| Tutorial 1: Solutions (Sep 14, 2007)- Simple Functions in Scheme
- Scheme notation vs. Mathematical notation
From Scheme to Math:(define (f x) (- (* 5 x) 4))⇒f(x) = 5x-4(define (g x) (- (/ (* (+ x 2) (- x 3)) 5) x))⇒g(x) = x(x + 2)(x - 3) / 5
From Math to Scheme:- f(x) = (x+5)/(8x-9)⇒
(define (f x) (/ (+ x 5) (- (* 8 x) 9)) - g(x,y) = (xy-7)(x+y) - (3x + 5y - 12)
⇒(define (g x y) (- (* (- (* x y) 7) (+ x y)) (+ (* 3 x) (- (* 5 y) 12)))
- Function Evaluation
Note the following steps are to illustrate the intermediate results only and do not necessarily follow the exact order of the evaluation steps performed by DrScheme.(- (* 4 5) (/ 6 3))
⇒(- 20 2)
⇒18(/ (+ 2 (- 5 2) (* 3 3)) (/ (- (* 5 5) 4) 3))
⇒(/ (+ 2 3 9) (/ (- 25 4) 3))
⇒(/ 14 (/ 21 3))
⇒2(define (f x) (* x (+ x 1)))
(+ (f 1) (/ (f 2) 3))
⇒(+ (* 1 (+ 1 1)) (/ (* 2 (+ 2 1)) 3))
⇒(+ 2 (/ 6 3))
⇒4(define (f x) (- x 1))
(define (g x) (* x (f (/ x 3)) 2))
(/ (g (g 6)) 2)
⇒(/ (g (* 6 (f (/ 6 3)) 2)) 2)
⇒(/ (g (* 6 (f 2) 2)) 2)
⇒(/ (g (* 6 (- 2 1) 2)) 2)
⇒(/ (g 12) 2)
⇒(/ (* 12 (f (/ 12 3)) 2) 2)
⇒(/ (* 12 (- 4 1) 2) 2)
⇒(/ 72 2)
⇒36
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