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 ;; assuming that the types are arranged in a simple tower shape. 
 (define (apply-generic op . args) 
   ;; raise s into t, if success, return s; else return #f 
   (define (raise-into s t) 
         (let ((s-type (type-tag s)) 
               (t-type (type-tag t))) 
           (cond ((equal? s-type t-type) s) 
                 ((get 'raise (list s-type))  
                  (raise-into ((get 'raise (list s-type)) (contents s)) t)) 
                 (else #f)))) 
   (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 ((a1 (car args)) 
                    (a2 (cadr args))) 
                   ((raise-into a1 a2) 
                    (apply-generic op (raise-into a1 a2) a2)) 
                   ((raise-into a2 a1) 
                    (apply-generic op a1 (raise-into a2 a1))) 
                   (else (error "No method for these types" 
                         (list op type-tags))))) 
            (error "No method for these types" 
                   (list op type-tags))))))) 


 ;; This solution is for an apply-generic that works with arbitrary arguments 
 ;; by raising all to the highest type. 
 ;; New types can be added to the tower easily. Only the procedure "level" has 
 ;; to be modified. 
 (define (level type) 
   (cond ((eq? type 'integer) 0) 
         ((eq? type 'rational) 1) 
         ((eq? type 'real) 2) 
         ((eq? type 'complex) 3) 
         (else (error "Invalid type: LEVEL" type)))) 
 (define (apply-generic op . args) 
   (let ((type-tags (map type-tag args))) 
     (define (no-method) 
       (error "No method for these types" (list op type-tags))) 
     (let ((proc (get op type-tags))) 
       (if proc 
           (apply proc (map contents args)) 
           (if (not (null? (cdr args))) ; length of args > 1 
               (let ((raised-args (raise-to-common args))) 
                 (if raised-args 
                     (let ((proc (get op (map type-tag raised-args)))) 
                       (if proc 
                           (apply proc (map contents raised-args)) 
 (define (raise-to-common args) 
   (let ((raised-args 
          (map (lambda (x) (raise-to-type (highest-type args) x)) 
     (if (all-true? raised-args) 
 (define (all-true? lst) 
   (cond ((null? lst) true) 
         ((car lst) (all-true? (cdr lst))) 
         (else false))) 
 (define (raise-to-type type item) 
   (let ((item-type (type-tag item))) 
     (if (eq? item-type type) 
         (let ((raise-fn (get 'raise item-type))) 
           (if raise-fn 
               (raise-to-type type (raise-fn item)) 
 (define (highest-type args) 
   (if (null? (cdr args)) 
       (type-tag (car args)) 
       (let ((t1 (type-tag (car args))) 
             (t2 (highest-type (cdr args)))) 
         (let ((l1 (level t1)) (l2 (level t2))) 
           (if (> l1 l2) t1 t2)))))