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