[Haskell-cafe] Distributing monadic(?) functions across dyadic
functions
David Menendez
zednenem at psualum.com
Sun Apr 2 16:09:12 EDT 2006
Jared Updike writes:
> Is there a common way (standard libs, higher order) to express the
> lambda part below? It's not particulary complicated but I think it is
> not higher-order enough
>
> > unionBy (\x y -> fst x == fst y) listOfPairs1 listOfPairs2
>
> Something like "distribute fst (==)" where
>
> > distribute f op x y = f x `op` f y
>
> would leave
>
> > unionBy (distribute fst (==)) listOfPairs1 listOfPairs2
>
> I imagine something involving Arrows and/or zip/curry/uncurry but I
> just can't see it. Is this a case of trying to make something more
> complicated than it is?
If you look at it in terms of folds over pairs,
cata (&) (x,y) = x & y -- corresponds to uncurry
ana f g x = (f x, g x) -- corresponds to (&&&)
Then you can de-forest:
hylo (&) f g x = f x & g x
-- hylo (&) f g == cata (&) . ana f g
-- == uncurry (&) . f &&& g
--
-- cata (&) == hylo (&) fst snd
-- ana f g == hylo (,) f g
This seems remeniscent of pull-backs (or push-outs) in category theory,
but I don't know enough to say for certain.
--
David Menendez <zednenem at psualum.com> | "In this house, we obey the laws
<http://www.eyrie.org/~zednenem> | of thermodynamics!"
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