python / python/typing

spec: Definition of materialization is insufficient

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topic: typing spec
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Python
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Description

The spec currently defines materialization as follows:

Given a gradual type A, if we replace zero or more occurrences of Any in A with some type (which can be different for each occurrence of Any), the resulting gradual type B is a materialization of A.

A type A is assignable to B if there exists a pair of materializations A' and B' of A and B such that A' is a subtype of B'.

Now let's consider whether list[int] | list[str] is assignable to list[Any]. To do so, we have to consider materializations of list[Any], created by substituting Any with some other type. But there's nothing we can substitute for Any that would make for a fully static type that is a supertype of list[int] | list[str], since list is invariant in its type parameter. Therefore, list[int] | list[str] is not assignable to list[Any]. Relatedly, this means list[Any] | list[Any] is not equivalent to list[Any]. This is obviously not a desirable conclusion; current type checkers treat list[int] | list[str] as assignable to list[Any], and they should.

I think to fix this, we could say that if A' and A'' are materializations of A, then the union A' | A'' must also be a materialization of A.

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Research direction

Start with the materialization definition in the linked typing specification and work through the list[int] | list[str] versus list[Any] example. Evaluate the proposed rule that unions of materializations remain materializations, including its effect on assignability and equivalence; done requires an agreed specification change and updated explanatory text.

Written by the indexing model from the issue text.

Assessment

Tech stack
python
Domain
documentation
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Quiet
Clarity
Mostly clear
Newbie friendliness
38/100

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