John, You write: > Yes, you are describing 'co-monads'. >
Good catch, but actually, that's too weak. i'm requesting something that is both a monad and a co-monad. That makes it something like a bi-algebra, or a Hopf algebra. This, however, is not the full story. i'm looking for a reference to the full story. Surely, someone has already developed this theory. Best wishes, --greg From: John Meacham <[EMAIL PROTECTED]> Subject: Re: [Haskell-cafe] monads with take-out options To: haskell-cafe@haskell.org Message-ID: <[EMAIL PROTECTED]> Content-Type: text/plain; charset=utf-8 On Mon, Nov 24, 2008 at 02:06:33PM -0800, Greg Meredith wrote: > Now, are there references for a theory of monads and take-out options? For > example, it seems that all sensible notions of containers have take-out. Can > we make the leap and define a container as a monad with a notion of > take-out? Has this been done? Are there reasons for not doing? Can we say > what conditions are necessary to ensure a notion of take-out? Yes, you are describing 'co-monads'. here is an example that a quick web search brought up, and there was a paper on them and their properties published a while ago http://www.eyrie.org/~zednenem/2004/hsce/Control.Comonad.html the duals in that version are extract - return duplicate - join extend - flip (>>=) (more or less) John -- John Meacham - ⑆repetae.net⑆john⑈ -- L.G. Meredith Managing Partner Biosimilarity LLC 806 55th St NE Seattle, WA 98105 +1 206.650.3740 http://biosimilarity.blogspot.com
_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
