;;;; Problem A1

;; 1.)

(define (fahrenheit->celsius f)
  (* 5/9 (- f 32)))

(define (celsius->fahrenheit c)
  (+ (* 9/5 c) 32))

(celsius->fahrenheit (fahrenheit->celsius 212))


;;Step 1 - Function application
(celsius->fahrenheit (* 5/9 (- 212 32)))

;;Step 2 - Arithmetic
(celsius->fahrenheit (* 5/9 180))

;;Step 3 - Arithmetic
(celsius->fahrenheit 100)

;;Step 4 - Function application
(+ (* 9/5 100) 32)

;;Step 5 - Arithmetic
(+ 180 32)

;;Step 6 - Arithmetic
212


;; 2.)

(define-struct customer (title first last))

(define (formal* loc)
  (cond [(empty? loc) empty]
        [else (cons (formal (first loc))
                    (formal* (rest loc)))]))

(define (formal c)
  (string-append "Dear "
                 (customer-title c)
                 " "
                 (customer-last c)))

(formal* (cons (make-customer "Dr." "Olin" "Shivers")
           (cons (make-customer "Mstr." "ZC" "Flatt")
                 empty)))

;;Step 1 - Function application
  (cond [(empty? (cons (make-customer "Dr." "Olin" "Shivers")
           (cons (make-customer "Mstr." "ZC" "Flatt")
                 empty))) empty]
        [else (cons (formal (first (cons (make-customer "Dr." "Olin" "Shivers")
           (cons (make-customer "Mstr." "ZC" "Flatt")
                 empty))))
                    (formal* (rest (cons (make-customer "Dr." "Olin" "Shivers")
           (cons (make-customer "Mstr." "ZC" "Flatt")
                 empty)))))])

;;Step 2 - Conditional
  (cond [false empty]
        [else (cons (formal (first (cons (make-customer "Dr." "Olin" "Shivers")
           (cons (make-customer "Mstr." "ZC" "Flatt")
                 empty))))
                    (formal* (rest (cons (make-customer "Dr." "Olin" "Shivers")
           (cons (make-customer "Mstr." "ZC" "Flatt")
                 empty)))))])

;;Step 3 - Conditional
  (cond [else (cons (formal (first (cons (make-customer "Dr." "Olin" "Shivers")
           (cons (make-customer "Mstr." "ZC" "Flatt")
                 empty))))
                    (formal* (rest (cons (make-customer "Dr." "Olin" "Shivers")
           (cons (make-customer "Mstr." "ZC" "Flatt")
                 empty)))))])

;;Step 4 - Conditional
(cons (formal (first (cons (make-customer "Dr." "Olin" "Shivers")
    (cons (make-customer "Mstr." "ZC" "Flatt") empty))))
        (formal* (rest (cons (make-customer "Dr." "Olin" "Shivers")
        (cons (make-customer "Mstr." "ZC" "Flatt") empty)))))

;;Step 5 - Function Application
(cons (formal (make-customer "Dr." "Olin" "Shivers"))
        (formal* (rest (cons (make-customer "Dr." "Olin" "Shivers")
        (cons (make-customer "Mstr." "ZC" "Flatt") empty)))))

;;Step 6 - Function Application
(cons (string-append "Dear "
                 (customer-title (make-customer "Dr." "Olin" "Shivers"))
                 " "
                 (customer-last (make-customer "Dr." "Olin" "Shivers")))
        (formal* (rest (cons (make-customer "Dr." "Olin" "Shivers")
        (cons (make-customer "Mstr." "ZC" "Flatt") empty)))))

;;Step 7 - Function Application
(cons (string-append "Dear "
                 "Dr."
                 " "
                 (customer-last (make-customer "Dr." "Olin" "Shivers")))
        (formal* (rest (cons (make-customer "Dr." "Olin" "Shivers")
        (cons (make-customer "Mstr." "ZC" "Flatt") empty)))))

;;Step 8 - Function Application
(cons (string-append "Dear "
                 "Dr."
                 " "
                 "Shivers")
        (formal* (rest (cons (make-customer "Dr." "Olin" "Shivers")
        (cons (make-customer "Mstr." "ZC" "Flatt") empty)))))

;;Step 9 - Function Application
(cons "Dear Dr. Shivers"
        (formal* (rest (cons (make-customer "Dr." "Olin" "Shivers")
        (cons (make-customer "Mstr." "ZC" "Flatt") empty)))))

;;Step 10 - Function Application
(cons "Dear Dr. Shivers"
        (formal* (cons (make-customer "Mstr." "ZC" "Flatt") empty)))

;;Step 11 - Function Application
(cons "Dear Dr. Shivers"
  (cond [(empty? (cons (make-customer "Mstr." "ZC" "Flatt") empty)) empty]
        [else (cons (formal (first (cons (make-customer "Mstr." "ZC" "Flatt") empty)))
                    (formal* (rest (cons (make-customer "Mstr." "ZC" "Flatt") empty))))]))

;;Step 12 - Conditional
(cons "Dear Dr. Shivers"
  (cond [false empty]
        [else (cons (formal (first (cons (make-customer "Mstr." "ZC" "Flatt") empty)))
                    (formal* (rest (cons (make-customer "Mstr." "ZC" "Flatt") empty))))]))

;;Step 13 - Conditional
(cons "Dear Dr. Shivers"
  (cond [else (cons (formal (first (cons (make-customer "Mstr." "ZC" "Flatt") empty)))
                    (formal* (rest (cons (make-customer "Mstr." "ZC" "Flatt") empty))))]))

;;Step 14 - Conditional
(cons "Dear Dr. Shivers"
  (cons (formal (first (cons (make-customer "Mstr." "ZC" "Flatt") empty)))
        (formal* (rest (cons (make-customer "Mstr." "ZC" "Flatt") empty)))))

;;Step 15 - Function Application
(cons "Dear Dr. Shivers"
  (cons (formal (make-customer "Mstr." "ZC" "Flatt"))
        (formal* (rest (cons (make-customer "Mstr." "ZC" "Flatt") empty)))))

;;Step 16 - Function Application
(cons "Dear Dr. Shivers"
  (cons (string-append "Dear "
                 (customer-title (make-customer "Mstr." "ZC" "Flatt"))
                 " "
                 (customer-last (make-customer "Mstr." "ZC" "Flatt")))
        (formal* (rest (cons (make-customer "Mstr." "ZC" "Flatt") empty)))))

;;Step 17 - Function application
(cons "Dear Dr. Shivers"
  (cons (string-append "Dear "
                 "Mstr."
                 " "
                 (customer-last (make-customer "Mstr." "ZC" "Flatt")))
        (formal* (rest (cons (make-customer "Mstr." "ZC" "Flatt") empty)))))

;;Step 18 - Function Application
(cons "Dear Dr. Shivers"
  (cons (string-append "Dear "
                 "Mstr."
                 " "
                 "Flatt")
        (formal* (rest (cons (make-customer "Mstr." "ZC" "Flatt") empty)))))

;;Step 19 - Function application
(cons "Dear Dr. Shivers"
  (cons "Dear Mstr. Flatt"
        (formal* (rest (cons (make-customer "Mstr." "ZC" "Flatt") empty)))))

;;Step 20 - Function Application
(cons "Dear Dr. Shivers"
  (cons "Dear Mstr. Flatt"
        (formal* empty)))

;;Step 21 - Function Application
(cons "Dear Dr. Shivers"
  (cons "Dear Mstr. Flatt"
        (cond [(empty? empty) empty]
        [else (cons (formal (first empty))
                    (formal* (rest empty)))])))

;;Step 22 - Conditional
(cons "Dear Dr. Shivers"
  (cons "Dear Mstr. Flatt"
        (cond [true empty]
        [else (cons (formal (first empty))
                    (formal* (rest empty)))])))

;;Step 23 - Conditional
(cons "Dear Dr. Shivers"
  (cons "Dear Mstr. Flatt"
     empty))






;;;;; Problem A2

(require 2htdp/image)

(define-struct ball (x y color))
;; Ball = (make-ball Number Number Color)
;; Color is one of 'red, 'yellow, 'blue, etc.

;;A LOB is one of
;; -- (cons Ball LOB)
;; -- empty

(define lob1 (cons (make-ball 50 50 'red)
                   (cons (make-ball 78 92 'blue)
                         (cons (make-ball 159 41 'green)
                             empty))))

;; (define (lob-temp a-lob)
;;   (cond [(empty? a-lob) ...]
;;         [else ( ... (lob-temp (rest a-lob)) ... )]))

;; lob-length : LOB -> Number
;; Counts the number of balls in a list of Balls
(check-expect (lob-length lob1) 3)

(define (lob-length lob)
  (cond [(empty? lob) 0]
        [else (+ 1 (lob-length (rest lob)))]))


;; lob-x : LOB -> List
;; Extracts all x coordinates in a list of Balls
(check-expect (lob-x lob1) (cons 50 (cons 78 (cons 159 empty))))

(define (lob-x lob)
  (cond [(empty? lob) empty]
        [else (cons (ball-x (first lob)) (lob-x (rest lob)))]))


;; lob-draw : LOB -> Image
;; Places all balls in a list onto an empty scene
(check-expect (lob-draw lob1) .)


(define (lob-draw lob)
  (cond [(empty? lob) (empty-scene 300 300)]
        [else
         (place-image
            (circle 3 "solid" (ball-color (first lob)))
            (ball-x (first lob)) (ball-y (first lob))
                    (lob-draw (rest lob)))]))



;; lob-filter : LOB -> List
;; Removes from the list any ball whose coordinates do not fall within 300x300
(check-expect
 (lob-filter
   (cons (make-ball 268 156 'purple) (cons (make-ball 346 295 'pink) lob1)))
     (cons (make-ball 268 156 'purple) lob1))


(define (lob-filter lob)
   (cond [(empty? lob) empty]
         [(or
           (> (ball-x (first lob)) 300)
           (< (ball-x (first lob)) 0)
           (> (ball-y (first lob)) 300)
           (< (ball-y (first lob)) 0)) (lob-filter (rest lob))]
         [else (cons (first lob) (lob-filter (rest lob)))]))



;; lob-member? : LOB Ball -> Boolean
;; Tells if the given Ball matches another Ball in the given LOB
(check-expect (lob-member? lob1 (make-ball 78 92 'blue)) true)
(check-expect (lob-member? lob1 (make-ball 78 4 'blue)) false)

(define (lob-member? lob b)
   (cond [(empty? lob) false]
         [(and
           (= (ball-x (first lob)) (ball-x b))
           (= (ball-y (first lob)) (ball-y b))
           (symbol=? (ball-color (first lob)) (ball-color b))) true]
         [else (lob-member? (rest lob) b)]))





;;;;; Problem A3

(require 2htdp/universe)

(define-struct txt (content x y))
;; Txt = (make-txt String Number Number)

;; LoTxt is one of:
;; -- empty
;; -- (cons Txt LoTxt)

(define orientx 200)
(define orienty 150)

(define txtlist
  (cons (make-txt "On your mark." orientx orienty)
    (cons (make-txt "Get set."
                    orientx (+ 25 orienty))
      (cons (make-txt "Go!"
                    orientx (+ 50 orienty))
           empty))))

(define-struct world (image hidden))
;; World = (make-world Image LoTxt)
;; intepretation:
;;  The world's image represents the image that the audience can see.
;;  The world's list of Txt represents the yet-to-be-revealed elements.

(define WORLD-0 (make-world (empty-scene 400 400) txtlist))

;; display : World -> Image
;; Renders current world state
(check-expect (display WORLD-0) .)


(define (display w)
  (world-image w))


;; next : World -> World
;; Consumes current world, produces next world with next text added

(define (next w)
  (cond [(empty? (world-hidden w)) WORLD-0]
        [else (make-world
               (place-image (text
                             (txt-content (first (world-hidden w))) 20 'blue)
                                 (txt-x (first (world-hidden w)))
                                 (txt-y (first (world-hidden w)))
                                 (world-image w)) (rest (world-hidden w)))]))