In the last post, we saw how to infer regions and their span. In this post, we will cover aliasing and how to ensure guarantees through region analysis.

## Aliasing, mutable aliasing, and unsafety.

Two pointers are said to be aliased, if they refer to the same object. Alias analysis is essential to program verification, optimizers, and compiler theory.

Alias analysis is the study of which pointers are aliased and, more importantly, which pointers aren’t aliased.

Rust guarantees that no mutable reference is aliased. This is statically checked, and we will show how in this post.

So, why is aliasing guarantees even needed?

The answer is that I need to be able to reason about the invariants of the pointers content, while being sure that those aren’t broken in the period of accessibility.

Furthermore, we want strict thread-safety, which requires guarantees about shared mutable state.

## Different values, different namespaces

To reason about mutability overlaps and aliasing through regions, we need a notion of different namespaces.

For example, say some variable X is referenced in a lifetime `'a`. Does that mean another variable Y living in the same scope can’t be mutated?

Of course not! Let’s consider:

``````{
let mut a = 2; // ------+ 'a
let b = &a;    // ----+ | 'b
let mut c = 0; // --+ | | 'c
c = 1;         //   | | |
c = 2;         //   | | |
} // -------------------+-+-+
``````

As you can see `a` is aliased, thus mutating it is not allowed. However, ```'a: 'c```, but that doesn’t mean they refer to the same.

Holding a global namespace would make the above example fail, since it has no distinction between `a` and `c` and their respective lifetimes.

For that reason, we need to segregate the regions, such that we can effectively reason about aliasing without mixing values up.

## Sublattices

We talked a bit about lattices and their applications in the last part. I recommend reading that if you do not know what a lattice is.

Now, let’s introduce the notion of a sublattice:

M is a sublattice of L, if M is a nonempty subset of L forming a lattice under L’s meet and join operators.

Take a lattice,

``````       Join(a, b, c)
/\
/  \
/    \
Join(a, b)  \c
/\      /
/  \    /
/    \  /
a/      \/b
\      /
\    /
\  /
\/
Meet(a, b)
``````

(by the way, this is why it is called a lattice)

then

``````   Join(a, b)
/\
/  \
/    \
a /      \b
\      /
\    /
\  /
\/
Meet(a, b)
``````

is a sublattice, since it holds all the conditions:

1. It is a nonempty subset.

2. It shares meet and join, while preserving closure (you can easily check this yourself).

## Region classes

Region classes has many names, but none which is universally agreed upon, I prefer the name region classes. As we say, a rose by any other name would still smell as sweet.

Let L be our region lattice, define a region class of L as a sublattice of L, in the context of segregating regions.

In particular, assign each value a region class. Say the value has the bounds (outlives) `{a, b, c, d...}`, then we derive our region class as the cyclic sublattice, `<a, b, c, d...>`. In particular, this means the smallest extension which forms a sublattice of L.

The compiler keeps a log of the region class of every variable. This is then used for alias analysis:

## Pointers and references

Taking an immutable reference extends our region class to contain the region of this particular reference, denoted `M[N]`.

Mutable references, on the other hand, works slightly different. The region class and the region of the reference must be disjoint, unless we get shared mutability. With this requirement satisfied, we can proceed to extend the region class with the new region.

## Mutating a local variable

You may ask, “Can you mutate a local variable while it is borrowed?”, the answer is, “No, you cannot”. The reason is the same for the mutable aliasing: it introduce shared mutable state.

But, how do we handle such mutations?

We introduced `empty(x)`, the empty region at `x`, in the earlier blog posts. And we can use this to interpret local mutations as well: as taking a mutable reference for region `empty(x)` and simply mutate it through the reference.

## Applying this method

If we get back to our example,

``````{
let mut a = 2; // ------+ 'a
let b = &a;    // ----+ | 'b
let mut c = 0; // --+ | | 'c
c = 1;         //   | | |
c = 2;         //   | | |
} // -------------------+-+-+
``````

We can see that the region class of `'a` is an extension of `'b`, but `'c` is not entangled with `'a`’s region class. In particular, `'c` and `'a` belong to different namespaces and thus, there is no shared mutability.

## Region classes and their relations

A natural question that arise is: Why don’t we do region inference seperately for each region class?

The answer is that distinct region classes are far from unrelated. Each region class simply defines a value and its aliases, but that doesn’t make it isolated for the rest of L.

If you look at our example above, you may notice that `'a` outlives `'c`, despite being associated with a different region class.

## Questions and errata

Ping me at #rust in Mozilla IRC.