Andreas Rossberg wrote: > Marshall wrote: > > > > What prohibits us from describing an abstract type as a set of values? > > If you identify an abstract type with the set of underlying values then > it is equivalent to the underlying representation type, i.e. there is no > abstraction.
I don't follow. Are you saying that a set cannot be described intentionally? How is "the set of all objects that implement the Foo interface" not sufficiently abstract? Is it possible you are mixing in implementation concerns? > >>There were papers observing this as early as 1970. > > > > References? > > This is 1973, actually, but most relevant: > > James Morris > Types Are Not Sets. > Proc. 1st ACM Symposium on Principles of Programming Languages, 1973 Okay. Since this paper is in the ACM walled garden, I'll have to wait until next week to get a look at it. But thanks for the reference. > >>(There are also theoretic problems with the types-as-sets view, because > >>sufficiently rich type systems can no longer be given direct models in > >>standard set theory. For example, first-class polymorphism would run > >>afoul the axiom of foundation.) > > > > There is no reason why we must limit ourselves to "standard set theory" > > any more than we have to limit ourselves to standard type theory. > > Both are progressing, and set theory seems to me to be a good > > choice for a foundation. What else would you use? > > I'm no expert here, but Category Theory is a preferred choice in many > areas of PLT. Fair enough. Marshall -- http://mail.python.org/mailman/listinfo/python-list
