SICP exercise 2.83

Introduction

Suppose you are designing a generic arithmetic system for dealing with the tower of types shown in figure 2.25: integer, rational, real, complex. For each type (except complex), design a procedure that raises objects of that type one level in the tower. Show how to install a generic raise operation that will work for each type (except complex).

Discussion

(define (install-raise)

  (put 'raise '(scheme-number)

    (lambda (x) (make-rat x 1)))

  (put 'raise '(rational)

    (lambda (x)

      (make-real (* (/ (numer x) (denom x)) 1.0))))

  (put 'raise '(real)

    (lambda (x) (make-from-real-imag x 0))))