Simon Peyton-Jones wrote: >... > msg :: forall a. Show a => String > >Urk! What "Show" dictionary should Hugs use when evaluating "msg"? > >You may say "it doesn't matter", but in general that's not the case. >In the case of class Num, for example, we might have > > expr = 3+4 > msg = show expr > >and then the type involved really does matter. > >I wonder if the following is true. Given the ambiguous type > > forall a. Show a => T (where a does not appear in T) > >it's OK to pass the bottom dictionary. ... > Type systems with subtyping have what is needed to determine when the choice of dictinionary "doesn't matter".
In type systems with subtyping, the most general type is the minimal type. This means that type variables that occur only positively (in covariant positions) can be minimized (and that negative variables can be maximized). If there is an empty type, Empty say, which is a subtype of all other types, then the type forall a . Show a => T is just as general as the type Show Empty => T since a occurs only positively in Show a => T, taking into account the occurences of a in the definition of the Show class. The requirement that a does not appear in T is overly restrictive. This simplification can be made as long as all occurences of a in T are positive. Assuming a language with subtyping that simplifes types in this way, expressions like show undefined show [] show Nothing show (Left False) would no longer be ambiguously overloaded. If the prelude provides instance Show Empty -- no methods need to be defined then types of the above expressions would all reduce to String, and they would all compute to the expected results (i.e., the result you would get by manually disambiguating the types, e.g., show ([]::[Int])). The same trick applies to the Eq class, so that, e.g., [] == [] would be unambiguous and compute to True. So, obviously, the next version of Haskell should have a type system with subtyping, don't you agree? :-) Thomas Hallgren PS In some previous version of Haskell (1.3?), the Prelude defined an empty type called Void, but it has since been removed. Apparently, people didn't see the potential of Void... PPS For those who are afraid of subtypes :-), I think you can use the information about variance of type variables used in subtype inference, to determine when the choice of dictinonary "doesn't matter", without introducing subtyping in the languange... _______________________________________________ Haskell mailing list [EMAIL PROTECTED] http://www.haskell.org/mailman/listinfo/haskell