I figured out an inductive approach as follows, which lets you derive stripeN from stripe(N-1). This could be TemplateHaskell'd if you have a bound on N; I'm still trying to figure out a type-magical alternative.
Suppose stripe(N-1) :: x -> [b] -> [c] Then stripeN :: (a -> [b]) -> x -> [a] -> [[c]] stripeN f x [] = [] stripeN f x (a:as) = case stripe(N-1) x (f a) of [] -> stripeN f x as (b:bs) -> [b]:zipCons bs (stripeN f x as) and then diagN is obtained by applying concat an appropriate number of times. It's fair. The real-question is how to type-magically work it for arbitrarily many coordinates... Louis Wasserman [email protected] http://profiles.google.com/wasserman.louis On Wed, Nov 4, 2009 at 4:38 AM, Martijn van Steenbergen < [email protected]> wrote: > Louis Wasserman wrote: > >> +1 on Control.Monad.Omega. In point of fact, your diagN function is >> simply >> >> diagN = runOmega . mapM Omega >> >> You'll find it an interesting exercise to grok the source of >> Control.Monad.Omega, obviously, but essentially, you're replacing concatMap >> with a fair (diagonal) traversal order version. >> > > Thanks for the replies! > > I've looked at Omega but it's not fair enough. The sums of the indices are > not non-decreasing: > > map sum $ runOmega . mapM each $ [[1..], [1..], [1..]] > [3,4,4,4,5,5,5,5,6,6,5,6,6,7,7,5,6,7,7,8,8,6,6,7,8,8,9,9,6,7,... > > Is there another way to use Omega that meets this (very important) > criterion or is Omega not the right tool here? > > Thanks, > > Martijn. >
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