SICP Chapter 2.1 Notes

SICP

Build abstractions by combining data to form compound data

(define a (cons x y))
(car a)     ; x
(cdr a)     ; y

Programs should make no assumptions about the data and its implementation details
The concrete data representation should be independent of the programs using the data

The interface between these two components are a set of procedures selectors and constructors

(define (make-rat x y) (cons x y))

(define (numer rat) (car rat))
(define (denom rat) (cdr rat))

Example of adding rational numbers

Use relationships to define a procedure, not the representation of a rational number
- (n1 / d1) + (n2 / d2) = (n1 * d2 + n2 * d1) / (d1 * d2)

(define (add-rat x y)
    (make-rat (+ (* (numer x) (denom y))
                 (* (numer y) (denom x)))
              (* (denom x) (denom y))))

The idea of data abstraction is to identify for each type of data object a basic set of operations in terms of which all manipulations of data objects of that type will be expressed
Only those set of operations should be used to manipulate the data
Barriers for rational number example:
- Programs that use rational numbers
- Rational numbers in problem domain: add-rat, sub-rat, etc.
- Rational numbers as numerators and denominators: make-rat, numer, denom**
- Rational numbers as pairs: cons, car, cdr
- Some implementation for pairs

Constructors and selectors must fulfill conditions to form a suitable basis for representations of data
- Ex. make-rat, numer and denom must satisfy the following condition
  - For any integer n and any non-zero integer d, if x is (make-rat n d)
  - (numer x) / (denom x) = n / d