Re: In precision typing we trust

["Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>]

On 2025-08-25 10:51, Paul Rubin wrote:
> "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> writes:
>>> It also has metaclasses.
>>> Because classes, like functions, are first-class objects.
>>
>> A useless thing in an untyped language and in general one should first
>> question what could be the purpose of a set of a set of types?
> 
> Python metaclasses let you specify what is supposed to happen when you
> instantiate a class, and that sort of thing.  I.e. it's about runtime
> behaviour.

Why do I need to instantiate a class? Provided that it is obviously 
impossible since the class is an open set of types. I simply cannot know 
what is in it. E.g. I can load a DLL at run-time and derive new types there.

The run-time behavior is not defined by "instantiation." It is partly by 
the root type specification and partly by the implementations of the 
class members = specific types.

>> Provided one could implement that thing (let's ignore pitiful Python),
>> What algorithmic problems one could solve with that?
> 
> Types in general aren't for solving algorithmic problems.  Thus the
> Turing tarpit.  Types are for being able to enforce rules about program
> behaviour.

... and the program behavior is about solving algorithmic problems.

In the hierarchy:

value
type (a set of values)
class (a set of types)
metaclass (a set of classes)

What sort of problems metaclass is supposed to help solving, describing, 
abstracting. What is a closure operation of. E.g. dynamically 
polymorphic classes are closed upon type derivation. What would be the 
type algebraic operation to construct a set of sets of types? What are 
the typical properties shared by the members of a metaclass?

You can continue the above hierarchy ad infinitum and beyond. But what for?

> This is still worth reading:
> 
> https://cdsmith.wordpress.com/2011/01/09/an-old-article-i-wrote/

It does not mention types of types.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de