[Haskell-cafe] Re: Looking for pointfree version

[Heinrich Apfelmus]

Benja Fallenstein wrote:
> Kim-Ee Yeoh wrote:
>>
>> On the same note, does anyone have ideas for the following snippet? Tried the
>> pointfree package but the output was useless.
>>
>> pointwise op (x0,y0) (x1,y1) = (x0 `op` x1, y0 `op` y1)
> 
> import Control.Monad.Reader  -- for the (Monad (a ->)) instance
> import Control.Bifunctor  -- package category-extras
> 
> dup = join (,)
> mapPair = uncurry bimap
> pointfree = (mapPair .) . mapPair . dup
> 
> Or if you're not afraid of *some* points, and want to avoid the imports:
> 
> dup x = (x,x)
> mapPair (f,g) (x,y) = (f x, g y)
> pointfree op = mapPair . mapPair (dup op)
> 
> That what you're looking for? :-)

The pairs are of course an applicative functor

  (<*>)  = uncurry (***)  -- from Control.Arrow
  pure x = (x,x)

  pointwise op x y = pure op <*> x <*> y


Regards,
apfelmus

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