I think the definition given here: http://en.wikibooks.org/wiki/Haskell/Category_theory
will suffice for my purpose, especially when expressed in terms of 'unit' and 'join'. Is that OK with you? On Tue, Nov 8, 2011 at 1:53 PM, Gabriel Dos Reis <g...@cs.tamu.edu> wrote: > Bill Page <bill.p...@newsynthesis.org> writes: > > | How can I implement Haskell monads in OpenAxiom (or any other Axiom > | variant including Aldor)? How does or how could the monad construction > | in Haskell fit into Axiom? > > OK. Show me your version of Haskell monad -- the reason I am asking is > that there are many things people call "monad" (including in Haskell) > and it would be not productive that I second guess what you meant. > > -- Gaby > > | > | On Tue, Nov 8, 2011 at 1:45 PM, Gabriel Dos Reis <g...@cs.tamu.edu> wrote: > | > Bill Page <bill.p...@newsynthesis.org> writes: > | > > | > | Bill Page <bill.p...@newsynthesis.org> 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 domain > | > | > | constructor (= functor). This is a rather deep issue in the > | > | > | fundamental design of SPAD and Aldor where types are supposed to be > | > | > | static and I am not sure if it was ever fully resolved. Maybe > | > | > | OpenAxiom has made some progress here as well? > | > | > | > | > | > | > | On Tue, Nov 8, 2011 at 10:44 AM, Gabriel Dos Reis wrote: > | > | > > | > | > I think this essentially goes back to a discussion we had recently. I > | > | > am not sure I succeeded in getting my points trough:-) > | > | > > | > | > | > | Yes, I have been listening. I think I understand this in the context > | > | of the changes that you have made to OpenAxiom. > | > > | > Hmm, I am not sure I understand, but let's see. > | > > | > | > Yes, functors and category constructors are functions, but they are > not > | > | > ordinary functions. In general type constructor (in SPAD or any ML > | > | > descendent, which includes Haskell) and data constructors are special > | > | > functions. In terms of formal semantics, they are not reducible. > | > | > This is a very important point. That allows the compiler to > internally > | > | > reason on some usage, including deciding equality when type checking > an > | > | > expression. > | > | > > | > | > | > | Do you think we should be allowed to write something like the > | > | following in the OpenAxiom compiler (SPAD)? > | > | > | > | (X:Domain):Domain+->List X > | > | > | > | i.e. define a function that takes a domain as an argument and returns > | > | a domain? Could we use such a thing in a statically typed language? I > | > | suppose not. > | > > | > In OpenAxiom, that depends on the context of usage. > | > > | > | > At the moment, all AXIOM variants do not allow you to pass a category > as > | > | > a parameter in a domain or category definition -- well, you can in > | > | > OpenAxiom but the usage then is limited. As a consequence, > | > | > you can't introduce a category as a parameter and a domain parameter > | > | > depending on the category parameter and expect anything useful to come > | > | > out. In your definition of MonadCat2, the compiler internally assumes > | > | > that the parameter 'C' designates a domain -- not a category as you > | > | > intended -- because its type is a category. You can check that by > | > | > looking at the dual signature (or COSIG property of the DB) of > MonadCat2. > | > | > So, your attempt to call it with SetCategory for C is a type > violation. > | > | > > | > | > | > | It is not so clear to me that Aldor intended to duplicate this part of > | > | the Axiom semantics. > | > > | > I am not sure I understand; could you elaborate? > | > > | > | > All AXIOM compilers assume that when they see a category form, the > | > | > head is a category constructor, not an arbritrary function (or > | > | > parameter) that may evaluate at runtime to a category. This allows > the > | > | > compiler to type check domains. The story is almost the same for > | > | > domain forms in certain situations. See the roundabout hack in > | > | > the implementation of Table (table.spad.pamphlet) just to > conditionally > | > | > select the representation domain (InnerTable.) OpenAxiom's compiler > | > | > tried to improve on the situation, but only marginally at the moment. > | > | > > | > | > | > | Yes, that is interesting. > | > | > | > | > But, whatever is done there is no way around the fact that a > constructor > | > | > is not an ordinary function -- being in Haskell or in Spad. > | > | > > | > | > | > | Yet in Haskell we do have functors and monads ... > | > > | > Yes, but I am not seeing the implication. Could you elaborate? > | > > | > | One question being asked here is "what is required in Axiom (and/or > | > | its descendants) to do something equivalent? > | > > | > Equivalent to what? I'm afraid I do not understand the description of the > | > thing being claimed to be in Haskell -- to remove any misunderstanding I > | > understand Haskell, but I do not understand the *claim* being made and > what > | > "equivalent" is being sought. > | > > | > Any clear elaboration of the original issue will help. > | > > | > -- Gaby > | > > | > -- > | > 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-de...@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. > | > > | > > ------------------------------------------------------------------------------ RSA(R) Conference 2012 Save $700 by Nov 18 Register now http://p.sf.net/sfu/rsa-sfdev2dev1 _______________________________________________ open-axiom-devel mailing list open-axiom-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/open-axiom-devel
