Re: [open-axiom-devel] [fricas-devel] Re: Monads in FriCAS

2011-11-10 Thread Gabriel Dos Reis
Ralf Hemmecke writes: [...] | Partial (which corresponds to Maybe) and List are completely | library-defined in libaldor. The same is true in OpenAxiom -- I would suspect in FriCAS too. -- Gaby -- RSA(R) Conference 20

Re: [open-axiom-devel] [fricas-devel] Re: Monads in FriCAS

2011-11-09 Thread Bill Page
1) Does this code (in principle) capture the notion of Monad? 2) If yes, is it useful? How to use it? 3) Why doesn't this compile? (Discussion of function versus functor.) 4) Is there another way to write it that does compile and that would be a useful way to represent a monad-like construction in

Re: [open-axiom-devel] [fricas-devel] Re: Monads in FriCAS

2011-11-09 Thread Gabriel Dos Reis
Bill Page writes: | Since this is a discussion of Monad and not categories as parameters | as such, consider instead | | Monad(A: SetCategory, M: SetCategory -> SetCategory): Category == with { |unit: A -> M A; |mult: M M A -> M A; | } OK, then what is the question? -- Gaby | | Regard

Re: [open-axiom-devel] [fricas-devel] Re: Monads in FriCAS

2011-11-09 Thread Bill Page
Since this is a discussion of Monad and not categories as parameters as such, consider instead Monad(A: SetCategory, M: SetCategory -> SetCategory): Category == with { unit: A -> M A; mult: M M A -> M A; } Regards, Bill Page On Wed, Nov 9, 2011 at 10:57 AM, Gabriel Dos Reis wrote: > Bill P

Re: [open-axiom-devel] [fricas-devel] Re: Monads in FriCAS

2011-11-09 Thread Gabriel Dos Reis
Bill Page writes: | On Wed, Nov 9, 2011 at 2:45 AM, Ralf Hemmecke wrote: | > Looking at http://en.wikibooks.org/wiki/Haskell/Category_theory#Monads and | > my previous attempt to model it in Aldor... | > http://groups.google.com/group/fricas-devel/msg/38e7d6dca39cc46c | > | > Actually, now I beli

Re: [open-axiom-devel] [fricas-devel] Re: Monads in FriCAS

2011-11-08 Thread Bill Page
Bill Page writes: > ... > | Second, we are trying to pass the functor M as a parameter. > | Specifying this is a currently very awkward in both SPAD and Aldor. > | What Ralph wrote involves passing a function which returns domain. In > | Axiom and it's derivatives this is not the same thing as a