On Thu, Dec 4, 2008 at 12:07 PM, Matt Hellige
Finally, there's a further disadvantage to both of these approaches: it seems to me that neither approach allows us to "cross pipes". For instance, we can't define flip using these techniques, or any "deep flip": \ x y z -> f x z y Is it true in general that operads cannot express pipe-crossing compositions? Or is it just a shortcoming of this particular implementation? Of course this is getting farther afield, and I don't believe that my approach can express this either.
This is not exactly true. It's possible in my scheme to express a deep flip, as long as it's the last thing you want to do: \ f x y z -> f x z y == id ~> flip It's not clear to me whether your operad class can express this (or whether operads in general can express this), or whether my scheme can express more general permutations of arguments. Matt