I'm always glad to see videos like this. I wish more people could have that
much fun playing with math ;).
It wouldn't really be suitable for your application but another interesting
generalization is to insert the 'Either' at the top level:
> data ConwayT m a
> = Pure a
> | ConwayT
> { runLeftConwayT :: m (ConwayT m a)
> , runRightConwayT :: m (ConwayT m a)
> }
Using this construction, the "handedness" of the structure doesn't appear until
you start implementing binary operations on games, so there is a unique monad
structure instead of just a unique bind/join:
> instance Functor m => Monad (ConwayT m) where
> return = Pure
> Pure x >>= f = f x
> ConwayT l r >>= f = ConwayT (fmap (>>= f) l) (fmap (>>= f) r)
but there are then (at least) two versions of every monoid structure. Given
that monoidal structures such as addition and multiplication are the main
purpose of a calculator it's probably simpler in this case to just give up the
'unit' as you chose to do. On the other hand, if for some reason a monadic
structure is the extent of one's interest then this version definitely
simplifies that structure.
-- James
On Jul 27, 2011, at 4:31 AM, Greg Meredith wrote:
> Dear Haskellians,
>
> A new C9 video in the series!
>
> So, you folks already know most of this... except for maybe the
> generalization of the Conway construction!
>
> Best wishes,
>
> --greg
>
> ---------- Forwarded message ----------
> From: Charles Torre <...>
> Date: Tue, Jul 26, 2011 at 1:12 PM
> Subject: C9 video in the Monadic Design Patterns for the Web series
> To: Meredith Gregory <[email protected]>
> Cc: Brian Beckman <...>
>
>
> And we’re live!
>
>
>
> http://channel9.msdn.com/Shows/Going+Deep/C9-Lectures-Greg-Meredith-Monadic-Design-Patterns-for-the-Web-4-of-n
>
> C
>
>
>
> From: Charles Torre
> Sent: Tuesday, July 26, 2011 11:51 AM
> To: 'Meredith Gregory'
> Cc: Brian Beckman
> Subject: C9 video in the Monadic Design Patterns for the Web series
>
>
>
> Here it ‘tis:
>
>
>
> Greg Meredith, a mathematician and computer scientist, has graciously agreed
> to do a C9 lecture series covering monadic design principles applied to web
> development. You've met Greg before in a Whiteboard jam session with Brian
> Beckman.
>
> The fundamental concept here is the monad, and Greg has a novel and
> conceptually simplified explanation of what a monad is and why it matters.
> This is a very important and required first step in the series since the
> whole of it is about the application of monadic composition to real world web
> development.
>
> In part 4, Greg primarily focuses on the idea that a monad is really an API
> -- it's a view onto the organization of data and control structures, not
> those structures themselves. In OO terms, it's an interface. To make this
> point concrete Greg explores one of the simplest possible data structures
> that supports at least two different, yet consistent interpretations of the
> same API. The structure used, Conway's partisan games, turned out to be
> tailor-made for this investigation. Not only does this data structure have
> the requisite container-like shape, it provided opportunities to see just
> what's necessary in a container to implement the monadic interface.
>
> Running throughout the presentation is a more general comparison of reuse
> between an OO approach versus a more functional one. When the monadic API is
> "mixed into" the implementing structure we get less reuse than when the
> implementing structure is passed as a type parameter. Finally, doing the work
> put us in a unique position to see not just how to generalize Conway's
> construction, monadically, but the underlying pattern which allows the
> generalization to suggest itself.
>
> See part 1
> See part 2
> See part 3
>
>
>
> --
> L.G. Meredith
> Managing Partner
> Biosimilarity LLC
> 7329 39th Ave SW
> Seattle, WA 98136
>
> +1 206.650.3740
>
> http://biosimilarity.blogspot.com
>
>
>
>
> --
> L.G. Meredith
> Managing Partner
> Biosimilarity LLC
> 1219 NW 83rd St
> Seattle, WA 98117
>
> +1 206.650.3740
>
> http://biosimilarity.blogspot.com
> _______________________________________________
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