; ABSTRACTION BARRIERS in functions as in data:
; I create imaginary friends, and I call them
;   clouds in paradise.
; In the clouds I see something called fractions (rationals).
; They have nominators and denominators. 2B:(5m16s)
; But how to represent them?
; The strategy => 2B:(6m5s) Thinking wishfully.
;       (make-rat n d)     ---> a cloud containing n and d.
;       (numer (make-rat n d))   ---> returns numerator.
;       (denom (make-rat n d))   ---> returns denominator
; assuming that constructor and selectors are already there... 2B:(10m55s)
(DEFINE (+RAT X Y)
  (MAKE-RAT
    (+ (* (NUMER X) (DENOM Y))
       (* (NUMER Y) (DENOM X)))
    (* (DENOM X) (DENOM Y))))
(DEFINE (*RAT X Y)
  (MAKE-RAT
    (* (NUMER X) (NUMER Y))
    (* (DENOM X) (DENOM Y))))

; 2B:(15m7s) Hal Abelson packt aus!
;    "Because the whole name of this GAME... is..."
; 2B:(15m50s) + important question
; BREAK 2B:(17m38)
; List Structures
;  ==> PAIRS
;   (cons x y)
;      constructs a pair whose first part
;      is x and whose second part is y
;   (car p)
;      selects the first part of the pair p
;   (cdr p)
;      selects the second part of the pair p
;
;   FOR ANY x AND y
;   (car (cons x y))
;      is x
;   (cdr (cons x y))
;      is y
(DEFINE (MAKE-RAT N D)
  (CONS N D))
(DEFINE (NUMER X)
  (CAR X))
(DEFINE (DENOM X)
  (CDR X))

; CASE-EXAMPLE 2B:(24m30s)
; 1/2 + 1/4
(DEFINE A (MAKE-RAT 1 2))
(DEFINE B (MAKE-RAT 1 4))
(DEFINE ANS (+RAT A B))
(NUMER ANS) ;=> 6
(DENOM ANS) ;=> 8
; 2B:(26m25s) The answer should be 3/4. (resolution)
; 2B:(29m10s) Abstraction Layer (barrier) and the methology of
;    seperating the USAGE from REPRESENTATION
; Hal talking about his favorite names, controlling spirits...
;    abstraction; it's just magic.
; 2B:(35m55s) "You'd like to make progress, but also never want to be 
;     bound by the consequences of your decisisons."
;    "You might not be able to decide... at the moment you're worrying
;     about these numbers. -another magic-problem."
; That could be one reason, why many people have names for everything, but
; are not ready to describe something thoroughly. (Which is a good thing!)
; 2B:(37m40s) Some very good QUESTIONS!
;       ==> (about religion vs magic, #[PROCEDURE LET] and tech-magazine's fantasies)
; 2B:(41m) BREAK
; Now about the question of what you can build with a given tool, which
; tries to reduce complexity. What importance do such tools play?
; -> Why do you want this reduction into just another name?

; now representing vectors in the plane:
; (define (make-vector x y) (cons x y))
; (define (xcor p) (car p))
; (define (ycor p) (cdr p))
; -> Why do you want this?
;    * MAKE-VECTOR is just like MAKE-RAT.
;    * XCOR is just like NUMER
;    * YCOR is just like DENOM
; I personally think, that this is important, because you relate something
; to NUMER. You think, that it gives you the numerator of a rational number.
; Why would you call NUMER on a vector data-type? A vector doesn't have a
; numerator. That's why you would implement the selector XCOR -- to get the
; coordinate X of a vector. It should not play a role in your mind, that
; the data-type for a vector is the same as the one for a rational number.

; Now you can use data-types to represent other data-types. 2B:(43m37s)
; (define (make-seg p q) (cons p q))
; (define (seg-start s) (car s))
; (define (seg-end s) (cdr s))
; (define (midpoint s) ;now we can define operations on them 2B:(44m41s)
;   (let ((a (seg-start s))
;         (b (seg-end s)))
;     (make-vector
;      (average (xcor a) (xcor b))
;      (average (ycor a) (ycor b)))))
; (define (length s)
;   (let
;    ((dx (- (xcor (seg-end s))
;            (xcor (seg-start s))))
;     (dy (- (ycor (seg-end s))
;            (ycor (seg-start s)))))
;    (sqrt (+ (square dx)
;             (square dy)))))
;
; Again creating ABSTRACTION BARRIERS. And again a section, where Hal
; explains why abstracting things is so important. (Talking about concepts
; like "PAIRS of PAIRS" and introducing the word "CLOSURE".)
; BREAK 2B:(56m37s) after an important question about PAIRS.

; Now describing what it all means. (AXIOM for PAIRS)
; Hal tries real hard to scare his audience this time...
; with this:
; (define (cons a b)
;   (lambda (pick)
;     (cond ((= pick 1) a)
;           ((= pick 2) b))))
; (define (car x) (x 1))
; (define (cdr x) (x 2))
;
; --> data built out of air? -my inner vacuums say yes.

; if you really believe this stuff:
; getting the hang of it... going philosophical!
; Fundamental QUESTIONS 2B:(1h10m5s) and then BREAK (END)