Add flipped fmap

[Brent Yorgey]

On Wed, Apr 07, 2010 at 04:12:24PM +0200, Bas van Dijk wrote:
> On Wed, Apr 7, 2010 at 3:58 PM, Felipe Lessa <felipe.lessa at gmail.com> wrote:
> > Simmetry, as the ticket says.
> 
> Indeed, I would like to emphasize that my main reason for adding a
> flipped fmap is symmetry. I find it hard to explain why <$$> shouldn't
> be in this list:
> 
> (<$>)  ∷ Functor f ⇒ (α → β) → (f α → f β)
> (<$$>) ∷ Functor f ⇒ f α → (α → β) → f β
> 
> (<*>)  ∷ Applicative f ⇒ f (α → β) → (f α → f β)
> (<**>) ∷ Applicative f ⇒ f α → f (α → β) → f β
> 
> (>>=)  ∷ Monad f ⇒ f α → (α → f β) → f β
> (=<<)  ∷ Monad f ⇒ (α → f β) → (f α → f β)

Let me point out that (<**>) is NOT defined as flip (<*>)!  In fact it is defined as

  (<**>) = liftA2 (flip ($))

which is quite different, since it performs effects in the opposite
order from flip (<*>).  So arguing for (<$$>) as something parallel to
(<**>) is a bit misleading.  I don't know whether this lends support
to one argument or another; I'm personally fairly neutral on the
proposal, but I thought this was important to point out.

-Brent