[Haskell-cafe] A handy little consequence of the Cont monad

[Conor McBride]

Folks

On 1 Feb 2008, at 22:19, Lennart Augustsson wrote:

> It's a matter of taste.  I prefer the function composition in this  
> case.
> It reads nicely as a pipeline.
>
>   -- Lennart
>

Dan L :


> On Fri, Feb 1, 2008 at 9:48 PM, Dan Licata <drl at cs.cmu.edu> wrote:
> Not to start a flame war or religious debate, but I don't think that
> eta-expansions should be considered bad style.

Cale:

> > > nest :: [(r -> a) -> a] -> ([r] -> a) -> a
> > > nest xs = runCont (sequence (map Cont xs))
> >

Derek:

> > This is what you write after all that time on #haskell?
> >
> > nest = runCont . sequence . map Cont

Pardon my voodoo (apologies to libraries readers,
but here we go again, slightly updated).

With these useful general purpose goodies...

 > module Newtype where

 > import Data.Monoid

 > class Newtype p u | p -> u where
 >   unpack :: p -> u

 > instance Newtype p u => Newtype (a -> p) (a -> u) where
 >   unpack = (unpack .)

 > op :: Newtype p u => (u -> p) -> p -> u
 > op _ p = unpack p

 > wrap :: Newtype p u => (x -> y) ->(y -> p) -> x -> u
 > wrap pack f = unpack . f . pack

 > ala ::  Newtype p' u' => (u -> p) ->
 >         ((a -> p) -> b -> p') ->
 >         (a -> u) -> b -> u'
 > ala pack hitWith = wrap (pack .) hitWith

...and the suitable Newtype instance for Cont, I
get to write...

   nest = ala Cont traverse id

..separating the newtype encoding from what's really
going on, fusing the map with the sequence, and
generalizing to any old Traversable structure.

Third-order: it's a whole other order.

Conor