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+#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))