;; Examples from Chapter 7 with added comments and tests

;; structure square represents a square shape
;; nw is posn that represents the coordinates of the north-west
;; (left-upper) corner of the square
;; length is a positive number that represents the length
;; of the side of the square
(define-struct square (nw length))

;; structure circle represents a circle shape
;; center is a posn that represents the coordinates
;; of the center of the circle
;; radius is a positive number that represents 
;; its radius
(define-struct circle (center radius))

(make-square (make-posn 20 20) 100)
(make-circle (make-posn 50 100) 50)

;; a shape is either a square or a circle

;; pi is a built-in constant. It's an inexact number.
pi

;; every structure comes with a function that checks for 
;; the structure type. The name of the function is the 
;; structure type followed by a question mark:
(circle? (make-circle (make-posn 50 100) 50))
(square? (make-circle (make-posn 50 100) 50))
(posn? (make-posn 3 5))
(posn? 7)

;; perimeter: shape -> number
;; purpose: to compute perimeter of a shape
(define (perimeter a-shape)
  (cond
    [(square? a-shape) (* (square-length a-shape) 4)]
    [(circle? a-shape) (* (* 2 (circle-radius a-shape)) pi)]))

;; a square with the side length of 100 has perimeter = 400:
(check-expect (perimeter (make-square (make-posn 20 20) 100)) 400)

;; a circle of radius 50 has perimeter = pi * 100
;; since this is an inexact number, we use check-within 
(check-within (perimeter (make-circle (make-posn 50 100) 50)) (* pi 100) 0.00001)

;; signaling errors: 
(define (perimeter2 a-shape)
  (cond
    [(square? a-shape) (* (square-length a-shape) 4)]
    [(circle? a-shape) (* (* 2 (circle-radius a-shape)) pi)]
    [else (error "a shape expected")] ;; a meaningful error message
  )
)

;(perimeter2 42)
;; using check-error to check for an error
(check-error (perimeter2 42) "a shape expected")


;; Exercise 7.1.3: develop the function called area, which consumes 
;; either a circle or a square and computes the area. 


;; Define a function that finds a middle point between two
;; positions and returns it as a position. 
;; If the function is given inputs that are not positions,
;; it should signal an error. 
;; Write tests for the function, including tests for errors.