;; The first three lines of this file were inserted by DrScheme. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-beginner-reader.ss" "lang")((modname conditionals) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ())))
(define a 5)
(define b 7)
(define c 5)
(< a b)
(< a c)
(<= a c)
(= a c)
(= a b)
(or (< a b) (< b a))
(and (< a b) (< a c))
(not (< a b))

; lazy evaluation: if the value is known from the first 
; argument of "and" or "or", the second one is not evaluated
; In the examples below (/ 5 0) never gets evaluated because
; it is not needed for computing the value of the expression
(and (> a b) (= 1 (/ 5 0)))
(or (< a b)  (= 1 (/ 5 0)))

;; Contract: number -> boolean

;; Purpose: to determine if the parameter is greater or equal
;; to 21
(define (is-over-21 age) 
  (>= age 21))

(is-over-21 18)
(is-over-21 25)
(is-over-21 21)

;; Is this correct?
(define (is-under-21 age) 
  (not (> age 21)))

;; write a function that returns true if the parameter x 
;; is satisfies the inequality 1 < x <= 3
;; and false otherwise


;; write a function that returns true if the parameter x 
;; is less than -1 or greater than 1
;; and false otherwise


;; conditionals ("if" statements)

(cond 
  [(< a 0) (- a)] ; if a < 0, return -a
  [(>= a 0) a])   ; if a >= 0, return a
  
(define d -5)
(cond 
  [(< d 0) (- d)]
  [(>= d 0) d])

;; using "else":
(cond 
  [(< d 0) (- d)]
  [else d])

;; make this conditional into a function so that
;; we can use it for multiple numbers

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;; Contract: number -> number

;; Purpose: find the absolute value of the parameter x

;; Examples: (abs-val 5) gives 5, (abs-val -5) gives 5,
;; (abs-val 0) gives 0
(define (abs-val x) 
  (cond 
  [(< x 0) (- x)] 
  [else x]))

;; Tests
(abs-val 5)
;; expected value
5
(abs-val -5)
;; expected value
5
(abs-val 0)
;; expected value
0

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;; more choices
(cond 
  [(< a 0) -1]
  [(> a 0) 1]
  [(= a 0) 0]
  )

;; same condition as a function:

;; Contract: number -> number

;; Purpose: computes the sign of x as follows: 
;; if x < 0 then the sign is -1, if x > 0, the sign is 1,
;; otherwise the sign is 0

;; Examples: (sign -10) is -1, (sign 10) is 1, (sign 0) is 0 
(define (sign x) 
  (cond 
    [(< x 0) -1]
    [(> x 0) 1]
    [(= x 0) 0]
))

;; Tests:
(sign -10)
;; expected value
-1
(sign 10)
;; expected value
1
(sign 0) 
;; expected value
0