David Hopwood wrote: >> >>"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.
Oh, I was not saying that this particular aspect cannot be described in set theory (that was a different argument, about different issues). Just that you cannot naively equate types with a set of underlying values, which is what is usually meant by the types-are-sets metaphor - to capture something like type abstraction you need to do more. (Even then it might be arguable if it really describes the same thing.) - Andreas -- http://mail.python.org/mailman/listinfo/python-list
