At 16:00 09/08/04 +0100, Simon Peyton-Jones wrote:
Any thoughts?
Well, a thought, but I'm not sure that it leads anywhere useful. In the process of learning Haskell, I've vaguely observed to myself that features introduced for describing data (i.e. type expressions) seem to also be usable in higher form to describe types. Mostly, the Haskell language definition resists such extension, by sticking with a very simple notion of kind and type construction (or is that a fundamental restriction of Hindley-Milner?). For example, if I choose the "wrong" parameter ordering for a type constructor in a class declaration, I sometimes find the resulting class cannot be used in the ways intended --only one possible sequence of partial instantiation is possible-- and have found myself wondering if type-level lambda abstraction wouldn't be a useful feature to overcome this. Your suggestion seems to be another feature in the same vein: extending data features to types. I find myself wondering where this might all end. If types acquire many of the manipulations that are available for data values, then might one find that, in turn, cases will be found that seem to require similar capabilities for kinds? Is there any possibility of a theory that will avoid the need to replicate features at higher and higher levels? (This all seems vaguely reminiscent of the theoretical issues that faced denotational program semantics --which I don't claim to understand-- until Dana Scott's work showed that there was a logical foundation for treating functions as values. [er, did I get that right?].) #g --
Closed classes are certainly interesting, but a better way to go in this case is to allow the programmer to declear new kinds, as well as new types. This is what Tim Sheard's language Omega lets you do, and I'm considering adding it to GHC.
kind HNat = HZero | HSucc HNat
class HNatC (a::HNat)
instance HNatC HZero instance HNatC n => HNatC (HSucc n)
Here the keyword 'kind' is like 'data', except that it introduces a new *kind* HNat with new *type* constructors HZero and HSucc, rather than a new *type* constructor with new *data* constructors.
There is no way to construct a value of type HZero, or (HSucc HZero); these are simply phantom types. Today we are forced to say data HNat data HSucc a which loses the connection between the two. A merit of declaring a kind is that the kind is closed -- the only types of kind HNat are HZero, HSucc HZero, and so on. So the class doesn't need to be closed; no one can add new instances to HNatC because they don't have any more types of kind HNat.
At the moment I'm only thinking of parameter-less kind declarations but one could easily imagine kind parameters, and soon we'll have kind polymorphism.... but one step at a time.
Any thoughts?
Simon
| -----Original Message----- | From: haskell-cafe-bounces@haskell.org [mailto:haskell-cafe-bounces@haskell.org] On Behalf Of | Duncan Coutts | Sent: 06 August 2004 15:11 | To: MR K P SCHUPKE | Cc: Haskell Cafe | Subject: [Haskell-cafe] closed classes [was: Re: exceptions vs. Either] | | On Fri, 2004-08-06 at 14:05, MR K P SCHUPKE wrote: | > >You should include the definitions of the classes before saying | > | > HOrderedList l' just has to prove by induction that for any element | > in the list, the next element is greater, so the class is simply: | > | > class HOrderedList l | > instance HNil | > instance HCons a HNil | > instance (HOrderedList (HCons b l),HLe a b) => HCons a (HCons b l) | | Somewhat off-topic, | | It's when we write classes like these that closed classes would be | really useful. | | You really don't want people to add extra instances to this class, it'd | really mess up your proofs! | | I come across this occasionally, like when modelling external type | systems. For example the Win32 registry or GConf have a simple type | system, you can store a fixed number of different primitive types and in | the case of GConf, pairs and lists of these primitive types. This can be | modelled with a couple type classes and a bunch of instances. However | this type system is not extensible so it'd be nice if code outside the | defining module could not interfere with it. | | The class being closed might also allow fewer dictionaries and so better | run time performance. | | It would also have an effect on overlapping instances. In my GConf | example you can in particular store Strings and lists of any primitive | type. But now these two overlap because a String is a list. However | these don't really overlap because Char is not one of the primitive | types so we could never get instances of String in two different ways. | But because the class is open the compiler can't see that, someone could | always add an instance for Char in another module. If the class were | closed they couldn't and the compiler could look at all the instances in | deciding if any of them overlap. | | So here's my wishlist item: | | closed class GConfValue v where | ... | | Duncan | | _______________________________________________ | Haskell-Cafe mailing list | Haskell-Cafe@haskell.org | http://www.haskell.org/mailman/listinfo/haskell-cafe _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
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