On Sep 16, 2010, at 6:45 AM, wren ng thornton wrote:
> Given that any functor for adding strictness will have to deal with the same
> issue of preserving bottom-eating compositions, I postulated that there
> exists no functor from (all of) Hask to !Hask. But, since !Hask is a
> subcategory of Hask, it's trivial to go the other direction. In fact, the
> Strict defined above can be considered as the inclusion functor from !Hask to
> Hask by making the strictness of !Hask explicit. This also allows Strict to
> be considered a pointed functor since fmap f . point = point . f for strict
> functions f.
For fun here's this idea implemented with data-category:
> {-# LANGUAGE TypeFamilies #-}
>
> import Prelude hiding ((.), id, Functor)
> import Data.Category
> import Data.Category.Functor
The definition of the subcategory of Hask with only strict functions:
> newtype StrictHask a b = StrictHask { unStrictHask :: a -> b }
>
> instance Category StrictHask where
> id _ = StrictHask $ \x -> x `seq` x
> StrictHask f . StrictHask g = StrictHask $ \x -> f $! g x
The definition of the inclusion functor:
((%) maps morphisms, i.e. fmap, (:%) maps objects)
> data StrictIncl = StrictIncl
>
> type instance Dom StrictIncl = StrictHask
> type instance Cod StrictIncl = (->)
>
> type instance StrictIncl :% a = a
>
> instance Functor StrictIncl where
> StrictIncl % (StrictHask f) = f
And indeed we have StrictIncl % (f . g) = StrictIncl % f . StrictIncl % g
But StrictIncl can't be a pointed functor, only endofunctors can be pointed.
--
Sjoerd Visscher
http://w3future.com
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