[Haskell-beginners] Pointfree expeiments

[Stephen Tetley]

On 25 November 2010 01:44, Paul Sargent <psarge at gmail.com> wrote:
[SNIP]

>
> I'm aware that 'ap' is related the liftM, but what is this monad, and why are we working in a monad at all?
>
> ...and surely this isn't the same as the original code as we now have a different type signature?_______________________________________________

Its the Reader monad.

The Reader monad introduces a "static argument" into the computation.

The code is equivalent to the original - if you want you can declare
it as a binding without generalizing it to Monad:

Prelude Control.Monad> let f = ap (+) id :: Num a => a -> a

Pointfree is presumably introducing it because it can't find
elementary definitions that are only functional types - the
combinators in the Haskell Prelude and Data.Function are perhaps a
little meagre. In one stroke it is a use of the 'w' combinator:

f :: Num a => a -> a
f = w (+)

-- | W combinator - warbler - elementary duplicator.
w :: (r1 -> r1 -> ans) -> r1 -> ans
w f x = f x x

Monadic ap for the Reader monad corresponds to the Starling 's'
combinator, so it is also:

g :: Num a => a -> a
g = starling (+) id

Again, Pointfree doesn't have starling available:

starling :: (r1 -> a -> ans) -> (r1 -> a) -> r1 -> ans
starling f g x = f x (g x)