# Understanding Effective Actions

In PolicyGlass we express ARPs (`Action` `Resource` `policyglass.principal.Principal`) as though they are potentially infinite sets.

In reality they are finite sets because there are only a finite number of allowed actions, resources, or principals. However because actions are being constantly updated by AWS, and new resources and princiapls are being created all the time, we here treat them as infinite sets because their extent is unknowable by us when we are parsing the policy.

## Components of an EffectiveAction

An `EffectiveAction` object has two components:

The inclusions indicate the `Action` that this effective action applies to and the exclusions indicate the actions that this effective action does not apply to.

At its simplest an effective action is just an inclusion, which you can think of as a Venn diagram containing `S3:*`.

Then if you have an exclusion of `S3:Get*` you can think of this as a hole punched in the Venn diagram.

The area in the middle indicating that `S3:Get*` is not included in the effective action.

## Difference

The difference between set x and set y is the elements that are contained in set x that are not contained in set y. In essence it’s a subtraction. Remove the elements in set y from set x and you have the difference.

### Simple

Let’s say we calculate the difference between two effective actions like so.

```>>> from policyglass import EffectiveAction, Action
>>> x = EffectiveAction(inclusion=Action("S3:*"))
>>> y = EffectiveAction(inclusion=Action("S3:Get*"))
>>> x.difference(y)
[EffectiveAction(inclusion=Action('S3:*'), exclusions=frozenset({Action('S3:Get*')}))]
```

The result is that the inclusion from y is added to the exclusions of x.

• `S3:*` is the `inclusion` from `x`

• `S3:Get*` is the `inclusion` from `y`

The inclusion from x is added as an exclusion of y is because our Actions are essentially infinite sets. The wildcard at the end of `S3:*` could extend to an infinitely long string for all we know, so we can’t create an `Action` that expresses S3:* but not S3:Get* so we must add it as an exclusion in an `EffectiveAction`.

This is the reason `EffectiveAction` s exist, so we can express the intersection of the complement of ininite set B with inifite set A.

### Complex

Let’s say we have two effective actions we want to diff. One is just `S3:*` and the other is `S3:Get*` except for `S3:GetObject`. To diff these we want to subtract `S3:Get*` from `S3:*` but leave `S3:GetObject` in place.

```>>> from policyglass import EffectiveAction, Action
>>> x = EffectiveAction(inclusion=Action("S3:*"))
>>> y = EffectiveAction(inclusion=Action("S3:Get*"), exclusions=frozenset({Action("S3:GetObject")}))
>>> print(x.difference(y))
[EffectiveAction(inclusion=Action('S3:*'), exclusions=frozenset({Action('S3:Get*')})),
EffectiveAction(inclusion=Action('S3:GetObject'), exclusions=frozenset())]
```

Let’s unpack what happened here.

1. We added the inclusion (`S3:get*`) from y to the exclusions of x

2. We returned a new effective action that is just `S3:GetObject`

• `S3:*` is our `inclusion` from `x`

• `S3:Get*` is our `inclusion` from `y`

• `S3:GetObject` is our `exclusion` from `y`

In the above Venn diagram we’re showing that the difference between the two effective actions is to include `S3:*` except `S3:Get*` but still include `S3:GetObject`. We can’t have an inclusion inside an exclusion so we represent this by adding another effective action object to represent the inclusion.

Outputting two effective actions makes a list of `PolicyShard` objects much easier to understand because you will end up with two shards (one for each effective action) rather than one super hard to understand shard that has an action inclusion inside an action exclusion inside an action inclusion.

Remember that the exclusions in an EffectiveAction are negations, they are holes punched in what’s allowed. As a result, what is in the exclusion of y should not be removed from x because it’s explicitly not part of y.

Because we can’t express the fact that we want to exclude B and C but include A in our result, we have to return two separate `EffectiveAction` s, one which includes A but the entirety of B, and another that just includes D.