Based on this lemma, we have the form:

-

with the projection -- which is a morphism of forms (natural transformation ) in .

8 The Form Pianoscore and the Denotator
Träumerei

Now we are going to present the example of the form Pianoscore, together with the denotator Träumerei, as developed in Montiel (1999). The motivation behind their elaboration was the materialization of the concepts that have been studied up until this point; the result was a rather complete form and denotator with which we can »do mathematics«. Also, with this particular example, forms of every type are used.

The form Pianoscore is an example, on the one hand, of the recursivity implicit in the theoretical development upon which it is based and, on the other, of the importance of the form in the existence of denotators. In Figure 1 we see a diagram of the form Pianoscore, in which it is evident in what way denotators were conceived to solve the problems that the universal characteristics of the encyclopedia present, as is described at the beginning of this article.

The denotator Träumerei is a »point« in the space Pianoscore. The question of how to define morphisms between points in this space is still open.

The notation is according to the format denoteX, and not the notation of the theoretical development that we have studied. We should note that denoteX  soon will be translatable to LaTeX, Mathematica, etc. Instead of having:

, we have ; if the identifier is the identity we just write:

In the same way, the denotator instead of being written as is (we had also written ) and if the address (module) is zero we write , where is the name of the denotator, is the address of the denotator, is the form of the denotator and are the coordinates. In the example, the address is always zero and the majority of the identifiers are the identity.