Compound Data

eg.1 Add Method for Relational Number

Every realational number can be expressed by a fractional number.

$$ x=\frac{m}{n},y=\frac{p}{q}, (x,y \in R;m,n,p,q\in Z) $$ $$ x+y=\frac{mq+pn}{nq} $$

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

List Structure

The feature can be used to implement make-rat.

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; constructs a pair whose first part is x and whose second part is y.
(cons x y) ; => [x, y]

; selects the first part of the pair p
(car p) ; => [x, y][0], aka x

; selects the second part of the pair p
(cdr p) ; => [x, y][1], aka y

ATTENTION cons can constructs a pair no matter what the type of x, y

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(define (make-rat n d)
    (cons n d)
)
(define (numer x)
    (car x)
)
(define (denam x)
    (cdr x)
)

`let`

use let to define a local variable.