On 6/18/19 1:25 PM, Stephen J. Turnbull wrote:
> Dan Sommers writes:
>
> > How would I "think of types as collections of their instances"?
>
> The canonical example of a type as a collection of instances is an
> enumeration, the simplest (useful) example of which is bool = {False,
> True}.
And now the light goes on. :-)
[...]
> > In my mind, a type is a description/container/shortand for a
> > collection of properties or behaviors of instances of that type.
>
> That's one way to think about it, of course. But the strong
> intuitions about the numeric tower (a natural number *is* an integer,
> an integer *is* a real number, and so on) as well as some useful but
> (intuitively) more artificial ideas such as a bool *is* a natural
> number are just as well expressed as set inclusions. This is useful
> in type theory, but explaining "how" is way beyond the scope of this
> post (and this whole list, in fact).
Thanks, Stephen; you've done just enough to give me a good shove in the
right direction.
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