[theory] What is a type?

[Ola Fosheim Grøstad]

On Monday, 15 January 2018 at 19:25:16 UTC, H. S. Teoh wrote:
> At the most abstract level, a type is just a set. The members 
> of the set represent what values that type can have.

Hm, yes, like representing an ordered pair (a,b) as {{a},{a,b}}.

But I think typing is more commonly viewed as a filter. So if you 
represent all values as sets, then the type would be a filter 
preventing certain combinations.

It is a matter of perspective, constructive or not constructive. 
Kinda like synthesis, additive (combine sines) or subtractive 
(filter noise).