sicpsgjd/2/4/jord/notes.org

• 2.4 Multiple Representations for Abstract Data
  • 2.4.1 representations for complex numbers
  • 2.4.2 tagged data
  • 2.4.3 data-directed programming and additivity

2.4 Multiple Representations for Abstract Data

how to isolate different design choices to coexist in a program?

type tags

data objects that include explicit information about how it should be processed

data-directed

style of programming by additively assembling systems with generic operations

2.4.1 representations for complex numbers

develop a system for complex number arithmetic with two underlying implementations:

• rectangular form

• polar form

  (define (add-complex z1 z2)
    (make-from-real-imag (+ (real-part z1) (real-part z2))
			 (+ (imag-part z1) (real-part z2))))
  (define (sub-complex z1 z2)
    (make-from-real-imag (- (real-part z1) (real-part z2))
			 (- (imag-part z1) (real-part z2))))
  (define (mul-complex z1 z2)
    (make-from-mag-ang (* (magnitude z1) (magnitude z2))
		       (+ (angle z1) (angle z2))))
  (define (div-complex z1 z2)
    (make-from-mag-ang (/ (magnitude z1) (magnitude z2))
		       (- (angle z1) (angle z2))))

two lispers take on the challenge…

  ;; BEN BITDIDDLE
  (define (real-part z) (car z))
  (define (imag-part z) (cdr z))
  (define (magnitude z)
    (sqrt (+ (square (real-part z)) (square (imag-part z)))))
  (define (angle z)
    (atan (imag-part z) (real-part z)))
  (define (make-from-real-imag x y) (cons x y))
  (define (make-from-mag-ang r a)
    (cons (* r (cos a)) (* r (sin a))))

  ;; ALYSSA P. HACKER
  (define (real-part z)
    (* (magnitude z) (cos (angle z))))
  (define (imag-part z)
    (* (magnitude z) (sin (angle z))))
  (define (magnitude z) (car z))
  (define (angle z) (cdr z))
  (define (make-from-real-imag x y)
    (cons (sqrt (+ (square x) (square y)))
	  (atan y x)))
  (define (make-from-mag-ang r a) (cons r a))

2.4.2 tagged data

to keep this two systems and to keep them separate, you could make a tagging system for data

  (define (attach-tag type-tag contents)
    (cons type-tag contents))
  (define (type-tag datum)
    (if (pair? datum)
	(car datum)
	(error "Bad tagged datum -- TYPE-TAG" datum)))
  (define (contents datum)
    (if (pair? datum)
	(cdr datum)
	(error "Bad tagged datum -- CONTENTS" datum)))

and then it would be simple to identify the said type

  (define (rectangular? z)
    (eq? (type-tag z) 'rectangular))
  (define (polar? z)
    (eq? (type-tag z) 'polar))

and so alyssa and ben could use this in their procedures, then name their procedures to reflect the work they are doing

  (define (magnitude z)
    (cond ((rectangular? z)
	   (magnitude-rectangular (contents z)))
	  ((polar? z)
	   (magnitude-polar (contents z)))
	  (else (error "Unknown type -- MAGNITUDE" z))))

we will come back to this in §2.5

2.4.3 data-directed programming and additivity