Adds _extended_purview attribute to Causal Links + pretty formatting of extended_purview

[renzocom]

In actual causation, when computing causal links, it often occurs that purviews have the same alpha. Currently, the find_causal_link() method returns one arbitrary purview from the ones with maximum alpha.
The find_causal_link() method now adds a hidden attribute _extended_purview to the returned CausalLink with all the purviews with equivalent maximum alpha which are not supersets of each other. For example, if purviews (A,B), (B,C), (A,B,D) have the same maximum alpha, the extended purview is ((A,B),(B,C)).

I've also added pretty formatting methods to print the CausalLinks when they have extended purviews so they look like:
α = 0.415 [[S1, A], [A, D]] ◀━━ [M1]

[coveralls]

Coverage increased (+0.003%) to 93.835% when pulling 40a0c63 on renzocom:develop into d965289 on wmayner:develop.

[wmayner]

Thanks for the PR @renzocom! The next thing to do is update the tests so that they check the new behavior (and pass); see here for how to run the tests on your local machine.

[renzocom]

Will, is this kind of inner function declaration, ok?

[wmayner]

Yes, that's a typical pattern when using filter. However, sometimes it makes sense to refactor the function into a general-purpose function that's available elsewhere. In this case, we can just leave it in here.

You don't need to use np.all here, since the argument is not already a NumPy array. You can just use the built-in all, which will be more efficient, since the argument doesn't need to be converted into a NumPy array first.

Finally, the logic here is overcomplicated. Your function is equivalent to the following:

def is_minimal(purview):
    return all(set(purview).issubset(other_purview) for other_purview in purviews)

Note that I'm not constructing a list here, but rather a generator expression (there are no square brackets around the comprehension inside all()). This is because we only need to look at each element in the sequence once, and in this type of situation it's generally more efficient to use generators.

[renzocom]

Fixed, except from the logic part becauseis_minimal is not equivalent to is_not_superset, e.g. purview = (1,2), purviews = [(1,2,3), (1,2), (0)], is_not_superset(purview) returns True, while is_minimal(purview) returns False.

[wmayner]

Yes, that's a typical pattern when using filter. However, sometimes it makes sense to refactor the function into a general-purpose function that's available elsewhere. In this case, we can just leave it in here.

You don't need to use np.all here, since the argument is not already a NumPy array. You can just use the built-in all, which will be more efficient, since the argument doesn't need to be converted into a NumPy array first.

Finally, the logic here is overcomplicated. Your function is equivalent to the following:

def is_minimal(purview):
    return all(set(purview).issubset(other_purview) for other_purview in purviews)

Note that I'm not constructing a list here, but rather a generator expression (there are no square brackets around the comprehension inside all()). This is because we only need to look at each element in the sequence once, and in this type of situation it's generally more efficient to use generators.

[wmayner]

I would cast this to a tuple:

self._extended_purview = tuple(extended_purview)

[renzocom]

if extended_purview is None wouldn't this cast lead to an type error?
Maybe something like self._extended_purview = tuple(extended_purview) if extended_purview is not None else None?

[wmayner]

@renzocom sup

[renzocom]

@renzocom sup

SUP WILL

[wmayner]

Nice work Renzo🥇