The NaN of types (in D)

[Stefan Koch]

On Sunday, 11 October 2020 at 12:46:53 UTC, Imperatorn wrote:
> On Sunday, 11 October 2020 at 12:18:59 UTC, Stefan Koch wrote:
>> Good Morning,
>>
>> today I would like to write about something which came up 
>> while implementing type functions.
>>
>> [...]
>
> Shouldn't this be the universe. The empty set is "there is no 
> _", while the "opposite" ¬∅ of the empty set is the universe?

The universe would be __type. (because it can hold any type in U)
If you set the __type.init to be __type; (And that's how it used 
to be)

The that means you cannot distinguish between a function 
returning __type.
(Assuming your type function gives you the return type of a 
function)
And the programmer having messed up the and forgot to set the 
value.

Therefore you need an initial value which cannot possibly be a 
valid type anywhere.
Hence a type which is no valid type is needed.