RE: [Haskell-cafe] generics question, logical variables
-----Original Message----- From: Frederik Eaton [mailto:frederik@a5.repetae.net] Sent: Sunday, September 18, 2005 7:50 PM To: Ralf Lammel Cc: haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] generics question, logical variables
Hi Ralf,
I'm revisiting this project and just have another question. The story seems to be that GHC cannot derive Typeable1, or Typeable when Typeable1 is available - so anyone who wants to use ext1Q must define special instances for all of the datatypes they use, is this correct? Will this change soon?
Aside from that, your 'idify' in PseudoFmap2 certainly seems to have the correct type for this application. However, the absence of automatic derivation is somewhat of an impediment.
Thanks for your help.
Frederik
On Tue, Aug 30, 2005 at 02:25:08PM -0700, Ralf Lammel wrote:
Frederik,
As for your code example, it looks very interesting, but are you saying that this could turn into an extension of the Data.Generics library, or that this is something I could be implementing in terms of what's already there?
The posted code works with GHC 6.4 (SYB2) intentionally and actually. I have attached another attempt (again GHC 6.4, based on SYB2) which might be more useful for your purposes, and it may be useful in general, in fact.
What I defined this time is a "certainty-improving" function:
idify :: (Typeable1 f, Monad m, Data (a f), Data (a Id)) => (forall a. f a -> m a) -> a f -> m (a Id)
That is, the function "idify get" takes a value whose type is parameterized in a type constructor f (such as Maybe or IORef), and
function attempts to establish Id instead of f on the basis of the function argument "get".
What is the 'a' parameter for in "force"?
force :: ( Data (t Maybe a) , Data (t Id a) , Term t Maybe a , Term t Id a ) => t Maybe a -> t Id a
The previous attempt was a more parameterized blow than required in your case. (I was guessing about what "typed logical variables" could mean. I was assuming that you would need some extra layer of embedding types on top of the Haskell term types. Looking at your code, this was not
case.)
For the part which I asked for help with, to get around my trouble with generics, I defined a class GenFunctor and an example instance. The intent is that generics should be able to provide this functionality automatically later on, but you can see what the functionality is.
Let's look at the type of your GenFunctor:
class GenFunctor f where gfmapM :: (Monad m, FunctorM b) => (forall x . a x -> m (b x)) -> f a -> m (f b)
This type can be seen as a more relaxed version of the idify operation above. That is, idify fixes GenFunctor's b to Id. The particular encoding of idify (attached) takes advantage of this restriction. I wonder whether I should bother. (Exercise for reader :-))
However, I am stuck on something else, the program doesn't typecheck because of use of another function I defined, 'cast1'. Maybe you can take a look. I had thought that I would be able to write a generic 'unify' but I get the error:
GenLogVar.hs:82:19: Ambiguous type variable `a' in the constraint: `Data a' arising from use of `cast1' at GenLogVar.hs:82:19-23 Probable fix: add a type signature that fixes these type variable(s)
This is because I need to do something special when I encounter a "Var" variable in unification, but the compiler seems to not like
fact that the type argument of the Var data type is not known.
Please try to avoid new cast operations at all costs. :-) Your code can be arranged as follows:
(i) Use extQ1 to dispatch to a special case for "Var x" for the first argument. (ii) In this special case, use again ext1Q to dispatch to a special case for "Var y" for the second argument. (iii) At this
Hi Frederik, [I call this "the dreadful lack of kind polymorphism strikes back" :-)] I put SPJ on cc; perhaps he can suggest a way to improve in this area. Based on input, I could try to work on this issue in the not so remote future. Let me briefly recapitulate. My recollection is that deriving works for Typeable, Tyepable1, ..., if all type parameters are of type kind "*". Whenever you can derive a Typeablen instance with n > 0, you can instead ask for Typeable to be derived. The reason why you cannot get both a Typeable and say a Typeable42 instance is that there are generic instances for getting an "n-1 instance" from the "n instance". However, this is also precisely the reason why you don't want them both. That is, you get everything you can ask for, if you have the "n instance" for the actual arity of the type constructor in question. (Getting a smaller n or no n just means that you limit polymorphic type case.) Recall that you *may* need a n>0 instance if you want to do polymorphic type case according to the SYB2 paper. As long as you are fine with monomorphic generic function extension, the plain Typeable instance should be fine. However, the real limitation is here, *indeed*, as said, that GHC does not derive Typeable[1|2|...] for parameter kinds other than "*". This was the reason that I had to hand-code some Typeable instances in your original example. Let us also be honest about another limitation of the current deriving code. "deriving Data" gives you Data instances that do *not* support polymorphic type case. That is the following code prints 0, 1, 0 whereas you may expect 0, 1, 2. newtype Foo x = Foo x deriving (Typeable, Data) f :: Data a => a -> Int f = const 0 `ext1Q` (\(_::Maybe x) -> 1) `ext1Q` (\(_::Foo y) -> 2) main = do print $ f True print $ f (Just True) print $ f (Foo (Just True)) This is the reason that I had to handcode some Data instances in your original example, which wasn't hard BTW. We thought that these two limitations were Ok since we didn't expect people to write many polymorphic datatype constructors on which SYB should work. Sounds like a feature request. Now I wonder how much work it is to improve the situation. We need to make the GHC deriving code a bit more kind-aware. I guess we are still not at the point where we want to add kind polymorphism to Haskell? Would be a nice topic for future work on SYB. Clearly, the GH folks have done splendid work in this area. Getting full-blown kind polymorphism in normal Haskell though seems to be less of a topic, simply because we do not have many scenarios around that would *really* require it. Does anyone want to speak up and mention scenarios that would benefit from kind polymorphism? (In Haskell, we are likely to see kind polymorphism, if at all, in the form of type classes whose type parameters can be of different, perhaps of all kinds.) Frederik, for the time being I propose to look into TH code for deriving Tyepable/Data instances and to make it fit for your purposes. There are several versions of Ulf Norell's code around. You may also use SYB3 with the TH code that readily comes with it. Thanks for bringing this up. Regards, Ralf the the the point,
*cast* the variable value of *one* variable to the type of the other.
So the problem with your code, as it stands, is that the target type of cast is ambiguous because you cast *both* arguments. The insight is to make the cast asymmetric. Then, not even polymorphism is in our way.
Interesting stuff!
Ralf
Ralf Lammel wrote:
Does anyone want to speak up and mention scenarios that would benefit from kind polymorphism? (In Haskell, we are likely to see kind polymorphism, if at all, in the form of type classes whose type parameters can be of different, perhaps of all kinds.)
Here are two possible simple examples. The first is from "real life": I once needed a polymorphic function "replace" that replaces an element of an n-dimensional list given its coordinates and a replacement value: replace :: Int -> a -> [a] -> [a] replace :: Int -> Int -> a -> [[a]] -> [[a]] etc. Also, trivially, in dimension zero: replace :: a -> a -> a So we have: dim 0: replace = const dim 1: replace i x (y:ys) | i == 0 = replace x y : ys | otherwise = y : replace (i-1) x ys replace _ _ _ = [] dim 2: replace i j x (y:ys) | i == 0 = replace j x y : ys | otherwise = y : replace (i-1) j x ys replace _ _ _ _ = [] etc. Intuitively, this ought to be simple. But I leave it as an exercise for the reader to implement it using the current type system. What a mess! Second example: It seems intuitive that the State monad should be isomorphic to the lazy ST monad with STRef, in the sense that it should be possible to implement each monad in terms of the other. (For the purpose of this discussion, let us ignore differences in strictness due to the execution strategies of any given compiler, though that also may be an interesting topic.) Well, in one direction that is trivial - it is easy to implement State using lazy ST and STRef. As for the other direction - yuck! Again, I leave it as an exercise for the reader. Regards, Yitz
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Ralf Lammel -
Yitzchak Gale