[Knowledge sharing] unions of any() about gradualizer HOT 4 CLOSED

@zuiderkwast, didn't we have a discussion about this? I think it was you who worked out that it was better to not throw away all the types in a union even if any is one of the types. I can't remember the argument for why this is a good idea. Do you remember?
The paper "The Recursive Union of Some Gradual Types" by Jeremy G. Siek and Sam Tobin-Hochstadt might talk about this. Unfortunately I haven't read that paper in detail yet (though I really should have!)

from gradualizer.

Yes, I implemented normalization of unions. We merge any non-any types but keep any separate. @josefs, you showed an example of this yourself during the demo in last Design Forum. The error message was something like integer() | any() is not a compatible subtype of non_neg_integer().

The reasoning was that a value of type integer() | any() can at least be any positive or negative integer. Apart from this, it can possibly also be a value of other types that we don't know.

We merge anything else, so for example integer() | 42 | any() = integer() | any().

from gradualizer.

just expanding on this, I think the optimisation only work one way.

(:: is compatible subtype).

• t2() :: t1() | any() is equivalent with t2() :: any() (in this case union means t2() :: t1() OR t2() :: any())
• but t1() | any() :: t2() is not equivalent with any() :: t2() (in this case union translates to t1() :: t2() AND any() :: t2()).

from gradualizer.

@gomoripeti I think that is what they say in "Fig. 8. Merge operator" of "The Recursive Union of Some Gradual Types" - don't hold me accountable though.

from gradualizer.