[Haskell-cafe] space-efficient, composable list transformers [was: Re: Reifying case expressions]
Heinrich Apfelmus
apfelmus at quantentunnel.de
Tue Jan 3 20:27:28 CET 2012
Jan Christiansen wrote:
> On Jan 2, 2012, at 2:34 PM, Heinrich Apfelmus wrote:
>
>> Without an explicit guarantee that the function is incremental, we can't do anything here. But we can just add another constructor to that effect if we turn ListTo into a GADT:
>>
>> data ListTo a b where
>> CaseOf :: b -> (a -> ListTo a b) -> ListTo a b
>> Fmap :: (b -> c) -> ListTo a b -> ListTo a c
>>
>> FmapCons :: b -> ListTo a [b] -> ListTo a [b]
>
> I did not follow your discussion but how about using an additional GADT for the argument of Fmap, that is
>
> data Fun a b where
> Fun :: (a -> b) -> Fun a b
> Cons :: a -> Fun [a] [a]
>
> data ListTo a b where
> CaseOf :: b -> (a -> ListTo a b) -> ListTo a b
> Fmap :: Fun b c -> ListTo a b -> ListTo a c
>
> and provide a function to interpret this data type as well
>
> interpretFun :: Fun a b -> a -> b
> interpretFun (Fun f) = f
> interpretFun (Cons x) = (x:)
>
> for the sequential composition if I am not mistaken.
>
> (<.) :: ListTo b c -> ListTo a [b] -> ListTo a c
> (CaseOf _ cons) <. (Fmap (Cons y) b) = cons y <. b
> (Fmap f a) <. (Fmap g b) = Fmap f $ a <. (Fmap g b)
> a <. (CaseOf nil cons) = CaseOf (interpret a nil) ((a <.) . cons)
> a <. (Fmap f b) = fmap (interpret a . interpretFun f) b
>
>
> -- functor instance
> instance Functor (ListTo a) where
> fmap f = normalize . Fmap (Fun f)
>
> normalize :: ListTo a b -> ListTo a b
> normalize (Fmap (Fun f) (Fmap (Fun g) c)) = fmap (f . g) c
> normalize x = x
>
> Cheers, Jan
Nice, that is a lot simpler indeed, and even closer to the core of the idea.
Best regards,
Heinrich Apfelmus
--
http://apfelmus.nfshost.com
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