Sam, hello. On 2011 Aug 17, at 13:12, Sam Tobin-Hochstadt wrote:
>> OoooKay. I was thinking of subtyping in terms of a naive mixture of the >> (set) extensions of types (the set of things which are instances of (List >> String String) is a subset of the things which are instances of (Listof >> String)), and assignment-compatibility. That understanding clearly fails in >> your example, because while (List String String) can be assigned to a >> (Listof String), the function test is declared to accept -- in the sense of >> have bound to its arguments -- (Listof String) which in this case isn't >> true. Gotcha (I think). > > It's ok to think of things as sets, and subtyping as subsets. The > trick is that functions are a little different than you expect. In > particular, if you have two types, (A -> B) and (C -> D), for the > first to be a subtype of the second, you do need B to be a subtype of > D. But for the arguments, it goes the other way: C must be a subtype > of A. Thanks for the explanation. Curses! I must have been reasonably close to working that out for myself, with the thought about what the function is intended to accept. > Here's how to see why you need that. To say that (A -> B) is a subtype > of (C -> D), you're saying that you can use (A -> B) anywhere you need > (C -> D). But some program that expects a (C -> D) function might > pass it a C, of course, so your new replacement function must accept > all of the Cs. Therefore, A needs to accept all of the Cs, which > means that A must be a subtype of C. Don't you mean "C must be a subtype of A", here? > The standard term for this is that function types are "contravariant" > (go the other way) in their argument type. Thanks for 'contravariant' in this context. It's led me to the relevant application of category theory, which I think is the underlying structure I was looking for. I suppose it's effectively a combination of 'define' and ':' which is in practice the functor in TR terms, with subtyping being the morphism in the type category. Or something like that. All is now clear. Best wishes, Norman -- Norman Gray : http://nxg.me.uk School of Physics and Astronomy, University of Glasgow, UK _________________________________________________ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/users
