Brandon,
Cool. Well spotted. i was thinking a lot about the symmetry in the type
space as a kind of group. i'll play around with your suggestion.
Best wishes,
--greg
On 8/11/07, Brandon Michael Moore
On Fri, Aug 10, 2007 at 03:54:23PM -0700, Greg Meredith wrote:
Haskellians,
A quick follow up. If you look at the code that i have written there is a great deal of repeated structure. Each of these different kinds of sets and atoms are isomorphic copies of each other. Because, however, of the alternation discipline, i could see no way to abstract the structure and simplify the code. Perhaps someone better versed in the Haskellian mysteries could enlighten me.
You could take a less absolute view of the game, and describe each node instead locally from the perspective of a player. Imagine Alice Bob and Carol sitting around a table:
data ThreePlayers a b c = Next (ThreePlayer b c a) | Prev (ThreePlayers c a b)
In general you can get subgroups of a symmetric group as your sets of colors this way (i.e, the set of elements of any group), I'm not quite sure how much freedom you have in the sets of allowed transitions (in particular, making some of the argument types identical can break symmetry).
You could also go for the obvious big hammer, pretend that Haskell has a strongly normalizing subset and encode inequality explicitly with GADTs and such.
date Eq a b where Refl a a data False type Neq a b = Eq a b -> False -- might be trouble if a and b are only equal non-constructively?
data Red = Red data Green = Green ....
data Set color where Red :: Neq Red color -> Set Red -> Set color ...
Brandon
-- L.G. Meredith Managing Partner Biosimilarity LLC 505 N 72nd St Seattle, WA 98103 +1 206.650.3740 http://biosimilarity.blogspot.com