sample hand evaluation

A hand-evaluation consists of a series of expressions, all of whom have the same value. They are the expressions that you see when using DrScheme's Stepper. For example, if we had these two functions defined:

;; square: number --> number         
;; Given a, return a^2.
;;
(define (square a) (* a a))         

;; hypotenuse: number, number --> number
;; Given the length of two legs a,b of a triangle,
;; return the length of the hypotenuse.
;; a,b are expected to be non-negative.
;;
(define (hypotenuse a b)
  (sqrt (+ (square a) (square b))))

;; Tests:
(square 7)
49

(square 0)
0

(square -2)
4

;; Tests:
(hypotenuse 0 0)
0

(hypotenuse 0 7)
7

(hypotenuse 3 4)
5

Here would be a sample hand-evaluation:

  (hypotenuse 12 5)
= (sqrt (+ (square 12) (square 5)))
= (sqrt (+ (* 12 12) (square 5)))
= (sqrt (+ 144 (square 5)))
= (sqrt (+ 144 (* 5 5)))
= (sqrt (+ 144 25))
= (sqrt 169)
= 13

You can double-check this in drscheme by typing this into the definition window without the =; pressing Execute you'll see 13, repeated eight times.

However, in what you turn in, include the equal-signs, since you really do want to link these eight statements together, asserting that they really are equal. Do not use other symbols instead of =. In particular, many people want to use arrows. You never wrote "2 + 3 --> 5" in junior high; 2+3 doesn't transform into 5; it is 5.

Alternately, if you don't like the disconnect between having to add the =s to your printout by hand, you can make the hand-evaluation into pure scheme by calling the function "=", applied to eight things:

(= (hypotenuse 12 5)
   (sqrt (+ (square 12) (square 5)))
   (sqrt (+ (* 12 12) (square 5)))
   (sqrt (+ 144 (square 5)))
   (sqrt (+ 144 (* 5 5)))
   (sqrt (+ 144 25))
   (sqrt 169)
   13)