David Menendez dave at zednenem.com
Sun Oct 26 01:18:47 EDT 2008

```On Sat, Oct 25, 2008 at 11:55 PM, Paul L <ninegua at gmail.com> wrote:
> Tnaks for the clarification, please see my further questions below
>
> On 10/25/08, Daniel Fischer <daniel.is.fischer at web.de> wrote:
>>
>> Sure, (g (flip readArray 0)) :: ST s Int, or, explicitly, forall s. ST s Int,
>> there's nothing to restrict the s, so it's legitimate to pass it to runST.
> ..[snipped]..
>> What would be a generic mapST, which type should it have?
>
> I tried this type for mapST, it doesn't work:
>
>  mapST :: (a -> ST s b) -> [a] -> [b]
>  mapST f (x:xs) = runST (f x) : mapST f xs
>  mapST f [] = []
>
> By your reasoning, (f x) should have type forall s . ST s b, and
> should match what runST expects, but apparently GHC complains

The problem is that the type variable s is determined by the caller of
mapST. If you write the type with explicit foralls, you get:

mapST :: forall a b s. (a -> ST s b) -> [a] -> [b]

>From the perspective of code inside the definition of mapST, f is not
polymorphic, because a, b, and s have already been determined.

The type you need is,

mapST :: forall a b. (forall s. a -> ST s b) -> [a] -> [b]

Now runST is able to pass an arbitrary type for s to f.

(GHC can silently convert between "forall s. a -> ST s b" and "a ->
forall s. ST s b".)

It may be helpful to rewrite the types with a more explicit notation.
For example,

runST :: (a :: *) -> ((s :: *) -> ST s a) -> a

mapST_wrong :: (a :: *) -> (b :: *) -> (s :: *) -> (f :: a -> ST s b)
-> [a] -> [b]
mapST_right :: (a :: *) -> (b :: *) -> (f :: (s :: *) -> a -> ST s b)
-> [a] -> [b]

--
Dave Menendez <dave at zednenem.com>
<http://www.eyrie.org/~zednenem/>
```