Paths

If all Rust had were values, then every value would be uniquely owned by a variable or composite structure. From this we naturally derive a tree of ownership. The stack itself is the root of the tree, with every variable as its direct children. Each variable's direct children would be their fields (if any), and so on.

From this view, every value in Rust has a unique path in the tree of ownership. References to a value can subsequently be interpreted as a path in this tree. Of particular interest are ancestors and descendants: if x owns y, then x is an ancestor of y, and y is a descendant of x. Note that this is an inclusive relationship: x is a descendant and ancestor of itself.

Tragically, plenty of data doesn't reside on the stack, and we must also accommodate this. Globals and thread-locals are simple enough to model as residing at the bottom of the stack (though we must be careful with mutable globals). Data on the heap poses a different problem.

If all Rust had on the heap was data uniquely owned by a pointer on the stack, then we can just treat that pointer as a struct that owns the value on the heap. Box, Vec, String, and HashMap, are examples of types which uniquely own data on the heap.

Unfortunately, data on the heap is not always uniquely owned. Rc for instance introduces a notion of shared ownership. Shared ownership means there is no unique path. A value with no unique path limits what we can do with it. In general, only shared references can be created to these values. However mechanisms which ensure mutual exclusion may establish One True Owner temporarily, establishing a unique path to that value (and therefore all its children).

The most common way to establish such a path is through interior mutability, in contrast to the inherited mutability that everything in Rust normally uses. Cell, RefCell, Mutex, and RWLock are all examples of interior mutability types. These types provide exclusive access through runtime restrictions. However it is also possible to establish unique ownership without interior mutability. For instance, if an Rc has refcount 1, then it is safe to mutate or move its internals.

In order to correctly communicate to the type system that a variable or field of a struct can have interior mutability, it must be wrapped in an UnsafeCell. This does not in itself make it safe to perform interior mutability operations on that value. You still must yourself ensure that mutual exclusion is upheld.

Liveness

Roughly, a reference is live at some point in a program if it can be dereferenced. Shared references are always live unless they are literally unreachable (for instance, they reside in freed or leaked memory). Mutable references can be reachable but not live through the process of reborrowing.

A mutable reference can be reborrowed to either a shared or mutable reference to one of its descendants. A reborrowed reference will only be live again once all reborrows derived from it expire. For instance, a mutable reference can be reborrowed to point to a field of its referent:

let x = &mut (1, 2);
{
    // reborrow x to a subfield
    let y = &mut x.0;
    // y is now live, but x isn't
    *y = 3;
}
// y goes out of scope, so x is live again
*x = (5, 7);

It is also possible to reborrow into multiple mutable references, as long as they are disjoint: no reference is an ancestor of another. Rust explicitly enables this to be done with disjoint struct fields, because disjointness can be statically proven:

let x = &mut (1, 2);
{
    // reborrow x to two disjoint subfields
    let y = &mut x.0;
    let z = &mut x.1;

    // y and z are now live, but x isn't
    *y = 3;
    *z = 4;
}
// y and z go out of scope, so x is live again
*x = (5, 7);

However it's often the case that Rust isn't sufficiently smart to prove that multiple borrows are disjoint. This does not mean it is fundamentally illegal to make such a borrow, just that Rust isn't as smart as you want.

To simplify things, we can model variables as a fake type of reference: owned references. Owned references have much the same semantics as mutable references: they can be re-borrowed in a mutable or shared manner, which makes them no longer live. Live owned references have the unique property that they can be moved out of (though mutable references can be swapped out of). This power is only given to live owned references because moving its referent would of course invalidate all outstanding references prematurely.

As a local lint against inappropriate mutation, only variables that are marked as mut can be borrowed mutably.

It is interesting to note that Box behaves exactly like an owned reference. It can be moved out of, and Rust understands it sufficiently to reason about its paths like a normal variable.

Aliasing

With liveness and paths defined, we can now properly define aliasing:

A mutable reference is aliased if there exists another live reference to one of its ancestors or descendants.

(If you prefer, you may also say the two live references alias each other. This has no semantic consequences, but is probably a more useful notion when verifying the soundness of a construct.)

That's it. Super simple right? Except for the fact that it took us two pages to define all of the terms in that definition. You know: Super. Simple.

Actually it's a bit more complicated than that. In addition to references, Rust has raw pointers: *const T and *mut T. Raw pointers have no inherent ownership or aliasing semantics. As a result, Rust makes absolutely no effort to track that they are used correctly, and they are wildly unsafe.

It is an open question to what degree raw pointers have alias semantics. However it is important for these definitions to be sound that the existence of a raw pointer does not imply some kind of live path.

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Paths

Liveness

Aliasing

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