Some more progress

sec-2-5.lisp

@@ -0,0 +1,60 @@
+;; 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.
+
+