; All this quotation is not *directly* possible in .rot
;  if you can't imagine it with direct ember;
;  you can't it!
; PUT IN ANOTHER WAY:
;  if you do it,
;   you can it.
;  if you take it,
;   you can it.
;  if you only request of it, (own it)
;   you cannot one single bit of it!

; Jay tries to again bring fear to his audience...
;  "What we actually want, is to confuse the idea of
;   procedures and data very badly -not just badly."

; Can we make programs, that do not just manipulate "data" (pictures),
; but also other algebraic expressions?

; Derivatives: make a complex problem into many, simpler problems.
; Integrals: make many, simpler problems into one complex problem.
; They both follow specific rules.
;  -to represent them is the difficulty.

; To begin with complex case-analysis; we begin with (cond ...

(DEFINE (DERIV EXPR VAR)
 (COND ((CONSTANT? EXPR VAR) 0)
       ((SAME-VAR? EXPR VAR) 1)
       ((SUM? EXPR)
        (MAKE-SUM (DERIV (A1 EXPR) VAR)
                  (DERIV (A2 EXPR) VAR)))
       ((PRODUCT? EXPR)
        (MAKE-SUM
         (MAKE-PRODUCT (M1 EXPR)
                       (DERIV (M2 EXPR) VAR))
         (MAKE-PRODUCT (DERIV (M1 EXPR) VAR)
                       (M2 EXPR))))
;....
     ))

(DEFINE (CONSTANT? EXPR VAR)
  (AND (ATOM? EXPR)
       (NOT (EQ? EXPR VAR))))
(DEFINE (SAME-VAR? EXPR VAR)
  (AND (ATOM? EXPR)
       (EQ? EXPR VAR)))
(DEFINE (SUM? EXPR)
  (AND (NOT (ATOM? EXPR))
       (EQ (CAR EXPR) '+)))
; 3B:(18m17s) Quotation (QUOTE) (')
(DEFINE (MAKE-SUM A1 A2)
  (LIST '+ A1 A2 ))
(DEFINE A1 CADR)
(DEFINE A2 CADDR)
; 3B:(22m32s) The history of CAR and CDR and (CADR -> CAR of CDR of some value)

(DEFINE (PRODUCT? EXPR)
  (AND (NOT (ATOM? EXPR)
       (EQ? (CAR EXPR) '*)))
(DEFINE (MAKE-PRODUCT M1 M2)
  (LIST '* M1 M2))
(DEFINE M1 CADR)
(DEFINE M2 CADDR)

; QUESTIONS 3B:(27m33s) BREAK
; Trying to produce simplified/normalized output.
(DEFINE (MAKE-SUM A1 A2)
  (COND ((AND (NUMBER? A1)
              (NUMBER? A2))
         (+ A1 A2))
        ((AND (NUMBER? A1) (= A1 0)) A2)
        ((AND (NUMBER? A2) (= A2 0)) A1)
        (ELSE (LIST '+ A1 A2))))
; 3B:(41m33s) Jay explaining the pun he made. And talking about the
; necessity of quotation in Lisp. (END)