Implement exercises till 2.6
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@ -51,6 +51,11 @@
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(print-rat (make-rat 3 -9))
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(print-rat (make-rat 3 -9))
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(print-rat (make-rat -3 -9))
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(print-rat (make-rat -3 -9))
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; More elegant (but harder to read?) solution
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(define (make-rat n d)
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(let ((g ((if (< d 0) - +) (abs (gcd n d)))))
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(cons (/ n g) (/ d g))))
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(display "\n\nex-2.2")
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(display "\n\nex-2.2")
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(define (make-point x y) (cons x y))
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(define (make-point x y) (cons x y))
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@ -79,17 +84,26 @@
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(display "\n\nex-2.3\n")
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(display "\n\nex-2.3\n")
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; The first representation takes the two opposite corners of the rectangle.
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; The first representation takes the two opposite corners of the rectangle.
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; This assumes that the rectangle is aligned in parallel to the X and Y axis.
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; If we use segments to represent two sides originating from the same point we
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; would first have to calculate the length of each of these sides. I am not
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; changing the code now but it shows how engineering decisions limit what can
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; be accomplished, but also make the problem more trivial.
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(define (make-rectangle p1 p2) (cons p1 p2))
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(define (make-rectangle p1 p2) (cons p1 p2))
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(define (corner-1-rectangle r) (car r))
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(define (corner-1-rectangle r) (car r))
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(define (corner-2-rectangle r) (cdr r))
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(define (corner-2-rectangle r) (cdr r))
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(define (x-length-rectangle r)
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(abs (- (x-point (corner-1-rectangle r)) (x-point (corner-2-rectangle r)))))
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(define (y-length-rectangle r)
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(abs (- (y-point (corner-1-rectangle r)) (y-point (corner-2-rectangle r)))))
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(define (area-rectangle r)
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(define (area-rectangle r)
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(abs (* (- (x-point (corner-1-rectangle r)) (x-point (corner-2-rectangle r)))
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(* (x-length-rectangle r) (y-length-rectangle r)))
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(- (y-point (corner-1-rectangle r)) (y-point (corner-2-rectangle r))))))
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(define (perimeter-rectangle r)
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(define (perimeter-rectangle r)
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(* 2 (+ (abs (- (x-point (corner-1-rectangle r)) (x-point (corner-2-rectangle r))))
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(* 2 (+ (x-length-rectangle r) (y-length-rectangle r))))
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(abs (- (y-point (corner-1-rectangle r)) (y-point (corner-2-rectangle r)))))))
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(define r (make-rectangle (make-point -2 -2) (make-point -8 -10)))
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(define r (make-rectangle (make-point -2 -2) (make-point -8 -10)))
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(display (area-rectangle r)) (newline)
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(display (area-rectangle r)) (newline)
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@ -111,3 +125,66 @@
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(display (perimeter-rectangle r)) (newline)
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(display (perimeter-rectangle r)) (newline)
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(display "\nex-2.4\n")
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(display "\nex-2.4\n")
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(define (cons x y)
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(lambda (m) (m x y)))
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(define (car z)
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(z (lambda (p q) p)))
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(define (cdr z)
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(z (lambda (p q) q)))
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; Process with substitution model.
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(let ((x 1) (y 2))
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(car (cons x y))
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(car (lambda (m) (m x y)))
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((lambda (m) (m x y)) (lambda (p q) p))
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((lambda (p q) p) x y)
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x)
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(display (car (cons 1 2))) (newline)
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(display (cdr (cons 1 2))) (newline)
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(display "\nex-2.5\n")
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(define (cons-ari a b)
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(cond ((and (>= a 0) (>= b 0))
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(* (expt 2 a) (expt 3 b)))
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(else (error "Negative integers not allowed" a b))))
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(define (count-factor n f)
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(if (and (> n 0) (= (remainder n f) 0))
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(+ 1 (count-factor (/ n f) f))
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0))
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(define (car-ari p) (count-factor p 2))
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(define (cdr-ari p) (count-factor p 3))
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(define p (cons-ari 13 3))
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(display (car-ari p)) (newline)
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(display (cdr-ari p)) (newline)
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(display "\nex-2.6\n")
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(define zero (lambda (f) (lambda (x) x)))
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(define one (lambda (f) (lambda (x) (f x))))
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(define two (lambda (f) (lambda (x) (f (f x)))))
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(define (add-1 n) (lambda (f) (lambda (x) (f ((n f) x)))))
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(display (((add-1 zero) inc) 0)) (newline)
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(display (((add-1 one) inc) 0)) (newline)
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(display (((add-1 (add-1 two)) inc) 0)) (newline)
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(define (add-church n m)
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(lambda (f) (lambda (x) ((n f) ((m f) x)))))
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(define (mul-church n m)
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(lambda (f) (lambda (x) ((n (m f)) x))))
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(define church-five (add-1 (add-church two two)))
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(display (((add-church church-five two) inc) 0)) (newline)
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(display (((mul-church church-five two) inc) 0)) (newline)
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20
ex-2_07-16.scm
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20
ex-2_07-16.scm
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@ -0,0 +1,20 @@
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(display "ex-2.7 - Start of extended exercise interval arithmetic\n")
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(display "\nex-2.8\n")
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(display "\nex-2.9\n")
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(display "\nex-2.10\n")
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(display "\nex-2.11\n")
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(display "\nex-2.12\n")
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(display "\nex-2.13\n")
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(display "\nex-2.14\n")
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(display "\nex-2.15\n")
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(display "\nex-2.16\n")
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0
ex-2_17-xx.scm
Normal file
0
ex-2_17-xx.scm
Normal file
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