[Haskell] is $ a no-op?

[Kevin Millikin]

On Wednesday, October 13, 2004 11:25 AM, Jacques Carette [SMTP:carette at mcmaster.ca] wrote:
> > > --  It's kind of like an converse map.
> > 
> > I have attempted, unsuccessfully, to write flist above in a point-free 
> > manner.  Is it possible?
> 
> > Of course it is, but why?
> > flist = flip (map . flip ($))
> 
> Some functions are simpler point-free, others are simpler with points.  I
> was curious about this one (I like the pointwise version better).
> 
> Also, the statement "It's kind of like a converse map" becomes quite clear
> from the point-free way to write it, while still not so obvious in the
> pointwise version.

I haven't proven it, but I think that this is the same function on lists:

> flist = (. return) . ap

-- Kevin