Gregg Reynolds <d...@mobileink.com> writes: > This gives a very interesting way of looking at Haskell type > constructors: a value of (say) Tcon Int is anything that satisfies > "isA Tcon Int".
Reminiscent of arguments between dynamic and static typing camps - as far as I understand, a "dynamic type" is just a predicate. So division by zero is a "type error", since the domain of division is the type of all numbers except zero. In contrast, I've always thought of (static) types as disjoint sets of values. > My reasoning is that we can > define an infinite number of data constructors for it, including at > least all possible polynomials (by which I mean data constructors of > any arity taking args of any type). I guess I don't quite understand what you mean by "Tcon Int" above. Could you give a concrete example of such a type? > To my naive mind this sounds suspiciously like the set of all sets, > so it's too big to be a set. I suspect that since types and values are separate domains, you avoid the complications caused by self reference. > In any case, Tcon Int does not depend on any particular constructor, > just as homo sapiens does not depend on any particular man. So it > can't be a set because it doesn't have its members essentially. I don't follow this argument. Are you saying you can remove a data constructor from a type, and still have the same type? And because of this, the values of the type do not constitute a set? I guess it boils down to how "Tcon Int" does not depend on any particular constructor. -k -- If I haven't seen further, it is by standing in the footprints of giants _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
