[Haskell-cafe] Pointless functors

[Brent Yorgey]

On Fri, Mar 13, 2009 at 02:32:23PM +0000, Ross Paterson wrote:
> On Fri, Mar 13, 2009 at 03:18:15PM +0100, Martijn van Steenbergen wrote:
> > Are there any functors f for which no point/pure/return :: a -> f a exists?
> 
> No.  Choose an arbitrary element shape :: f () and define
> 
>         point x = fmap (const x) shape

But since f may be polymorphic in some other types, it may not be
possible to choose such an arbitrary shape.  For example, ((,) w) is a
Functor but it is not possible to define a function point :: a ->
(w,a) without (1) using undefined for the value of type w, or (2)
putting some sort of constraint on w which lets us choose a canonical
value of type w, such as Monoid.

-Brent