Taras Bunyk

SICP 2.4 Multiple representations for abstract data

Published: 2020-08-26T17:03:55.000Z

I went on vacation and lost cadence on this project. Need to get back on track, remember how to lauch interpreter, etc. :)

Link to the chapter

In this chapter we will need get and put functions which could be implemented by similar system functions.

Found this on StackOverflow, of course.

(define put 2d-put!)
(define (get a b)
    ;(display "get ") (display a) (display b) (newline)
    (2d-get a b)

And some setup from previous section:

(define variable? symbol?)
(define (same-variable? v1 v2)
  (and (variable? v1) (variable? v2) (eq? v1 v2)))
(define (=number? exp num)
  (and (number? exp) (= exp num)))

Exercise 2.73

(define (deriv exp var)
   (cond ((number? exp) 0)
         ((variable? exp) (if (same-variable? exp var) 1 0))
         (else ((get 'deriv (operator exp)) (operands exp)
(define (operator exp) (car exp))
(define (operands exp) (cdr exp))

a) So, in our new derive we do lookup in table instead of cond expression. We are not able to move number? into lookup, because number? is condition for a set of values, not just one value, and table works only with one value.


(define (make-sum args) 
    (define (sum items total nonnum)
            ((null? items)
                (if (null? nonnum)
                    (cons '+ (if (= total 0)
                                (cons total nonnum)
            ((number? (car items))
                (sum (cdr items) (+ (car items) total) nonnum))
                (sum (cdr items) total (cons (car items) nonnum)))
    (sum args 0 '())

(define (make-prod m1 m2)
  (cond ((or (=number? m1 0) (=number? m2 0)) 0)
        ((=number? m1 1) m2)
        ((=number? m2 1) m1)
        ((and (number? m1) (number? m2)) (* m1 m2))
        (else (list '* m1 m2))))

(define (install-derivatives-package) 
  (define (deriv-sum items var)
    (make-sum (map (lambda (e) (deriv e var)) items))
  (put 'deriv '+ deriv-sum)

  (define (deriv-prod items var)
    (let ((tail
        (if (null? (cddr items))
            (cadr items)
            (cons '* (cdr items))
        (make-sum (list 
           (make-prod (car items)
                      (deriv tail var))
           (make-prod (deriv (car items) var)
  (put 'deriv '+ deriv-sum)
  (put 'deriv '* deriv-prod)

I think I wrote too much code here because I wanted to support sums and products of multiple arguments.

c) Exponentation

(define (make-exp base e)
  (cond ((=number? e 0) 1)
        ((=number? e 1) base)
        (else (list '** base e))))

  (define (deriv-exp items var)
    (let (
        (base (car items))
        (e (cadr items))
            (make-exp base (- e 1))
  (put 'deriv '** deriv-exp)

(deriv '(+ (** x 3) (** x 2)) 'x)

d) We could switch arguments inside get, or inside put, or switch arguments when we call put. That's all what will be needed.

Exercise 2.74

I skipped it because it is too abstract.

Exercise 2.75

(define (make-from-mag-ang r a) 
  (define (dispatch op)
    (cond ((eq? op 'real-part) (* r (cos a)))
          ((eq? op 'imag-part) (* r (sin a)))
          ((eq? op 'magnitude) r)
          ((eq? op 'angle) a)
           (error "Unknown op -- MAKE-FROM-REAL-IMAG" op))))

Exercise 2.76

Skip this too. Because I see no way to verify that I did it correctly. Learning needs feedback.