web: Type SUPPORTED_METHODS so it can be overridden.

[alexmv]

Its default type is Tuple[str, str, str, str, str, str, str], which can only be overridden by a tuple of the exact same length. Which is not terribly useful for its stated purpose.

Type it as a Collection[str], which should support folks overriding it as any number of reasonable things, as it is only used by way of if request.method not in self.SUPPORTED_METHODS.

[andersk]

Mypy reveals some implicit reliances on it being a Tuple:

tornado/web.py:1795: error: Item "None" of "Optional[str]" has no attribute "lower"  [union-attr]
tornado/test/web_test.py:2190: error: Unsupported left operand type for + ("Collection[str]")  [operator]
tornado/test/httpclient_test.py:124: error: Unsupported left operand type for + ("Collection[str]")  [operator]

(The first error is a result of Mypy permitting type narrowing of the left operand of in when the right operand is a Tuple but not when it’s a Collection.)

We could remove these reliances, or keep them and use Tuple[str, ...] (the literal ellipsis makes this a variable-length tuple type).

[alexmv]

It ideally should be a set, since it's primarily used for an in query. However, that would be a non-backwards-compatible change, since subclasses in the wild which are doing RequestHandler.SUPPORTED_METHODS + ("OTHER",) would break.

Maintainers, do you have a preference between Tuple[str, ...] or the backwards-incompatible Set[str]?