I don't like that a tuple of strings is no longer supported. Why does it need to be a list?

The idea was to tighten the interface to prevent user errors leading to valid, but unwanted, dimension objects. This is most surely inspired by my uses of type-checkers in python, as the above makes the signature of check_dimension not depend on the actual values contained in the passed sequence:

• list becomes a Categorical
• tuple[int, int] (and the 3- and 4-long forms) become Integer
• tuple[int, float], tuple[float, int] and tuple[float, float] (and corresponding 3 and 4-long forms) become Real

It was also to avoid an incorrect tuple silently becoming a Categorical, e.g.

• (0, 1, "uniform", base) where base="10" was no parsed from a data source, silently returning a Categorical instead of the intended Integer
• (0, 1, *params) where params=(5, "log-uniform", 2) because the semantic/content of params is wrong, silently falling back to a Categorical
• [True, False] being inferred to an Integer (though the old implementation has a dedicated branch to avoid that).

We could make it so that tuples that fail the Integer/Real inference default to a Categorical as before. This would also allow to use any Iterable, like so:

if isinstance(dimension, tuple) and 2 <= len(dimension) <= 4:
    low, high, *args = dimension
    if (not args or isinstance(args[0], str)) and (len(args) < 2 or isinstance(args[1], int)):
        if isinstance(low, numbers.Integral) and isinstance(high,  numbers.Integral):
              return Integer(...)
        elif isinstance(low, numbers.Real) and isinstance(high, numbers.Real):
            return Real(...)
# not an else, fallback
if isinstance(dimension, Iterable):
    return Categorical(...)
raise ValueError(...)

Do you prefer that other type-tightness ?

low and high are already int (or float). Why cast?

The float cast is because one of the boundaries might be an int, and a Real dimension asks for two float in its doc.
The int cast was to support other integral types like bool or np.int32.

Since int is not a sublcass of float, I think the float cast is necessary to respect Real's interface. I'm not too sure about the int cast, I mostly did it for symmetry.

Likewise, why this map()?

see above