Question: How does PDEtoos[declare] work?

I don't quite understand the behavior of PDEtools[declare].  My reading of the documentation is that PDEtools[declare](y(t)) tells Maple that y is a function of t, and therefore y(t) is displayed as y and the derivative of y is displayed as yt.  I did not expect other variables to be similarly affected but apparently they are.  For instance, in the worksheet below, why is the derivative of p displayed as ps?


The normal display of derivatives:


diff(y(t), t)

diff(p(s), s)

Declare y as a function of t:


` y`(t)*`will now be displayed as`*y

diff(y(t),t);    # this is displayed in subscript notation, as expected
diff(p(s),s);    # why is this displayed in subscript notation?

diff(y(t), t)

diff(p(s), s)



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