Very much a part of the standard. i.e. not specific to SBCL.

Think of defgeneric as the function signature and defmethod as the template specialization. Not sure why you say this is an error in CLOS. Looks fine to me.

That said, most implementations try to auto-infer the generic function metaobject when you use defmethod without defgeneric. SBCL raises a warning.

Good reads on the topic:

http://www.gigamonkeys.com/book/object-reorientation-generic...

https://mitpress.mit.edu/books/art-metaobject-protocol

http://mop.lisp.se/

The DEFGENERIC line is wrong. It can't have a body like that. It should be something like

    (defgeneric xplusone (x)
      (:method (x) (+ 1 x)))

Also, generic functions are slower than regular functions (due to dynamic dispatch), so using them for type optimization would be rather counterproductive.

Yes, thanks. I only wanted to point out similarities to abstract classes, generic slow methods.