Add chapter 2 part 1

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+#lang sicp
+
+;; Chapter 2
+;; Building Abstractions with Data
+
+;; 2.1
+;; Introduction to Data Abstraction
+
+(define (make-rat-1 n d) (cons n d))
+
+(#%provide numer)
+(define (numer x) (car x))
+
+(#%provide denom)
+(define (denom x) (cdr x))
+
+(#%provide print-rat)
+(define (print-rat x)
+  (newline)
+  (display (numer x))
+  (display "/")
+  (display (denom x)))
+
+(#%provide add-rat)
+(define (add-rat x y)
+  (make-rat
+    (+
+      (* (numer x) (denom y))
+      (* (numer y) (denom x)))
+    (* (denom x) (denom y))))
+
+(#%provide sub-rat)
+(define (sub-rat x y)
+  (make-rat
+    (-
+      (* (numer x) (denom y))
+      (* (numer y) (denom x)))
+    (* (denom x) (denom y))))
+
+(#%provide mul-rat)
+(define (mul-rat x y)
+  (make-rat
+    (* (numer x) (numer y))
+    (* (denom x) (denom y))))
+
+(#%provide div-rat)
+(define (div-rat x y)
+  (make-rat
+    (* (numer x) (denom y))
+    (* (denom x) (numer y))))
+
+(#%provide equal-rat?)
+(define (equal-rat? x y)
+  (=
+    (* (numer x) (denom y))
+    (* (numer y) (denom x))))
+
+(define (make-rat-2 n d)
+  (let ((g (gcd n d)))
+    (cons (/ n g) (/ d g))))
+
+#| 2.1 |#
+
+(#%provide make-rat)
+(define (make-rat n d)
+  (let ((g (gcd n d)))
+    (let
+      ((n-norm (/ n g))
+       (d-norm (/ d g)))
+      (if (< d 0)
+        (cons (* -1 n-norm) (* -1 d-norm))
+        (cons n-norm d-norm)))))
+
+(define one-half (make-rat 1 2))
+(define one-third (make-rat 1 3))
+
+(print-rat one-half)
+(print-rat (add-rat one-half one-third))
+(print-rat (add-rat one-third one-third))
+
+#| 2.2 |#
+
+(#%provide make-segment)
+(define (make-segment p q) (cons p q))
+
+(#%provide start-segment)
+(define (start-segment pq) (car pq))
+
+(#%provide end-segment)
+(define (end-segment pq) (cdr pq))
+
+(#%provide make-point)
+(define (make-point x y) (cons x y))
+
+(#%provide x-point)
+(define (x-point p) (car p))
+
+(#%provide y-point)
+(define (y-point p) (cdr p))
+
+(#%provide print-point)
+(define (print-point p)
+  (newline)
+  (display "(")
+  (display (x-point p))
+  (display ",")
+  (display (y-point p))
+  (display ")"))
+
+(define (average a b)
+  (/ (+ a b) 2))
+
+(#%provide midpoint-segment)
+(define (midpoint-segment pq)
+  (let
+    ((p (start-segment pq))
+     (q (end-segment pq)))
+    (make-point
+      (average (x-point p) (x-point q))
+      (average (y-point p) (y-point q)))))
+
+#| 2.3 |#
+
+(#%provide make-rect-1)
+(define (make-rect-1 p width height) (cons p (cons width height)))
+(define (rect-corner-1 rect) (car rect))
+(define (rect-width-1 rect) (car (cdr rect)))
+(define (rect-height-1 rect) (cdr (cdr rect)))
+
+(#%provide make-rect-2)
+(define (make-rect-2 p width height)
+  (cons
+    p
+    (make-point
+      (+ (x-point p) width)
+      (+ (y-point p) height))))
+
+(define (rect-corner-2 rect) (car rect))
+(define (rect-width-2 rect)
+  (-
+    (x-point (cdr rect))
+    (x-point (car rect))))
+(define (rect-height-2 rect)
+  (-
+    (y-point (cdr rect))
+    (y-point (car rect))))
+
+(#%provide perimeter)
+(define (perimeter rect)
+  (* 2 (+ (rect-width-2 rect) (rect-height-2 rect))))
+
+(#%provide area)
+(define (area rect)
+  (* (rect-width-2 rect) (rect-height-2 rect)))
+
+(define (cons- x y)
+  (define (dispatch m)
+    (cond
+      ((= m 0) x)
+      ((= m 1) y)
+      (else (error "Argument not 0 or 1 -- CONS" m))))
+  dispatch)
+
+(define (car- z) (z 0))
+(define (cdr- z) (z 1))
+
+#| 2.4 |#
+
+(define (cons-- x y)
+  (lambda (m) (m x y)))
+
+(define (car-- z)
+  (z (lambda (p q) p)))
+
+(define (cdr-- z)
+  (z (lambda (p q) q)))
+
+#| (car-- (cons-- x y)) |#
+#| (car-- (lambda (m) (m x y))) |#
+#| ((lambda (m) (m x y)) (lambda (p q) p)) |#
+#| ((lambda (p q) p) x y) |#
+#| x |#
+
+#| (cdr-- (cons-- x y)) |#
+#| (cdr-- (lambda (m) (m x y))) |#
+#| ((lambda (m) (m x y)) (lambda (p q) q)) |#
+#| ((lambda (p q) q) x y) |#
+#| y |#
+
+#| 2.5 |#
+
+(#%provide cons-3)
+(define (cons-3 x y)
+  (* (expt 2 x) (expt 3 y)))
+
+(#%provide car-3)
+(define (car-3 z)
+  (define (iter z res)
+    (if (= (remainder z 2) 0)
+      (iter (/ z 2) (+ res 1))
+      res))
+  (iter z 0))
+
+(#%provide cdr-3)
+(define (cdr-3 z)
+  (define (iter z res)
+    (if (= (remainder z 3) 0)
+      (iter (/ z 3) (+ res 1))
+      res))
+  (iter z 0))
+
+#| 2.6 |#
+
+(define zero (lambda (f) (lambda (x) x)))
+(define (add-1 n)
+  (lambda (f) (lambda (x) (f ((n f) x)))))
+
+(define one (lambda (f) (lambda (x) (f x))))
+(define two (lambda (f) (lambda (x) (f (f x)))))
+
+(define (add n m)
+  (lambda (f) (lambda (x) (n f ((m f) x)))))
+
+(define (add-interval x y)
+  (make-interval
+    (+ (lower-bound x) (lower-bound y))
+    (+ (upper-bound x) (upper-bound y))))
+
+(define (mul-interval x y)
+  (let
+    ((p1 (* (lower-bound x) (lower-bound y)))
+     (p2 (* (lower-bound x) (upper-bound y)))
+     (p3 (* (upper-bound x) (lower-bound y)))
+     (p4 (* (upper-bound x) (lower-bound y))))
+    (make-interval
+      (min p1 p2 p3 p4)
+      (max p1 p2 p3 p4))))
+
+(define (div-interval x y)
+  (mul-interval
+    x
+    (make-interval
+      (/ 1.0 (upper-bound y))
+      (/ 1.0 (lower-bound y)))))
+
+#| 2.7 |#
+
+(#%provide make-interval)
+(define (make-interval a b)
+  (cons a b))
+
+(#%provide upper-bound)
+(define (upper-bound x)
+  (cdr x))
+
+(#%provide lower-bound)
+(define (lower-bound x)
+  (car x))
+
+#| 2.8 |#
+
+(define (sub-interval x y)
+  (let
+    ((p1 (- (lower-bound x) (lower-bound y)))
+     (p2 (- (lower-bound x) (upper-bound y)))
+     (p3 (- (upper-bound x) (lower-bound y)))
+     (p4 (- (upper-bound x) (lower-bound y))))
+    (make-interval
+      (min p1 p2 p3 p4)
+      (max p1 p2 p3 p4))))
+
+(#%provide make-center-width)
+(define (make-center-width c w)
+  (make-interval (- c w) (+ c w)))
+
+(#%provide center)
+(define (center i)
+  (/ (+ (lower-bound i) (upper-bound i)) 2))
+
+(#%provide width)
+(define (width i)
+  (/ (- (upper-bound i) (lower-bound i)) 2))
+
+#| 2.12 |#
+
+(#%provide make-center-percent)
+(define (make-center-percent c p)
+  (make-interval (- c (* c p)) (+ c (* c p))))
+
+(#%provide percent)
+(define (percent i)
+  (/ (width i) (center i)))