Laws for Monad and MonadPlus.
Hi all. I was revising a short article I've written about Monads in Haskell and started wondering about the identities associated with Monads. I think it is generally agreed (and in the report) that the following identities should be true of a Monad: Left identity: return a >>= k = k a Right identity: p >>= return = p Associativity: (p >>= j) >= k = p >>= (\x->(j x >>= k)) [provided x is not free in j or k] What about MonadPlus? By analogy with semirings, I came up with: Zero:mzero >>= k = mzero = p >>= (\x -> mzero) Identity: p `mplus` mzero = p = mzero `mplus` p Commutativity: p `mplus` q = q `mplus` p Right distributivity: (p `mplus` q) >>= k = (p >>= k) `mplus` (q >>= k) Left distributivity: p >>= (\x->j x `mplus` k x) = (p >>= j) `mplus` (p >== k) [provided x is not free in j or k] But commutativity does not hold for Maybe or [], left distributivity does not hold for Maybe and right distributivity does not hold for [], so these can't be right. Are the other identities I've listed ok? Are there other identities that I've missed? Cheers, Theodore Norvell Dr. Theodore Norvell[EMAIL PROTECTED] Electrical and Computer Engineering http://www.engr.mun.ca/~theo Engineering and Applied SciencePhone: (709) 737-8962 Memorial University of Newfoundland Fax: (709) 737-4042 St. John's, NF, Canada, A1B 3X5 ___ Haskell mailing list [EMAIL PROTECTED] http://www.haskell.org/mailman/listinfo/haskell
Re: Haskell and the NGWS Runtime
Thanks to Nigel for answering my question Tyson Dowd wrote: > > Microsoft indicates that C# will not support "genericity", through > > even anything as crude as C++'s templates, so it is unlikely that > > they will seek to support functional programming languages in the > > short term. Perhaps this limitation is part of the impetus for the > > Mondrian variant. That they are not supporting templates ala C++ can only be a good thing. It leaves the door open for something closer to Haskell's or ML's styles of genericity. This is certainly something that the functional language community can contribute to the world of mainstream imperative programming languages, and thence to the bulk of software development. Yes, I know it's been done; for example pizza; but pizza is not a widely adopted standard. If C# adopts parametric polymorphism and either type classes or ML style modules, and C# becomes more than a proprietary language, then it could make a contribution to getting some of the ideas developed by the functional community into the mainstream. With Haskell# or Mondrian: Can I use C# to create an instance of a Haskell class? Can I use Haskell to extend a C# abstract class? I suspect the answer to both these questions is currently no. If future versions of .NET and Haskell variants change that, it will be very interesting. Cheers, Theodore Norvell Dr. Theodore Norvell[EMAIL PROTECTED] Electrical and Computer Engineering http://www.engr.mun.ca/~theo Engineering and Applied SciencePhone: (709) 737-8962 Memorial University of Newfoundland Fax: (709) 737-4042 St. John's, NF, Canada, A1B 3X5
Re: Haskell and the NGWS Runtime
I've been following this discussion, but there are so many new buzzwords coming out of microsoft that it's a bit confusing for those not in the know. Is there a quick way to summarize the relationships between .NET NGWS C# (which I've discovered is intended to be pronounces C-sharp rather than C-hash) the .NET virtual machine COM Why does the world need C# when it already has Java and C++? Why does the world need a .NET virtual machine when it has dozens of Java Virtual Machines? Don't COM and Corba already provide interlanguage and network interoperability? Why is it important for Haskell to fit into .NET? I hope this isn't too far off topic. Cheers, Theodore Norvell ---- Dr. Theodore Norvell[EMAIL PROTECTED] Electrical and Computer Engineering http://www.engr.mun.ca/~theo Engineering and Applied SciencePhone: (709) 737-8962 Memorial University of Newfoundland Fax: (709) 737-4042 St. John's, NF, Canada, A1B 3X5
