (+ x y) 2))
-
-(define (good-enough? guess x)
-  (< (abs (- (square guess) x)) 0.001))
-
-(define (square x)
-  (* x x))
-
-(define (sqrt x)
-  (sqrt-iter 1.0 x))
-
-(sqrt 2) ; 1.4142156862745097
-
-(define (good-enough-alternative? guess x)
-  (< (abs (/ (- (improve guess x) guess)
-             guess))
+(define (sqrt-iter guess x)
+  (if (good-enough? guess x)
+      guess
+      (sqrt-iter (improve guess x)
+                 x)))
+
+(define (improve guess x)
+  (average guess (/ x guess)))
+
+(define (average x y)
+  (/ (+ x y) 2))
+
+(define (good-enough? guess x)
+  (< (abs (- (square guess) x)) 0.001))
+
+(define (square x)
+  (* x x))
+
+(define (sqrt x)
+  (sqrt-iter 1.0 x))
+
+(sqrt 2) ; 1.4142156862745097
+
+(define (good-enough-alternative? guess x)
+  (< (abs (/ (- (improve guess x) guess)
+             guess))
      0.001))

1.08.scm

@@ -1,20 +1,20 @@
-(define (cbrt-iter guess x)
-  (if (good-enough? guess x)
-      guess
-      (cbrt-iter (improve guess x)
-                 x)))
-
-(define (good-enough? guess x)
-  (< (abs (- (cube guess) x)) 0.001))
-
-(define (cube x)
-  (* x x x))
-
-(define (improve guess x)
-  (/ (+ (/ x (square guess)) (* 2 guess)) 3))
-
-(define (square x)
-  (* x x))
-
-(define (cbrt x)
+(define (cbrt-iter guess x)
+  (if (good-enough? guess x)
+      guess
+      (cbrt-iter (improve guess x)
+                 x)))
+
+(define (good-enough? guess x)
+  (< (abs (- (cube guess) x)) 0.001))
+
+(define (cube x)
+  (* x x x))
+
+(define (improve guess x)
+  (/ (+ (/ x (square guess)) (* 2 guess)) 3))
+
+(define (square x)
+  (* x x))
+
+(define (cbrt x)
   (cbrt-iter 1.0 x))

1.09.scm

@@ -1,27 +1,27 @@
-(define (+ a b)
-  (if (= a 0)
-      b
-      (inc (+ (dec a) b))))
-
-; (+ 4 5)
-; (inc (+ 3 5))
-; (inc (inc (+ 2 5)))
-; (inc (inc (inc (+ 1 5))))
-; (inc (inc (inc (inc (+ 0 5)))))
-; (inc (inc (inc (inc 5))))
-; (inc (inc (inc 6)))
-; (inc (inc 7))
-; (inc 8)
-; 9
-
-; (define (+ a b)
-;   (if (= a 0)
-;       b
-;       (+ (dec a) (inc b))))
-
-; (+ 4 5)
-; (+ 3 6)
-; (+ 2 7)
-; (+ 1 8)
-; (+ 0 9)
+(define (+ a b)
+  (if (= a 0)
+      b
+      (inc (+ (dec a) b))))
+
+; (+ 4 5)
+; (inc (+ 3 5))
+; (inc (inc (+ 2 5)))
+; (inc (inc (inc (+ 1 5))))
+; (inc (inc (inc (inc (+ 0 5)))))
+; (inc (inc (inc (inc 5))))
+; (inc (inc (inc 6)))
+; (inc (inc 7))
+; (inc 8)
+; 9
+
+; (define (+ a b)
+;   (if (= a 0)
+;       b
+;       (+ (dec a) (inc b))))
+
+; (+ 4 5)
+; (+ 3 6)
+; (+ 2 7)
+; (+ 1 8)
+; (+ 0 9)
 ; 9

1.10.scm

@@ -1,13 +1,13 @@
-(define (A x y)
-  (cond ((= y 0) 0)
-        ((= x 0) (* 2 y))
-        ((= y 1) 2)
-        (else (A (- x 1) (A x (- y 1))))))
-
-(A 1 10) ; 1024
-(A 2 2)  ; 4
-(A 3 3)  ; 65536
-
-(define (f n) (A 0 n)) ; 2n
-(define (g n) (A 1 n)) ; n=0: 0, n>0: 2^n
+(define (A x y)
+  (cond ((= y 0) 0)
+        ((= x 0) (* 2 y))
+        ((= y 1) 2)
+        (else (A (- x 1) (A x (- y 1))))))
+
+(A 1 10) ; 1024
+(A 2 2)  ; 4
+(A 3 3)  ; 65536
+
+(define (f n) (A 0 n)) ; 2n
+(define (g n) (A 1 n)) ; n=0: 0, n>0: 2^n
 (define (h n) (A 2 n)) ; n=0: 0; n=1: 2; n>1: 2^2^...(n-1) times

1.11.scm

@@ -1,15 +1,15 @@
-(define (f n)
-  (if (< n 3)
-      n
-      (+ (f (- n 1))
-         (* 2 (f (- n 2)))
-         (* 3 (f (- n 3))))))
-
-(define (f.iter n)
-  (define (f-iter a b c count)
-    (if (= n count)
-        c
-        (f-iter b c (+ c (* 2 b) (* 3 a)) (+ count 1))))
-  (if (< n 3)
-      n
+(define (f n)
+  (if (< n 3)
+      n
+      (+ (f (- n 1))
+         (* 2 (f (- n 2)))
+         (* 3 (f (- n 3))))))
+
+(define (f.iter n)
+  (define (f-iter a b c count)
+    (if (= n count)
+        c
+        (f-iter b c (+ c (* 2 b) (* 3 a)) (+ count 1))))
+  (if (< n 3)
+      n
       (f-iter 0 1 2 2)))

1.12.scm

@@ -1,6 +1,5 @@
-(define (pascal c r)
-  (if (or (= r c) (= 0 c))
-      1
-      (+ (pascal c (- r 1))
-         (pascal (- c 1) (- r 1)))))
-
+(define (pascal c r)
+  (if (or (= r c) (= 0 c))
+      1
+      (+ (pascal c (- r 1))
+         (pascal (- c 1) (- r 1)))))

1.16.scm

@@ -1,15 +1,14 @@
-(define (square a)
-  (* a a))
-
-(define (halve a)
-  (/ a 2))
-
-(define (fast-expt b n)
-  (define (fast-expt-iter b n product)
-    (if (= n 0)
-        product
-        (if (even? n)
-            (fast-expt-iter (square b) (halve n) product)
-            (fast-expt-iter b (dec n) (* b product)))))
-
-  (fast-expt-iter b n 1))
+(define (square x)
+  (* x x))
+
+(define (halve x)
+  (/ x 2))
+
+(define (fast-expt b n)
+  (define (fast-expt-iter b n a)
+    (cond
+      ((= n 0) a)
+      ((even? n) (fast-expt-iter (square b) (halve n) a))
+      (else (fast-expt-iter b (- n 1) (* b a)))))
+
+  (fast-expt-iter b n 1))

1.17.scm

@@ -1,12 +1,11 @@
-(define (double x)
-  (+ x x))
-
-(define (halve x)
-  (/ x 2))
-
-(define (multiply a b)
-  (if (= b 0)
-      0
-      (if (even? b)
-          (multiply (double a) (halve b))
-          (+ a (multiply a (- b 1))))))
+(define (double x)
+  (+ x x))
+
+(define (halve x)
+  (/ x 2))
+
+(define (* a b)
+  (cond
+    ((= b 0) a)
+    ((even? b) (* (double a) (halve b)))
+    (else (+ a (* a (- b 1))))))