Implement exercises till 2.6

This commit is contained in:
Felix Martin 2020-10-25 21:40:51 -04:00
parent 69e6d171d4
commit c4fbf3dabe
4 changed files with 103 additions and 5 deletions

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@ -51,6 +51,11 @@
(print-rat (make-rat 3 -9)) (print-rat (make-rat 3 -9))
(print-rat (make-rat -3 -9)) (print-rat (make-rat -3 -9))
; More elegant (but harder to read?) solution
(define (make-rat n d)
(let ((g ((if (< d 0) - +) (abs (gcd n d)))))
(cons (/ n g) (/ d g))))
(display "\n\nex-2.2") (display "\n\nex-2.2")
(define (make-point x y) (cons x y)) (define (make-point x y) (cons x y))
@ -79,17 +84,26 @@
(display "\n\nex-2.3\n") (display "\n\nex-2.3\n")
; The first representation takes the two opposite corners of the rectangle. ; The first representation takes the two opposite corners of the rectangle.
; This assumes that the rectangle is aligned in parallel to the X and Y axis.
; If we use segments to represent two sides originating from the same point we
; would first have to calculate the length of each of these sides. I am not
; changing the code now but it shows how engineering decisions limit what can
; be accomplished, but also make the problem more trivial.
(define (make-rectangle p1 p2) (cons p1 p2)) (define (make-rectangle p1 p2) (cons p1 p2))
(define (corner-1-rectangle r) (car r)) (define (corner-1-rectangle r) (car r))
(define (corner-2-rectangle r) (cdr r)) (define (corner-2-rectangle r) (cdr r))
(define (x-length-rectangle r)
(abs (- (x-point (corner-1-rectangle r)) (x-point (corner-2-rectangle r)))))
(define (y-length-rectangle r)
(abs (- (y-point (corner-1-rectangle r)) (y-point (corner-2-rectangle r)))))
(define (area-rectangle r) (define (area-rectangle r)
(abs (* (- (x-point (corner-1-rectangle r)) (x-point (corner-2-rectangle r))) (* (x-length-rectangle r) (y-length-rectangle r)))
(- (y-point (corner-1-rectangle r)) (y-point (corner-2-rectangle r))))))
(define (perimeter-rectangle r) (define (perimeter-rectangle r)
(* 2 (+ (abs (- (x-point (corner-1-rectangle r)) (x-point (corner-2-rectangle r)))) (* 2 (+ (x-length-rectangle r) (y-length-rectangle r))))
(abs (- (y-point (corner-1-rectangle r)) (y-point (corner-2-rectangle r)))))))
(define r (make-rectangle (make-point -2 -2) (make-point -8 -10))) (define r (make-rectangle (make-point -2 -2) (make-point -8 -10)))
(display (area-rectangle r)) (newline) (display (area-rectangle r)) (newline)
@ -111,3 +125,66 @@
(display (perimeter-rectangle r)) (newline) (display (perimeter-rectangle r)) (newline)
(display "\nex-2.4\n") (display "\nex-2.4\n")
(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)))
; Process with substitution model.
(let ((x 1) (y 2))
(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)
(display (car (cons 1 2))) (newline)
(display (cdr (cons 1 2))) (newline)
(display "\nex-2.5\n")
(define (cons-ari a b)
(cond ((and (>= a 0) (>= b 0))
(* (expt 2 a) (expt 3 b)))
(else (error "Negative integers not allowed" a b))))
(define (count-factor n f)
(if (and (> n 0) (= (remainder n f) 0))
(+ 1 (count-factor (/ n f) f))
0))
(define (car-ari p) (count-factor p 2))
(define (cdr-ari p) (count-factor p 3))
(define p (cons-ari 13 3))
(display (car-ari p)) (newline)
(display (cdr-ari p)) (newline)
(display "\nex-2.6\n")
(define zero (lambda (f) (lambda (x) x)))
(define one (lambda (f) (lambda (x) (f x))))
(define two (lambda (f) (lambda (x) (f (f x)))))
(define (add-1 n) (lambda (f) (lambda (x) (f ((n f) x)))))
(display (((add-1 zero) inc) 0)) (newline)
(display (((add-1 one) inc) 0)) (newline)
(display (((add-1 (add-1 two)) inc) 0)) (newline)
(define (add-church n m)
(lambda (f) (lambda (x) ((n f) ((m f) x)))))
(define (mul-church n m)
(lambda (f) (lambda (x) ((n (m f)) x))))
(define church-five (add-1 (add-church two two)))
(display (((add-church church-five two) inc) 0)) (newline)
(display (((mul-church church-five two) inc) 0)) (newline)

20
ex-2_07-16.scm Normal file
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@ -0,0 +1,20 @@
(display "ex-2.7 - Start of extended exercise interval arithmetic\n")
(display "\nex-2.8\n")
(display "\nex-2.9\n")
(display "\nex-2.10\n")
(display "\nex-2.11\n")
(display "\nex-2.12\n")
(display "\nex-2.13\n")
(display "\nex-2.14\n")
(display "\nex-2.15\n")
(display "\nex-2.16\n")

0
ex-2_17-xx.scm Normal file
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@ -11,5 +11,6 @@
(if (= b 0) (abs a) (gcd b (remainder a b)))) (if (= b 0) (abs a) (gcd b (remainder a b))))
(define (average a b) (/ (+ a b) 2.0)) (define (average a b) (/ (+ a b) 2.0))
(define (id n) n)
(define (inc n) (+ n 1))
;(assert (gcd 93 15) 3)