It would definitely be nice to be able to work with a partial Category class, where for example the objects could be constrained to belong to a class. One could then restrict a Category to a type level representation of the natural numbers or any other desired set. Kind polymorphism should make this easy to define, but I still don't have a good feel for whether it is worth the complexity. On Dec 21, 2012 6:37 AM, "Tillmann Rendel" <ren...@informatik.uni-marburg.de> wrote:
> Hi, > > Christopher Howard wrote: > >> instance Category ... >> > > The Category class is rather restricted: > > Restriction 1: > You cannot choose what the objects of the category are. Instead, the > objects are always "all Haskell types". You cannot choose anything at all > about the objects. > > Restriction 2: > You cannot freely choose what the morphisms of the category are. Instead, > the morphisms are always Haskell values. (To some degree, you can choose > *which* values you want to use). > > > These restrictions disallow many categories. For example, the category > where the objects are natural numbers and there is a morphism from m to n > if m is greater than or equal to n cannot be expressed directly: Natural > numbers are not Haskell types; and "is bigger than or equal to" is not a > Haskell value. > > Tillmann > > ______________________________**_________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/**mailman/listinfo/haskell-cafe<http://www.haskell.org/mailman/listinfo/haskell-cafe> >
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