Lecture 3 : Moving Beyond Numbers (Clash the Symbols!)

Recap: Steps to develop programs with conditions:

1. contract, purpose, header
3. develop examples
5. body (write the cond questions first, then fill in the answers)
6. test

A dorm survey determines that if slices are less than $1, students
collectively eat 50 slices.  If slices are at most $1, but no more than
$1.50, students eat 34 slices.  If slices are more than $1.50, students
only eat 21 slices.  Write a program order, which determines how many
pizzas to order based on the cost of a slice (assume a pizza has 8 slices).

;; order : num -> num
;; calcuate how many pizzas to order based on the price
(define (order price)
  (cond [(<= price 1) (num-pizzas 50)]
	[(and (< 1 price) (<= price 1.5)) (num-pizzas 34)]
	[else (num-pizzas 21)]))

;; test cases
; (order .50) = 7
; (order 1) = 7
; (order 1.25) = 5
; (order 1.5) = 5
; (order 2) = 3

;; num-pizzas : num -> num
;; calculate how many pizzas are needed to cover the number of slices
(define (num-pizzas slices)
  (ceiling (/ slices 8)))

;; test cases
; (num-pizzas 8) = 1
; (num-pizzas 14) = 2

Let's move beyond numbers.  Often, we want to compute over data other than
numbers.  People who study language processing, for example, need a way to
represent words.  In Scheme, we represent words using symbols.  A symbol
resembles a word, but has a quote mark on the front and can contain
characters other than letters (but no spaces):

	'kathi 'Rice 'comp210 'class-of-2003

What operations can we perform on symbols?  Does (+ 'kathi 3) make
sense?  No, because 'kathi isn't a number.  The only thing we can do
with symbols is compare them for equality.  We do this using an
operator called symbol=?:

	(symbol=? 'kathi 'kathi) = true
	(symbol=? 'kathi 'john) = false
	(symbol=? 'kathi 'Kathi) = false

Write a program babel that takes the name of a language and produces
the word for hello in that language if the language is spanish,
french, or pig-latin.  The program produces 'hello for any other

;; babel : symbol -> symbol
;; translate hello into the given language
(define (babel lang)
  (cond [(symbol=? lang 'spanish) 'hola]
        [(symbol=? lang 'french) 'bonjour]
        [(symbol=? lang 'pig-latin) 'ellohay]
        [else 'hello]))

;; test-cases
; (babel 'spanish) = 'hola
; (babel 'french) = 'bonjour
; (babel 'pig-latin) = 'ellohay
; (babel 'esperanto) = 'hello