[Comment moved to this thread.] On Thu, Jan 19, 2012 at 12:59 PM, Gabriel Dos Reis <[email protected]> wrote: > Ralf Hemmecke <[email protected]> writes: > > | On 01/19/2012 06:17 PM, Bill Page wrote: > | > Ok, so Aldor builds these into the language too. Why not Rep? > | > | Because that is just a convention and not necessary as a language > | construct. (cf. the thread from 2007 that I mentioned earlier). > > if the argument hinges on 'convention', then I am a bit disturbed: are > you claiming that the builtin types Record, Union, Mapping, Category, > etc., are all free of conventions? >
I think there are very good reasons to consider at least Record, Union and Mapping as constructs that are essentially free of conventions - at least from the point of view of the intended application: expressing mathematical algorithms. We want a language that supports some concept of mathematical category or at least universal algebra. Thing is these constructs collectively make the language cartesian closed in the sense of category theory. This notion is essentially universal, in fact it is universal in a technical sense... typed lambda calculus etc. This means that we can do many things (almost up to set theory) as a "first order" language. The only thing missing here is the concept of sub-object (sub-domain) and how it should interact with logic, otherwise the underlying structure of the language would essentially be a topos (algebraic set theory). And a lot (maybe almost all of mathematics or at least the constructive part of mathematics?) can be done as internal structures of such a mathematical category. In my view Rep is also essential in this picture since what we do most of the time is to define new domains in terms of old ones essentially functorially, speaking loosely. Of course it would be ideal if all of this could be made completely rigorous in terms of language specifications and mathematics. Regards, Bill Page. -- 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.
