On Mon, Feb 16, 2009 at 8:13 PM, wren ng thornton <w...@freegeek.org> wrote:
> Isaac Dupree wrote: > >> Natural numbers under min don't form a monoid, only naturals under max do >> (so you can have a zero element) >> > > Though, FWIW, you can use Nat+1 with the extra value standing for Infinity > as the identity of min (newtype Min = Maybe Nat). Indeed, as well as you can use lazy naturals with infinity as the unit: data Nat = Zero | Succ Nat infinity = Succ infinity min Zero _ = Zero min _ Zero = Zero min (Succ x) (Succ y) = Succ (min x y) > > > I bring this up mainly because it can be helpful to explain how we can take > the "almost monoid" of m...@nat and monoidize it. Showing how this is > similar to and different from m...@nat is enlightening. Showing the min > monoid on negative naturals with 0 as the identity, and no need for the > "special" +1 value, would help drive the point home. (Also, the min/max > duality is mirrored in intersection/union on sets where we need to introduce > either the empty set (usually trivial) or the universal set (usually > overlooked).) > > Or maybe that would be better explained in a reference rather than the main > text. > > -- > Live well, > ~wren > > _______________________________________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe >
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