[Haskell-cafe] Assorted AT fun and games
andrewcoppin at btinternet.com
Sun Aug 15 09:00:59 EDT 2010
It all began with
class (Vector (Point x)) => HasSpace x where
type Point x :: *
So far, so good.
I was rather surprised that you _can_ write
class (Complete (Completed x)) => Incomplete x where
type Completed x :: *
complete :: x -> Completed x
I was almost as surprised to discover that you _cannot_ write
class (HasSpace x, Complete (Completed x), HasSpace (Completed x),
Point x ~ Point (Completed x)) => Incomplete where...
It just means that every time you write an Incomplete instance, you
might have to add the Point constraint manually. Which is mildly irritating.
More worrying, adding Point foo ~ Point bar to an instance declaration
causes GHC to demand that you turn on Undecidable Instances, for reasons
beyond my comprehension.
It's also interesting that when you write a class instance that has some
constraint on it, and then you try to write a subclass instance, you
still have to repeat the exact same constraint, even though the
superclass instance declaration implies it. The only reason I can think
of is that theoretically somebody could add a new superclass instance
without the constraint. (Wouldn't that be an overlapping instance though?)
And now things get *really* interesting. Consider this:
data Foo x = Foo !x !(Point x)
Surprisingly, GHC accepts this. This despite the rather obvious fact
that "Point x" can exist if and only if "x" has a HasSpace instance. And
yet, the type definition appears to say that "x" is simply an
unconstrained type variable. Intriguing...
Next, you can't derive Eq or Show for this type, but you *can* declare
instance (Show x, Show (Point x)) => Show (Foo x) where
show (Foo x px) = "Foo (" ++ show x ++ ") (" ++ show px ++ ")"
Again, no hint of the fact that this will only work if we have HasSpace
x. And yet GHC happily accepts this.
I'm starting to think maybe I'm pushing the type system further than it
can cope, and I should just completely redesign the whole thing...
More information about the Haskell-Cafe