Split chapter 1 into multiple files

3 files changed, 612 insertions, 598 deletions

diff --git a/chap1/part1.rkt b/chap1/part1.rkt
new file mode 100644
index 0000000..78c7768
--- /dev/null
+++ b/chap1/part1.rkt
@@ -0,0 +1,168 @@
+#lang sicp
+
+;; Chapter 1
+;; Building Abstractions with Procedures
+
+;; 1.1
+;; The Elements of Programming
+
+#| 1.1 |#
+
+#| 10 |#
+#| 10 |#
+
+#| (+ 5 3 4) |#
+#| 12 |#
+
+#| (- 9 1) |#
+#| 8 |#
+
+#| (/ 6 2) |#
+#| 3 |#
+
+#| (+ (* 2 4) (- 4 6)) |#
+#| 6 |#
+
+#| (define a 3) |#
+#| () |#
+
+#| (define b (+ a 1)) |#
+#| () |#
+
+#| (+ 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 |#
+
+#| 1.2 |#
+
+(/
+  (+ 5 4 (- 2 (- 3 (+ 6 (/ 4 5)))))
+  (* 3 (- 6 2) (- 2 7)))
+
+
+(#%provide square)
+(define (square x) (* x x))
+(define (sum-of-squares x y) (+ (square x) (square y)))
+
+#| 1.3 |#
+
+(#%provide sos-two-larger)
+(define (sos-two-larger a b c)
+  (if (> a b)
+    (sum-of-squares a (if (> b c) b c))
+    (sum-of-squares b (if (> a c) a c))))
+
+#| 1.4 |#
+
+(#%provide a-plus-abs-b)
+(define (a-plus-abs-b a b)
+  ((if (> b 0) + -) a b))
+
+#| 1.5 |#
+
+(#%provide p)
+(#%provide test)
+(define (p) (p))
+(define (test x y)
+  (if (= x 0)
+    0
+    y))
+
+#| Applicative order: this will loop forever |#
+#| Normal order: this will terminate after one call to test |#
+
+#| (test 0 (p)) |#
+
+
+(define (average x y)
+  (/ (+ x y) 2))
+
+(#%provide sqrt-)
+(define (sqrt- x)
+  (define (good-enough? guess)
+    (< (abs (- (square guess) x)) 0.001))
+  (define (improve guess)
+    (average guess (/ x guess)))
+  (define (sqrt-iter guess)
+    (if (good-enough? guess)
+      guess
+      (sqrt-iter (improve guess))))
+  (sqrt-iter 1.0))
+
+#| 1.6 |#
+
+(define (new-if pred then-clause else-clause)
+  (cond
+    (pred then-clause)
+    (else else-clause)))
+
+(#%provide sqrt-new)
+(define (sqrt-new x)
+  (define (good-enough? guess)
+    (< (abs (- (square guess) x)) 0.001))
+  (define (improve guess)
+    (average guess (/ x guess)))
+  (define (sqrt-iter guess)
+    (new-if (good-enough? guess)
+      guess
+      (sqrt-iter (improve guess))))
+  (sqrt-iter 1.0))
+
+#| 1.7 |#
+
+(#%provide sqrt-delt)
+(define (sqrt-delt x)
+  (define (good-enough? last-guess guess)
+    (< (/ (abs (- last-guess guess)) x) 0.000000000001))
+  (define (improve guess)
+    (average guess (/ x guess)))
+  (define (sqrt-iter last-guess guess)
+    (if (good-enough? last-guess guess)
+      guess
+      (sqrt-iter guess (improve guess))))
+  (sqrt-iter 1.0 (improve 1.0)))
+
+(square (sqrt-delt 479800023432748679))
+(square (sqrt-delt 0.00000024353))
+
+#| 1.8 |#
+
+(#%provide cube)
+(define (cube x) (* x x x))
+
+(#%provide cbrt)
+(define (cbrt x)
+  (define (good-enough? guess)
+    (< (abs (- (cube guess) x)) 0.001))
+  (define (improve y)
+    (/ (+ (/ x (square y)) (* 2 y)) 3))
+  (define (cbrt-iter guess)
+    (if (good-enough? guess)
+      guess
+      (cbrt-iter (improve guess))))
+  (cbrt-iter 1.0))
diff --git a/chap1.rkt b/chap1/part2.rkt
index d91a345..d749de9 100644
--- a/chap1.rkt
+++ b/chap1/part2.rkt
@@ -3,169 +3,8 @@
 ;; Chapter 1
 ;; Building Abstractions with Procedures
 
-;; 1.1
-;; The Elements of Programming
-
-#| 1.1 |#
-
-#| 10 |#
-#| 10 |#
-
-#| (+ 5 3 4) |#
-#| 12 |#
-
-#| (- 9 1) |#
-#| 8 |#
-
-#| (/ 6 2) |#
-#| 3 |#
-
-#| (+ (* 2 4) (- 4 6)) |#
-#| 6 |#
-
-#| (define a 3) |#
-#| () |#
-
-#| (define b (+ a 1)) |#
-#| () |#
-
-#| (+ 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 |#
-
-#| 1.2 |#
-
-(/
-  (+ 5 4 (- 2 (- 3 (+ 6 (/ 4 5)))))
-  (* 3 (- 6 2) (- 2 7)))
-
-
-(#%provide square)
-(define (square x) (* x x))
-(define (sum-of-squares x y) (+ (square x) (square y)))
-
-#| 1.3 |#
-
-(#%provide sos-two-larger)
-(define (sos-two-larger a b c)
-  (if (> a b)
-    (sum-of-squares a (if (> b c) b c))
-    (sum-of-squares b (if (> a c) a c))))
-
-#| 1.4 |#
-
-(#%provide a-plus-abs-b)
-(define (a-plus-abs-b a b)
-  ((if (> b 0) + -) a b))
-
-#| 1.5 |#
-
-(#%provide p)
-(#%provide test)
-(define (p) (p))
-(define (test x y)
-  (if (= x 0)
-    0
-    y))
-
-#| Applicative order: this will loop forever |#
-#| Normal order: this will terminate after one call to test |#
-
-#| (test 0 (p)) |#
-
-
-(define (average x y)
-  (/ (+ x y) 2))
-
-(#%provide sqrt-)
-(define (sqrt- x)
-  (define (good-enough? guess)
-    (< (abs (- (square guess) x)) 0.001))
-  (define (improve guess)
-    (average guess (/ x guess)))
-  (define (sqrt-iter guess)
-    (if (good-enough? guess)
-      guess
-      (sqrt-iter (improve guess))))
-  (sqrt-iter 1.0))
-
-#| 1.6 |#
-
-(define (new-if pred then-clause else-clause)
-  (cond
-    (pred then-clause)
-    (else else-clause)))
-
-(#%provide sqrt-new)
-(define (sqrt-new x)
-  (define (good-enough? guess)
-    (< (abs (- (square guess) x)) 0.001))
-  (define (improve guess)
-    (average guess (/ x guess)))
-  (define (sqrt-iter guess)
-    (new-if (good-enough? guess)
-      guess
-      (sqrt-iter (improve guess))))
-  (sqrt-iter 1.0))
-
-#| 1.7 |#
-
-(#%provide sqrt-delt)
-(define (sqrt-delt x)
-  (define (good-enough? last-guess guess)
-    (< (/ (abs (- last-guess guess)) x) 0.000000000001))
-  (define (improve guess)
-    (average guess (/ x guess)))
-  (define (sqrt-iter last-guess guess)
-    (if (good-enough? last-guess guess)
-      guess
-      (sqrt-iter guess (improve guess))))
-  (sqrt-iter 1.0 (improve 1.0)))
-
-(square (sqrt-delt 479800023432748679))
-(square (sqrt-delt 0.00000024353))
-
-#| 1.8 |#
-
-(#%provide cube)
-(define (cube x) (* x x x))
-
-(#%provide cbrt)
-(define (cbrt x)
-  (define (good-enough? guess)
-    (< (abs (- (cube guess) x)) 0.001))
-  (define (improve y)
-    (/ (+ (/ x (square y)) (* 2 y)) 3))
-  (define (cbrt-iter guess)
-    (if (good-enough? guess)
-      guess
-      (cbrt-iter (improve guess))))
-  (cbrt-iter 1.0))
+;; 1.2
+;; Procedures and the Processes They Generate
 
 #| 1.9 |#
 
@@ -1015,438 +854,3 @@
 (define (integral f a b dx)
   (define (add-dx x) (+ x dx))
   (* (sum f (+ a (/ dx 2.0)) add-dx b) dx))
-
-#| 1.29 |#
-
-(#%provide simpson)
-(define (simpson f a b n)
-  (define h (/ (- b a) n))
-  (define (single-term k)
-    (f (+ a (* k h))))
-  (define (simpson-term k)
-    (+
-      (single-term (- k 1))
-      (* 4.0 (single-term k))
-      (single-term (+ k 1))))
-  (define (simpson-next k) (+ k 2))
-  (* (/ h 3.0) (sum simpson-term 1 simpson-next n)))
-
-#| 1.30 |#
-
-(#%provide sum-iter)
-(define (sum-iter term a next b)
-  (define (iter a result)
-    (if (> a b)
-      result
-      (iter (next a) (+ (term a) result))))
-  (iter a 0))
-
-#| 1.31 |#
-
-(#%provide product)
-(define (product term a next b)
-  (if (> a b)
-    1
-    (*
-      (term a)
-      (product term (next a) next b))))
-
-(#%provide factorial)
-(define (factorial n)
-  (product id 1 inc n))
-
-(#%provide pi-prod)
-(define (pi-prod n)
-  (define (pi-term x) (/ (* (- x 1) (+ x 1)) (square x)))
-  (define (pi-next x) (+ x 2))
-  (* 4.0 (product pi-term 3 pi-next n)))
-
-(#%provide product-iter)
-(define (product-iter term a next b)
-  (define (iter a result)
-    (if (> a b)
-      result
-      (iter (next a) (* (term a) result))))
-  (iter a 1))
-
-#| 1.32 |#
-
-(#%provide accumulate)
-(define (accumulate combiner null-value term a next b)
-  (if (> a b)
-    null-value
-    (combiner
-      (term a)
-      (accumulate combiner null-value term (next a) next b))))
-
-(#%provide prod-acc)
-(define (prod-acc term a next b)
-  (accumulate * 1 term a next b))
-
-(#%provide sum-acc)
-(define (sum-acc term a next b)
-  (accumulate + 0 term a next b))
-
-(#%provide acc-iter)
-(define (acc-iter combiner null-value term a next b)
-  (define (iter a result)
-    (if (> a b)
-      result
-      (iter (next a) (combiner (term a) result))))
-  (iter a null-value))
-
-#| 1.33 |#
-
-(#%provide filtered-accumulate)
-(define (filtered-accumulate combiner null-value pred term a next b)
-  (if (> a b)
-    null-value
-    (if (pred a)
-      (combiner
-        (term a)
-        (filtered-accumulate combiner null-value pred term (next a) next b))
-      (filtered-accumulate combiner null-value pred term (next a) next b))))
-
-(#%provide sum-prime-square)
-(define (sum-prime-square a b)
-  (filtered-accumulate + 0 prime? square a inc b))
-
-(#%provide prod-coprime)
-(define (prod-coprime n)
-  (define (pred i) (= (gcd- i n) 1))
-  (filtered-accumulate * 1 pred id 1 inc n))
-
-(#%provide pi-sum-lam)
-(define (pi-sum-lam a b)
-  (sum
-    (lambda (x) (/ 1.0 (* x (+ x 2))))
-    a
-    (lambda (x) (+ x 4))
-    b))
-
-(#%provide integral-lam)
-(define (integral-lam f a b dx)
-  (*
-    (sum
-      f
-      (+ a (/ dx 2.0))
-      (lambda (x) (+ x dx))
-      b)
-    dx))
-
-(#%provide f-help)
-(define (f-help x y)
-  (define (f-helper a b)
-    (+
-      (* x (square a))
-      (* y b)
-      (* a b)))
-  (f-helper
-    (+ 1 (* x y))
-    (- 1 y)))
-
-(#%provide f-lam)
-(define (f-lam x y)
-  ((lambda (a b)
-     (+
-       (* x (square a))
-       (* y b)
-       (* a b)))
-   (+ 1 (* x y))
-   (- 1 y)))
-
-(#%provide f-let)
-(define (f-let x y)
-  (let
-    ((a (+ 1 (* x y)))
-     (b (- 1 y)))
-    (+
-     (* x (square a))
-     (* y b)
-     (* a b))))
-
-(#%provide f-def)
-(define (f-def x y)
-  (define a (+ 1 (* x y)))
-  (define b (- 1 y))
-  (+
-    (* x (square a))
-    (* y b)
-    (* a b)))
-
-#| 1.34 |#
-
-;; (define (f g) (g 2))
-
-;; (f square) 4
-
-;; (f (lambda (z) (* z (+ z 1)))) 6
-
-;; (f f) (f 2) (2 2) error
-
-(#%provide search)
-(define (search f neg-point pos-point)
-  (let ((midpoint (average neg-point pos-point)))
-    (if (close-enough? neg-point pos-point)
-      midpoint
-      (let ((test-value (f midpoint)))
-        (cond
-          ((positive? test-value)
-           (search f neg-point midpoint))
-          ((negative? test-value)
-           (search f midpoint pos-point))
-          (else midpoint))))))
-
-(define (close-enough? x y)
-  (< (abs (- x y)) 0.001))
-
-(#%provide half-interval-method)
-(define (half-interval-method f a b)
-  (let
-    ((a-value (f a))
-     (b-value (f b)))
-    (cond
-      ((and (negative? a-value) (positive? b-value))
-       (search f a b))
-      ((and (negative? b-value) (positive? a-value))
-       (search f b a))
-      (else
-        (error "Values are not of opposite sign" a b)))))
-
-(define tolerance 0.0001)
-
-(#%provide fixed-point)
-(define (fixed-point f first-guess)
-  (define (close-enough? v1 v2)
-    (< (abs (- v1 v2)) tolerance))
-  (define (try guess)
-    (display guess)
-    (newline)
-    (let ((next (f guess)))
-      (if (close-enough? guess next)
-        next
-        (try next))))
-  (try first-guess))
-
-(#%provide sqrt-fix)
-(define (sqrt-fix x)
-  (fixed-point
-    (lambda (y) (average y (/ x y)))
-    1.0))
-
-#| 1.35 |#
-
-(#%provide golden)
-(define (golden)
-  (fixed-point
-    (lambda (x) (+ 1.0 (/ 1.0 x)))
-    1.0))
-
-#| 1.36 |#
-
-(#%provide x-to-the-x)
-(define (x-to-the-x)
-  (fixed-point
-    (lambda (x) (/ (log 1000.0) (log x)))
-    2.0))
-
-#| 1.37 |#
-
-(#%provide cont-frac)
-(define (cont-frac n d k)
-  (define (iter res i)
-    (if (= i 0)
-      res
-      (iter (/ (n i) (+ (d i) res)) (- i 1))))
-  (iter 0 k))
-
-;; (cont-frac (lambda (i) 1.0) (lambda (i) 1.0) 11)
-;; 0.6180555555555556
-
-;; Accurate to 4 places after 11 iterations
-
-(#%provide cont-frac-rec)
-(define (cont-frac-rec n d k)
-  (define (rec i)
-    (if (> i k)
-      0
-      (/ (n i) (+ (d i) (rec (+ i 1))))))
-  (rec 1))
-
-#| 1.38 |#
-
-(#%provide e-approx)
-(define (e-approx k)
-  (define (n i) 1.0)
-  (define (d i)
-    (if (divides? 3 (+ i 1))
-      (* 2 (/ (+ i 1) 3))
-      1.0))
-  (+ (cont-frac n d k) 2))
-
-#| 1.39 |#
-
-(#%provide tan-cf)
-(define (tan-cf x k)
-  (define (rec prod sum)
-    (let ((stop (+ 1 (* 2 (- k 1)))))
-      (if (> sum stop)
-        0
-        (/ prod (- sum (rec (* prod x) (+ sum 2)))))))
-  (rec x 1.0))
-
-(define (average-damp f)
-  (lambda (x) (average x (f x))))
-
-((average-damp square) 10)
-
-(#%provide sqrt-avg-damp)
-(define (sqrt-avg-damp x)
-  (fixed-point
-    (average-damp (lambda (y) (/ x y)))
-    1.0))
-
-(#%provide cbrt-avg-damp)
-(define (cbrt-avg-damp x)
-  (fixed-point
-    (average-damp (lambda (y) (/ x (square y))))
-    1.0))
-
-(define (deriv g)
-  (lambda (x)
-    (/
-      (- (g (+ x dx)) (g x))
-      dx)))
-
-(define dx 0.00001)
-
-((deriv cube) 5)
-
-(define (newton-transform g)
-  (lambda (x)
-    (- x (/ (g x) ((deriv g) x)))))
-
-(#%provide newtons-method)
-(define (newtons-method g guess)
-  (fixed-point (newton-transform g) guess))
-
-(#%provide sqrt-newt)
-(define (sqrt-newt x)
-  (newtons-method
-    (lambda (y) (- (square y) x))
-    1.0))
-
-(define (fixed-point-of-transform g transform guess)
-  (fixed-point (transform g) guess))
-
-(#%provide sqrt-ad-trans)
-(define (sqrt-ad-trans x)
-  (fixed-point-of-transform
-    (lambda (y) (/ x y))
-    average-damp
-    1.0))
-
-(#%provide sqrt-newt-trans)
-(define (sqrt-newt-trans x)
-  (fixed-point-of-transform
-    (lambda (y) (- (square y) x))
-    newton-transform
-    1.0))
-
-#| 1.40 |#
-
-(#%provide cubic)
-(define (cubic a b c)
-  (lambda (x)
-    (+
-      (cube x)
-      (* a (square x))
-      (* b x)
-      c)))
-
-;; (newtons-method (cubic 0 0 -8.0) 4.0)
-
-#| 1.41 |#
-
-(#%provide twice)
-(define (twice f)
-  (lambda (x) (f (f x))))
-
-;; (twice inc 1)
-;; 3
-
-;; (((twice (twice twice)) inc) 5)
-;; 21
-
-#| 1.42 |#
-
-(#%provide compose-)
-(define (compose- f g)
-  (lambda (x) (f (g x))))
-
-;; ((compose- square inc) 6)
-;; 49
-
-#| 1.43 |#
-
-(#%provide repeated)
-(define (repeated f n)
-  (if (= n 0)
-    (lambda (x) x)
-    (compose- (repeated f (- n 1)) f)))
-
-;; ((repeated square 2) 5)
-;; 625
-
-#| 1.44 |#
-
-(#%provide smooth)
-(define (smooth f)
-  (lambda (x)
-    (/
-      (+
-        (f (- x dx))
-        (f x)
-        (f (+ x dx)))
-      3.0)))
-
-(#%provide n-smooth)
-(define (n-smooth f n)
-  (repeated smooth n))
-
-#| 1.45 |#
-
-(#%provide flog2)
-(define (flog2 n) (floor (/ (log n) (log 2))))
-
-(#%provide nth-root)
-(define (nth-root n x)
-  (fixed-point
-    ((repeated average-damp (flog2 n))
-     (lambda (y) (/ x (fast-expt-iter y (- n 1)))))
-    1.0))
-
-#| 1.46 |#
-
-(#%provide iterative-improve)
-(define (iterative-improve good-enough? improve)
-  (lambda (guess)
-    (define (iter x)
-      (if (good-enough? x)
-        x
-        (iter (improve x))))
-    (iter guess)))
-
-(#%provide sqrt-it-imp)
-(define (sqrt-it-imp x)
-  ((iterative-improve
-     (lambda (guess) (< (abs (- (square guess) x)) 0.001))
-     (lambda (guess) (average guess (/ x guess))))
-   1.0))
-
-(#%provide fixed-point-it-imp)
-(define (fixed-point-it-imp f first-guess)
-  ((iterative-improve
-     (lambda (guess) (< (abs (- guess (f guess))) tolerance))
-     f)
-   first-guess))
diff --git a/chap1/part3.rkt b/chap1/part3.rkt
new file mode 100644
index 0000000..74cd2e6
--- /dev/null
+++ b/chap1/part3.rkt
@@ -0,0 +1,442 @@
+#lang sicp
+
+;; Chapter 1
+;; Building Abstractions with Procedures
+
+;; 1.3
+;; Formulating Abstractions with Higher-Order Procedures
+
+#| 1.29 |#
+
+(#%provide simpson)
+(define (simpson f a b n)
+  (define h (/ (- b a) n))
+  (define (single-term k)
+    (f (+ a (* k h))))
+  (define (simpson-term k)
+    (+
+      (single-term (- k 1))
+      (* 4.0 (single-term k))
+      (single-term (+ k 1))))
+  (define (simpson-next k) (+ k 2))
+  (* (/ h 3.0) (sum simpson-term 1 simpson-next n)))
+
+#| 1.30 |#
+
+(#%provide sum-iter)
+(define (sum-iter term a next b)
+  (define (iter a result)
+    (if (> a b)
+      result
+      (iter (next a) (+ (term a) result))))
+  (iter a 0))
+
+#| 1.31 |#
+
+(#%provide product)
+(define (product term a next b)
+  (if (> a b)
+    1
+    (*
+      (term a)
+      (product term (next a) next b))))
+
+(#%provide factorial)
+(define (factorial n)
+  (product id 1 inc n))
+
+(#%provide pi-prod)
+(define (pi-prod n)
+  (define (pi-term x) (/ (* (- x 1) (+ x 1)) (square x)))
+  (define (pi-next x) (+ x 2))
+  (* 4.0 (product pi-term 3 pi-next n)))
+
+(#%provide product-iter)
+(define (product-iter term a next b)
+  (define (iter a result)
+    (if (> a b)
+      result
+      (iter (next a) (* (term a) result))))
+  (iter a 1))
+
+#| 1.32 |#
+
+(#%provide accumulate)
+(define (accumulate combiner null-value term a next b)
+  (if (> a b)
+    null-value
+    (combiner
+      (term a)
+      (accumulate combiner null-value term (next a) next b))))
+
+(#%provide prod-acc)
+(define (prod-acc term a next b)
+  (accumulate * 1 term a next b))
+
+(#%provide sum-acc)
+(define (sum-acc term a next b)
+  (accumulate + 0 term a next b))
+
+(#%provide acc-iter)
+(define (acc-iter combiner null-value term a next b)
+  (define (iter a result)
+    (if (> a b)
+      result
+      (iter (next a) (combiner (term a) result))))
+  (iter a null-value))
+
+#| 1.33 |#
+
+(#%provide filtered-accumulate)
+(define (filtered-accumulate combiner null-value pred term a next b)
+  (if (> a b)
+    null-value
+    (if (pred a)
+      (combiner
+        (term a)
+        (filtered-accumulate combiner null-value pred term (next a) next b))
+      (filtered-accumulate combiner null-value pred term (next a) next b))))
+
+(#%provide sum-prime-square)
+(define (sum-prime-square a b)
+  (filtered-accumulate + 0 prime? square a inc b))
+
+(#%provide prod-coprime)
+(define (prod-coprime n)
+  (define (pred i) (= (gcd- i n) 1))
+  (filtered-accumulate * 1 pred id 1 inc n))
+
+(#%provide pi-sum-lam)
+(define (pi-sum-lam a b)
+  (sum
+    (lambda (x) (/ 1.0 (* x (+ x 2))))
+    a
+    (lambda (x) (+ x 4))
+    b))
+
+(#%provide integral-lam)
+(define (integral-lam f a b dx)
+  (*
+    (sum
+      f
+      (+ a (/ dx 2.0))
+      (lambda (x) (+ x dx))
+      b)
+    dx))
+
+(#%provide f-help)
+(define (f-help x y)
+  (define (f-helper a b)
+    (+
+      (* x (square a))
+      (* y b)
+      (* a b)))
+  (f-helper
+    (+ 1 (* x y))
+    (- 1 y)))
+
+(#%provide f-lam)
+(define (f-lam x y)
+  ((lambda (a b)
+     (+
+       (* x (square a))
+       (* y b)
+       (* a b)))
+   (+ 1 (* x y))
+   (- 1 y)))
+
+(#%provide f-let)
+(define (f-let x y)
+  (let
+    ((a (+ 1 (* x y)))
+     (b (- 1 y)))
+    (+
+     (* x (square a))
+     (* y b)
+     (* a b))))
+
+(#%provide f-def)
+(define (f-def x y)
+  (define a (+ 1 (* x y)))
+  (define b (- 1 y))
+  (+
+    (* x (square a))
+    (* y b)
+    (* a b)))
+
+#| 1.34 |#
+
+;; (define (f g) (g 2))
+
+;; (f square) 4
+
+;; (f (lambda (z) (* z (+ z 1)))) 6
+
+;; (f f) (f 2) (2 2) error
+
+(#%provide search)
+(define (search f neg-point pos-point)
+  (let ((midpoint (average neg-point pos-point)))
+    (if (close-enough? neg-point pos-point)
+      midpoint
+      (let ((test-value (f midpoint)))
+        (cond
+          ((positive? test-value)
+           (search f neg-point midpoint))
+          ((negative? test-value)
+           (search f midpoint pos-point))
+          (else midpoint))))))
+
+(define (close-enough? x y)
+  (< (abs (- x y)) 0.001))
+
+(#%provide half-interval-method)
+(define (half-interval-method f a b)
+  (let
+    ((a-value (f a))
+     (b-value (f b)))
+    (cond
+      ((and (negative? a-value) (positive? b-value))
+       (search f a b))
+      ((and (negative? b-value) (positive? a-value))
+       (search f b a))
+      (else
+        (error "Values are not of opposite sign" a b)))))
+
+(define tolerance 0.0001)
+
+(#%provide fixed-point)
+(define (fixed-point f first-guess)
+  (define (close-enough? v1 v2)
+    (< (abs (- v1 v2)) tolerance))
+  (define (try guess)
+    (display guess)
+    (newline)
+    (let ((next (f guess)))
+      (if (close-enough? guess next)
+        next
+        (try next))))
+  (try first-guess))
+
+(#%provide sqrt-fix)
+(define (sqrt-fix x)
+  (fixed-point
+    (lambda (y) (average y (/ x y)))
+    1.0))
+
+#| 1.35 |#
+
+(#%provide golden)
+(define (golden)
+  (fixed-point
+    (lambda (x) (+ 1.0 (/ 1.0 x)))
+    1.0))
+
+#| 1.36 |#
+
+(#%provide x-to-the-x)
+(define (x-to-the-x)
+  (fixed-point
+    (lambda (x) (/ (log 1000.0) (log x)))
+    2.0))
+
+#| 1.37 |#
+
+(#%provide cont-frac)
+(define (cont-frac n d k)
+  (define (iter res i)
+    (if (= i 0)
+      res
+      (iter (/ (n i) (+ (d i) res)) (- i 1))))
+  (iter 0 k))
+
+;; (cont-frac (lambda (i) 1.0) (lambda (i) 1.0) 11)
+;; 0.6180555555555556
+
+;; Accurate to 4 places after 11 iterations
+
+(#%provide cont-frac-rec)
+(define (cont-frac-rec n d k)
+  (define (rec i)
+    (if (> i k)
+      0
+      (/ (n i) (+ (d i) (rec (+ i 1))))))
+  (rec 1))
+
+#| 1.38 |#
+
+(#%provide e-approx)
+(define (e-approx k)
+  (define (n i) 1.0)
+  (define (d i)
+    (if (divides? 3 (+ i 1))
+      (* 2 (/ (+ i 1) 3))
+      1.0))
+  (+ (cont-frac n d k) 2))
+
+#| 1.39 |#
+
+(#%provide tan-cf)
+(define (tan-cf x k)
+  (define (rec prod sum)
+    (let ((stop (+ 1 (* 2 (- k 1)))))
+      (if (> sum stop)
+        0
+        (/ prod (- sum (rec (* prod x) (+ sum 2)))))))
+  (rec x 1.0))
+
+(define (average-damp f)
+  (lambda (x) (average x (f x))))
+
+((average-damp square) 10)
+
+(#%provide sqrt-avg-damp)
+(define (sqrt-avg-damp x)
+  (fixed-point
+    (average-damp (lambda (y) (/ x y)))
+    1.0))
+
+(#%provide cbrt-avg-damp)
+(define (cbrt-avg-damp x)
+  (fixed-point
+    (average-damp (lambda (y) (/ x (square y))))
+    1.0))
+
+(define (deriv g)
+  (lambda (x)
+    (/
+      (- (g (+ x dx)) (g x))
+      dx)))
+
+(define dx 0.00001)
+
+((deriv cube) 5)
+
+(define (newton-transform g)
+  (lambda (x)
+    (- x (/ (g x) ((deriv g) x)))))
+
+(#%provide newtons-method)
+(define (newtons-method g guess)
+  (fixed-point (newton-transform g) guess))
+
+(#%provide sqrt-newt)
+(define (sqrt-newt x)
+  (newtons-method
+    (lambda (y) (- (square y) x))
+    1.0))
+
+(define (fixed-point-of-transform g transform guess)
+  (fixed-point (transform g) guess))
+
+(#%provide sqrt-ad-trans)
+(define (sqrt-ad-trans x)
+  (fixed-point-of-transform
+    (lambda (y) (/ x y))
+    average-damp
+    1.0))
+
+(#%provide sqrt-newt-trans)
+(define (sqrt-newt-trans x)
+  (fixed-point-of-transform
+    (lambda (y) (- (square y) x))
+    newton-transform
+    1.0))
+
+#| 1.40 |#
+
+(#%provide cubic)
+(define (cubic a b c)
+  (lambda (x)
+    (+
+      (cube x)
+      (* a (square x))
+      (* b x)
+      c)))
+
+;; (newtons-method (cubic 0 0 -8.0) 4.0)
+
+#| 1.41 |#
+
+(#%provide twice)
+(define (twice f)
+  (lambda (x) (f (f x))))
+
+;; (twice inc 1)
+;; 3
+
+;; (((twice (twice twice)) inc) 5)
+;; 21
+
+#| 1.42 |#
+
+(#%provide compose-)
+(define (compose- f g)
+  (lambda (x) (f (g x))))
+
+;; ((compose- square inc) 6)
+;; 49
+
+#| 1.43 |#
+
+(#%provide repeated)
+(define (repeated f n)
+  (if (= n 0)
+    (lambda (x) x)
+    (compose- (repeated f (- n 1)) f)))
+
+;; ((repeated square 2) 5)
+;; 625
+
+#| 1.44 |#
+
+(#%provide smooth)
+(define (smooth f)
+  (lambda (x)
+    (/
+      (+
+        (f (- x dx))
+        (f x)
+        (f (+ x dx)))
+      3.0)))
+
+(#%provide n-smooth)
+(define (n-smooth f n)
+  (repeated smooth n))
+
+#| 1.45 |#
+
+(#%provide flog2)
+(define (flog2 n) (floor (/ (log n) (log 2))))
+
+(#%provide nth-root)
+(define (nth-root n x)
+  (fixed-point
+    ((repeated average-damp (flog2 n))
+     (lambda (y) (/ x (fast-expt-iter y (- n 1)))))
+    1.0))
+
+#| 1.46 |#
+
+(#%provide iterative-improve)
+(define (iterative-improve good-enough? improve)
+  (lambda (guess)
+    (define (iter x)
+      (if (good-enough? x)
+        x
+        (iter (improve x))))
+    (iter guess)))
+
+(#%provide sqrt-it-imp)
+(define (sqrt-it-imp x)
+  ((iterative-improve
+     (lambda (guess) (< (abs (- (square guess) x)) 0.001))
+     (lambda (guess) (average guess (/ x guess))))
+   1.0))
+
+(#%provide fixed-point-it-imp)
+(define (fixed-point-it-imp f first-guess)
+  ((iterative-improve
+     (lambda (guess) (< (abs (- guess (f guess))) tolerance))
+     f)
+   first-guess))