Experiment with backtracking in the new solver

Depend on https://github.com/python/mypy/issues/15906. This is a follow-up for series started by https://github.com/python/mypy/pull/15287

Currently when getting both upper and lower bounds for a type variable we randomly choose the lower one. This is not always the best choice and can lead to inference failures. A possible example is:

def dec(fn: Callable[[S, S, int], float]) -> Callable[[S], float]: ... 
def f(x: List[float], y: List[T], z: T) -> T: ...
dec(f)

this will infer constraints like

S <: List[float], S <: List[T], T <: float, T :> int

They split into two SCCs each containing one variable {T} and {S}, and the second depends on first one. So we would first solve T = int and then we will get updated constraints for S: S <: List[float], S <: List[int], with the only solution S = <nothing>. At the same time T = float, S = List[float] is a totally valid solution. We could get it by backtracking when we get <nothing> and trying different bound(s) in the previous SCC.

One possible problem I see is that this backtracking is exponential in worst case of inference failure (e.g. due to actual user error). Another problem is that backtracking can make implementation much less readable.

cc @JukkaL

Inizia leggendo l’issue #15906 e la serie di seguito nella pull request #15287 per comprendere le modifiche al solver già in corso. Esamina poi l’esempio di vincolo su variabili di tipo in questa issue e determina come circoscrivere un esperimento di backtracking. Il lavoro sarebbe completo quando saranno disponibili un design condiviso e dati sugli insuccessi dell’inferenza e sul comportamento nel caso peggiore.