> If Product and Sum where built-in to some new version of SPAD they > would include the 'product' and 'sum' operations as an inherent part > of their definition. The existence of these operations is dictated by > describing them as categorical limits. So for example
> See: http://axiom-wiki.newsynthesis.org/LimitsAndColimits > Then for example the definition of a simple piecewise function might > look like this: > > p:Sum(NegativeInteger,ZeroInteger,PositiveInteger)->Integer := > sum(Integer,x +-> -(x^2), x +-> 0,x +-> x^2) That looks nice. But, of course it involves quite a lot. (You have demonstrated that by the package Sum2Functions.) Namely, if I define (or rather just use) for two domains X and Y the type Sum(X, Y), then for every other domain A the compiler would know about a function sum: (X->A,Y->A) -> Sum(X,Y)->A (of course *without* the need of some package like Sum2Functions). But then Sum and Product are just special cases of (Co-)Limits. So maybe a Limit and CoLimit constructor should be built-in to the language. My question would then be, does such a general construction allow to recover the concret handling of Record/Cross/Union etc.? (Record, Cross, and Union would then, of course, not be built-in.) By "concrete" I don't just mean theoretically, but it rather concerns the question how could this Limit stuff really be implemented into the compiler? > What makes you think that polynomials of the kind you describe should > look different in a more categorical-oriented language? I don't see > it. Invent some other concrete application for which you could demonstrate the benefit of the categorical programming language SPAD-CAT. Your example, I cited above, is already something. Other examples? Ralf --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~----------~----~----~----~------~----~------~--~---
