Johannes Grabmeier wrote:
>
> I would see more benefit by providing mechanisms for being able to
> choose the operation symbol free, e.g. for construction of lattices
> having two semigroups (L, /\) and (L, \/). Additive and Multiplicative
> structures would be unified and generalized.
Yes, that is desirable. IIRC there were few experiments in
this direction. However, it is not clear how such mechanism
will fit into our typechecker. More precisely, one way is to
allow renaming operations. AFAICS this does not pose any
theoretical problems. On practical level we would need
resonable syntax and of course sombody would have to do
actual implementation. Another way is to allow operation
symbols as parameters. One aspect is that operation
names would be treated in quite different way then other
parameters -- it is not clear for me how much syntactic
difference should be there. Also, current type checker
depends on ability to produce finite list of operations
for any category/domain. In this list some operations
are conditional (present only when their condition
hold), but no other operation can appear independent
on value of parameters. Parametised operation names
break this propery: set of exported operation names
depends on parameters.
Hopefully, we will work out problems at some time in
the future. However, I do not think such generalization
excludes creating now categories with fixed operation
names. First, we need to work out good category
structure anyway. Second, even with ability to
use parametric names we will need categories
with concrete names.
--
Waldek Hebisch
[email protected]
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