;; 2.77
;; obviously magnitude isn't defined yet on the complex type,
;; it is only defined in the internal types, i.e. the secondary types.
;; this means that the first apply-generic will immediately fail.
;; the reason Alyssa's fix works, is because this makes the
;; maginute function dispatch to itself when seing the type
;; '(complex). Then, magnitude will be called with the
;; internal type - e.g. '(rectangular 3 4), which gives
;; the correct answer.

;; 2.78

(defun type-tag (datum)
  (cond
    ((consp datum) (car datum))
    ((numberp datum) 'number)
    (t (error "unkown type"))))

(defun contents (datum)
  (cond
    ((consp datum) (cdr datum))
    ((numberp datum) datum)
    (t (error "unknown type"))))

;; assuming the dispatch function actually calls the function with
;; the contents of each datum, then you should now be able to just
;; insert #'+, #'*, #'- and #'/

;; 2.79

;; 2.81
;; First, apply-generic is called.
;; 'exp is not defined on complex numbers. Therefore, the apply-generic
;; function somewhat mistakenly enters the second branch, and first tries
;; to find a coercion from the first argument's type to the second argument's
;; type. It finds this coercion function. But then it calls:
;; (apply-generic op (t1->t2 a1) a2)
;; this is a problem, because it now enters an infinite loop. Every time,
;; apply-generic will try to find the 'exp method, not find it, and try
;; to coerce the first argument to the second argument's type.
;; It will succeed, and call itself again.
;; Since this is a tail call, it will be optimised and this will be reduced
;; to an infinite loop.
;;
;; Something can be done about it. We can simply compare the tags of
;; the objects before trying to coerce - and we can simply raise an error
;; if both objects have been coerced to the same type and there is still
;; no function found. Coincidentally, this would also prevent Louis Reasouner's
;; previous infinite loop.



;; In order to be extra spicy, I will be completing the exercises in
;; the symbolic algebra section through the use of CLOS.
;; I.e. I will actually build an AST of these objects, and use
;; methods to parse, interpret and modify them.

;; Tomorrow. I will do that tomorrow.