Sure, I'm just saying that Mypy is a real type checker. The distinction is one of degree, not of kind. Writing a spec for Mypy wouldn't make its types more "true", just as deleting Haskell's spec wouldn't make its types less true types.
The academic usage holds that the distinction between the true type systems and the pretenders is that the first are sound: a well-typed program either evaluates to a normal form (value) or fails to terminate, but can never get stuck (segfault, terminate with an uncaught exception, however your environment implements that).
Of course, a gradual system like Mypy can never both be sound in this sense and remain gradual (which is a major selling point for Mypy), so for them the rule is usually amended with “provided the program is fully annotated” (and it should be obvious whether any given program is fully annotated or not, otherwise the system is just user-hostile regardless of how sound it is; at the very least it must be decidable). That is still obviously not satisfied for Mypy, because it doesn’t track exceptions (and including uncaught exceptions in normal forms would be useless because then no Python programs would ever get stuck). The actual guarantee Mypy is supposed to provide sounds kind of wimpy, like “never gets a TypeError that is not explicitly raised in user code”, but would still be useful regardless... Except that soundness is usually a pretty non-trivial theorem, and the lack of a readable specification for Mypy’s type system precludes it from being proven.
While well-typed Haskell (or SML) programs can in fact crash from the user’s perspective, the possible sources of crashes are rare and avoidable enough (for Haskell, only non-exhaustive patterns and explicit use of undefined, error, or throw) that you can call them additional normal forms without making the whole thing trivial. Every other way an untyped program could get stuck is disallowed by the type system, and there is a proof (SML) or at least a proof sketch (Haskell) of that (although of course not every untyped program that can’t get stuck is allowed by the type system, that is impossible by Turing—Gödel). Even the horrendously complicated systems that GHC implements nowadays still have papers that prove their soundness for a good enough toy example that one walks away convinced that the real thing works just as well.
So yes, there is a sense in which Mypy’s system is less “true” than SML’s or Haskell’s, and it is directly caused by (though not completely reducible to) the lack of a complete human-readable spec for both Mypy and Python itself. (I love Python to bits, but its object model is surreal and its only complete description is Objects/object.c together with Objects/typeobject.c.) If a wizard waved his wand and made every copy of the Haskell Report disappear, its type system would technically remain sound, but illegibly so to human mathematicians, thus it would in fact become less “true” in this sense than previously. Multiple implementations help, but I expect that without a prose spec it wouldn’t be easy to tell that GHC, UHC and Hugs implement the same system, the same way I have no idea if Mypy and Pytype do.
It's hard to find people who are knowledgeable enough about both static and dynamic systems and able to explain in layman's terms. Is there somewhere (online?) I can go to talk with people like you?
Calling me “knowledgeable” on this stuff might be a bit of a stretch, but then my standard of “knowledgeable” here is probably somewhere around “did a thesis on it”.
The people on #haskell at Freenode (nowadays Libera) were extremely friendly and helpful when I frequented it about five to ten years ago, although of course there are a subtle but important limits to initiating discussions that are interesting to people on the channel but not strictly on topic for it.
My more general advice is (for a double combo of both trite and condescending) read a book. Specifically, read Pierce’s “Types and programming languages”. I usually cherry-pick paragraphs and sections from books rather than read them from start to finish, but this particular book I basically gulped down in two sittings on two-hour flights (being trapped in economy seating helps) and found extremely enlightening both in that it dissolved the mystery around some lofty-sounding words I was always afraid of (“corecursion” and “coinduction”, “terminating” vs “productive”) and in that it contained completely elementary mathematical insights that have previously passed me by (Tarski fixed point theorem and order theory in general).
While I did have an advantage of having encountered, if not understood, basically all of the words inside it beforehand, I still believe it might be helpful even if you have absolutely no background in type systems. And don’t be put off by the use of Java in the case study, it is genuinely on point there.
For a more practical and yet more advanced (dependent types!) view, you can try “Type-driven programming in Idris” and “The little typer”, but I haven’t studied the former as carefully and have only skimmed the latter, so can’t recommend either with the same degree of certainty. I guess just follow the general advice on difficult literature: look around, follow references, don’t hesitate to put down things that don’t work for you, and if all else fails, let it stew for a week before trying again.
