[Haskell-cafe] Scrap your rolls/unrolls
Sjoerd Visscher
sjoerd at w3future.com
Sat Oct 23 10:32:50 EDT 2010
A little prettier (the cata detour wasn't needed after all):
data IdThunk a
type instance Force (IdThunk a) = a
type Alg f a = f (IdThunk a) -> a
fold :: CFunctor f ForceCat (->) => Alg f a -> Fix f -> a
fold alg = alg . cmap (ForceCat $ fold alg)
sumAlg :: Alg (ListF Int) Int
sumAlg Nil = 0
sumAlg (Cons a r) = a + r
sumList :: List Int -> Int
sumList = fold sumAlg
It all works out very well, so this trick seems to be really useful!
Sjoerd
On Oct 23, 2010, at 4:05 PM, Sjoerd Visscher wrote:
>
> On Oct 23, 2010, at 1:27 PM, Sebastian Fischer wrote:
>>
>> I think `Control.Functor.Categorical.CFunctor` is a more natural replacement for functor here. One can define
>>
>> instance CFunctor (ListF a) ForceCat Hask
>>
>> and I was hoping that I could define `fold` based on CFunctor but I did not succeed. The usual definition of `fold` is
>>
>> fold :: Functor f => (f a -> a) -> Fix f -> a
>> fold f = f . fmap (fold f)
>>
>> and I tried to replace this with
>>
>> fold :: CFunctor f ForceCat Hask => ...
>>
>> but did not find a combination of type signature and definition that compiled.
>
> The catamorphism lies in the ForceCat category. Also, you can't just pass "a" to "f" because Force a is undefined.
>
> data IdThunk a
> type instance Force (IdThunk a) = a
>
> cata :: CFunctor f ForceCat (->) => (f (IdThunk a) -> a) -> ForceCat (FixThunk f) (IdThunk a)
> cata alg = ForceCat $ alg . cmap (cata alg)
>
> Then you can define fold as follows:
>
> fold :: CFunctor f ForceCat (->) => (f (IdThunk a) -> a) -> Fix f -> a
> fold = unForceCat . cata
>
> Fortunately the IdThunk does not get in the way when defining algebras:
>
> sumAlg :: ListF Int (IdThunk Int) -> Int
> sumAlg Nil = 0
> sumAlg (Cons a r) = a + r
>
> greetings,
> Sjoerd Visscher
>
>
>
>
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--
Sjoerd Visscher
http://w3future.com
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