This paper demonstrates the existence of self-generating program specializers and uses a language-independent projection to obtain them. The projection is considered from the viewpoint of the interpretive approach and a bootstrapping technique is identified by which a specializer can optimize its own implementation. A theorem is presented that equates the set of self-generating specializers and the set of specializers produced by the new projection. A practical consequence of the theorem is that an implementation of a specializer must contain an error if it is not possible to observe self-generation, which requires only a textual program comparison. Self-generation may thus provide a method for testing specializers and self-interpreters while they are under development.