[Haskell-cafe] Name My Functor Classes

[Ross Paterson]

On Mon, Feb 07, 2005 at 06:54:50PM -0800, Ashley Yakeley wrote:
> These classes seem like they might correspond to concepts in category 
> theory:
> 
>     class (Functor f) => C1 f where
>         f1 :: f (a -> b) -> f a -> f b
> 
>     class (C1 f) => C2 f where
>         return :: a -> f a
>     -- must satisfy:
>     --   fmap = f1 . return

fmap+return is often called a premonad.  I don't know of a good name for
fmap+return+f1.  Doaitse Swierstra calls the class Sequence and calls f1
(<*>), Conor McBride calls it Idiom, and I'd call it a weakly symmetric
lax monoidal functor or a strong lax monoidal functor.  There are more
equations, too; see
	http://www.haskell.org/arrows/arrows/Control.Sequence.html
Also Conor's hack:
	http://www.haskell.org//pipermail/haskell/2004-July/014315.html