In a domain and in categories referenced in a domain the notation %
represents "this domain" (or self in some programming languages). So
we commonly write for example
with
f: (%,%) -> %
to indicate a function f which takes a pair of values in this domain
and returns a value in this same domain - whatever domain we happten
to be talking about in this context.
But what if we are interested in the domain as a functor? Suppose I
was writing an "endofunctor" domain constructor like 'Set' and I
wanted to treat constructions like 'Set Set R', i.e. sets of sets as
something special. E.g.
MySet:(T:SetCategory):SetCategory == with
join: MySet MySet T -> MySet T
...
I cannot really use MySet here because MySet is not defined yet and
the compiler complains. I cannot use % here like this:
join: % % T -> % T
because % refers to 'MySet(T)' for some domain T in SetCategory. But
MySet(T) is itself a domain in SetCategory so it does make sense to
iterate it. How can I do this?
I recall another related notation %% (perhaps only in Aldor?) what is
it used for?
Regards,
Bill Page.
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