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From: Paul Rubin <no.email@nospam.invalid>
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Subject: Re: In precision typing we trust
Date: Mon, 25 Aug 2025 14:27:55 -0700
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"Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> writes:
> Call the thing (a set of types closed under derivation) the way you want.

Classes in Python aren't sets of types.  For example, 3 isn't a type,
but in Python 3 it's a member of class 'int'.

    >>> a = 3
    >>> a.__class__
    <class 'int'>

Classes in Python are analogous to types in type theory, but Python
isn't lambda calculus.

    How is that, except for sloppiness "class is ... a class", different
    from a set of sets of types?

Metaclasses in Python are used to control the runtime semantics of newly
created classes.  E.g. what happens when you create a class instance.

It's not really useful to think of Python types as sets.  Python isn't
that mathematical.  You could think of them as sorts, in the sense of
multi-sorted logic.  Each Python value has a label attached to it (the
type tag) that can be inspected at runtime.  Those types are also
sometimes called latent types.