Recursive

Some prossible methods to implement operator+.

prerequisites

There exists some primitive procedures, which are implemented in other method finally.

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; 1-
(define (1- x) ...)
; 1+
(define (1+ x) ...)

eg.1 operator+

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; provided that x is non-negative integer
(define (+ x y)
    if (= 0 x)
    x
    (+ (1- x) (1+ y)))

an instance

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(+ 3 4)

inspect the compute procedure:

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(+ 3 4)
(+ (1- 3) (1+ 4))
(+ 2, 5)
(+ (1- 2) (1+ 5))
(+ 1, 6)
(+ (1- 1) (1+ 6))
(+ 0, 7)
7

eg.2 fibonacci

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(define (fib x) 
    (if (< x 3)
    1
    (+ (fib (- x 1)) (fib (- x 2)))
    )
)

duplicate compute procedure fib(- x 2)