Bottom Type--Type Theory

[Olivier FAURE]

On Thursday, 17 January 2019 at 12:40:18 UTC, H. S. Teoh wrote:
> No! A unit type is one inhabited by a single value. A top type 
> is a type that can represent *every* value.  Very crudely 
> speaking, if types were numbers, then a unit type is 1, a 
> bottom type is 0, and a top type is infinity. Or, to use a set 
> analogy, a unit type corresponds with a singleton set, a bottom 
> type to the empty set (the subtype of every type), and the top 
> type to the universal set (the supertype of every type).

I think I'm confused.

Actually, I think I have a pretty good question. Let's imagine we 
implement two types in D, Unit and Top, so that they match their 
type theory concepts as best as they can.

Given this code:

     int foo(Unit u) {
         ...
     }

     int bar(Top t) {
         ...
     }

what could you do in `bar` that you couldn't do in `foo`?

(I'd appreciate if you could answer with pseudocode examples, to 
help communication)