On Tuesday 15 Nov 2011 13:37:04 Bill Page wrote: > Martin, > > I would be glad if you could add "more information about the > relationship between 'functors' and 'type constructors'.
Bill, I really don't feel qualified to do this, as I will try to explain by demonstrating my ignorance: What I had in mind was an explanation starting with a mathematical approach. That is in the same way that morphisms compare certain concrete categories (preserve certain elements of structure) then functors generalise this to allow us to compare different categories. When we try to implement this in SPAD then all sorts of issues start to arise: 1) Are we representing a category-theoretic-category with a SPAD- category and what are the conditions for doing that? 2) How do we relate the concepts of category, type and domain? At some stage we appear to move from functors comparing categories to functors 'generating' one category from another: 3) Is this valid? That is might there be some elements of structure that are not related by the structure? 4) If we generate an SPAD-category in code then I assume that domain will also have to be generated in code? I get the impression that we are not modelling functors in general here but only specific endofunctors which 'generate' hierarchical types. So in the case of list-monad we start with built-in List rather than generating it? So if a SPAD programmer wants to implement their own monad then I assume they would have to start by defining an inductively defined type? I think there need to be advise to potential users on how to go about this. Once all this is clarified then I think it would be good to preserve all the Nuggets of information in the conversations between Bill, Gaby and Waldek on this topic. I certainly would not dare to attempt that. There is something else I would like to ask here. When Googling this subject there is masses of stuff around monads and Haskell. I get the impression that Haskell monads are not derived from functors but people seem to think they should be (and in some libraries they are). Haskell also seems to have the concept of 'applicative functors' which are half way between functors and monads. I have only seen these terms defined in a Haskell context by giving examples. Has anyone come across the terms: 1) Applicative functor 2) Generative functor 3) Generative type in this more general context? Would they be useful here? How would you define them? It seems to me that, if this code is ever going to go into the SPAD library then this type of information need to be available for end users and maintainers of the code - otherwise its no use to anyone, so why not do it now while it is clearer in your mind? As I think I have demonstrated above I am not really qualified to do it. I'm prepared to do my share but I'm not looking for the role of chief documenter. Martin -- 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 fricas-devel@googlegroups.com. To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en.
