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? > > "Values" refers to the concrete values existent in the semantics of a > programming language. This set is usually infinite, but basically fixed. > To describe the set of "values" of an abstract type you would need > "fresh" values that did not exist before (otherwise the abstract type > would be equivalent to some already existent type). So you'd need at > least a theory for name generation or something similar to describe > abstract types in a types-as-sets metaphor.
Set theory has no difficulty with this. It's common, for example, to see "the set of strings representing propositions" used in treatments of formal systems. -- David Hopwood <[EMAIL PROTECTED]> -- http://mail.python.org/mailman/listinfo/python-list
