# weima learns to program

my attempt to do the exercises in sicp.

## Wednesday, August 6, 2008

### sicp exercise 2.81

;; Exercise 2.81.  Louis Reasoner has noticed that apply-generic may try to coerce the arguments to each other's type even if they already have the same type. Therefore, he reasons, we need to put procedures in the coercion table to "coerce" arguments of each type to their own type. For example, in addition to the scheme-number->complex coercion shown above, he would do:

;; (define (scheme-number->scheme-number n) n)
;; (define (complex->complex z) z)
;; (put-coercion 'scheme-number 'scheme-number
;;               scheme-number->scheme-number)
;; (put-coercion 'complex 'complex complex->complex)

;; a. With Louis's coercion procedures installed, what happens if apply-generic is called with two arguments of type scheme-number or two arguments of type complex for an operation that is not found in the table for those types? For example, assume that we've defined a generic exponentiation operation:

;; (define (exp x y) (apply-generic 'exp x y))

;; and have put a procedure for exponentiation in the Scheme-number package but not in any other package:

;; following added to Scheme-number package
;; (put 'exp '(scheme-number scheme-number)
;;      (lambda (x y) (tag (expt x y)))) ; using primitive expt

;; What happens if we call exp with two complex numbers as arguments?

;; b. Is Louis correct that something had to be done about coercion with arguments of the same type, or does apply-generic work correctly as is?

;; c. Modify apply-generic so that it doesn't try coercion if the two arguments have the same type.

;; a. this will lead to an infinite recursion of coercions.

;; b. apply-generic works correctly.

;; c.

(define (apply-generic op . args)
(let ((type-tags (map type-tag args)))
(let ((proc (get op type-tags)))
(if proc
(apply proc (map contents args))
(if (= (length args) 2)
(let ((type1 (car type-tags))
(a1 (car args))
(let ((t1->t2 (get-coercion type1 type2))
(t2->t1 (get-coercion type2 type1)))
(cond ((eq? type1 type2) (error "same type - no coercion"))
(t1->t2
(apply-generic op (t1->t2 a1) a2))
(t2->t1
(apply-generic op a1 (t2->t1 a2)))
(else
(error "No method for these types"
(list op type-tags))))))
(error "No method for these types"
(list op type-tags)))))))