[Haskell-cafe] re: monads with take-out options

[Greg Meredith]

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 <john at repetae.net>
Subject: Re: [Haskell-cafe] monads with take-out options
To: haskell-cafe at haskell.org
Message-ID: <20081124231451.GG32430 at sliver.repetae.net>
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


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John Meacham - ⑆repetae.net⑆john⑈

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