Type inference

Type inference is the process of automatic detection of the type of an expression.

It is what allows Rust to work with fewer or no type annotations, making things easier for users:

fn main() {
    let mut things = vec![];

Here, the type of things is inferred to be Vec<&str> because of the value we push into things.

The type inference is based on the standard Hindley-Milner (HM) type inference algorithm, but extended in various way to accommodate subtyping, region inference, and higher-ranked types.

A note on terminology

We use the notation ?T to refer to inference variables, also called existential variables.

We use the terms "region" and "lifetime" interchangeably. Both refer to the 'a in &'a T.

The term "bound region" refers to a region that is bound in a function signature, such as the 'a in for<'a> fn(&'a u32). A region is "free" if it is not bound.

Creating an inference context

You create an inference context by doing something like the following:

let infcx = tcx.infer_ctxt().build();
// Use the inference context `infcx` here.

infcx has the type InferCtxt<'tcx>, the same 'tcx lifetime as on the tcx it was built from.

The tcx.infer_ctxt method actually returns a builder, which means there are some kinds of configuration you can do before the infcx is created. See InferCtxtBuilder for more information.

Inference variables

The main purpose of the inference context is to house a bunch of inference variables – these represent types or regions whose precise value is not yet known, but will be uncovered as we perform type-checking.

If you're familiar with the basic ideas of unification from H-M type systems, or logic languages like Prolog, this is the same concept. If you're not, you might want to read a tutorial on how H-M type inference works, or perhaps this blog post on unification in the Chalk project.

All told, the inference context stores five kinds of inference variables (as of March 2023):

  • Type variables, which come in three varieties:
    • General type variables (the most common). These can be unified with any type.
    • Integral type variables, which can only be unified with an integral type, and arise from an integer literal expression like 22.
    • Float type variables, which can only be unified with a float type, and arise from a float literal expression like 22.0.
  • Region variables, which represent lifetimes, and arise all over the place.
  • Const variables, which represent constants.

All the type variables work in much the same way: you can create a new type variable, and what you get is Ty<'tcx> representing an unresolved type ?T. Then later you can apply the various operations that the inferencer supports, such as equality or subtyping, and it will possibly instantiate (or bind) that ?T to a specific value as a result.

The region variables work somewhat differently, and are described below in a separate section.

Enforcing equality / subtyping

The most basic operations you can perform in the type inferencer is equality, which forces two types T and U to be the same. The recommended way to add an equality constraint is to use the at method, roughly like so:

infcx.at(...).eq(t, u);

The first at() call provides a bit of context, i.e. why you are doing this unification, and in what environment, and the eq method performs the actual equality constraint.

When you equate things, you force them to be precisely equal. Equating returns an InferResult – if it returns Err(err), then equating failed, and the enclosing TypeError will tell you what went wrong.

The success case is perhaps more interesting. The "primary" return type of eq is () – that is, when it succeeds, it doesn't return a value of any particular interest. Rather, it is executed for its side-effects of constraining type variables and so forth. However, the actual return type is not (), but rather InferOk<()>. The InferOk type is used to carry extra trait obligations – your job is to ensure that these are fulfilled (typically by enrolling them in a fulfillment context). See the trait chapter for more background on that.

You can similarly enforce subtyping through infcx.at(..).sub(..). The same basic concepts as above apply.

"Trying" equality

Sometimes you would like to know if it is possible to equate two types without error. You can test that with infcx.can_eq (or infcx.can_sub for subtyping). If this returns Ok, then equality is possible – but in all cases, any side-effects are reversed.

Be aware, though, that the success or failure of these methods is always modulo regions. That is, two types &'a u32 and &'b u32 will return Ok for can_eq, even if 'a != 'b. This falls out from the "two-phase" nature of how we solve region constraints.


As described in the previous section on can_eq, often it is useful to be able to do a series of operations and then roll back their side-effects. This is done for various reasons: one of them is to be able to backtrack, trying out multiple possibilities before settling on which path to take. Another is in order to ensure that a series of smaller changes take place atomically or not at all.

To allow for this, the inference context supports a snapshot method. When you call it, it will start recording changes that occur from the operations you perform. When you are done, you can either invoke rollback_to, which will undo those changes, or else confirm, which will make them permanent. Snapshots can be nested as long as you follow a stack-like discipline.

Rather than use snapshots directly, it is often helpful to use the methods like commit_if_ok or probe that encapsulate higher-level patterns.

Subtyping obligations

One thing worth discussing is subtyping obligations. When you force two types to be a subtype, like ?T <: i32, we can often convert those into equality constraints. This follows from Rust's rather limited notion of subtyping: so, in the above case, ?T <: i32 is equivalent to ?T = i32.

However, in some cases we have to be more careful. For example, when regions are involved. So if you have ?T <: &'a i32, what we would do is to first "generalize" &'a i32 into a type with a region variable: &'?b i32, and then unify ?T with that (?T = &'?b i32). We then relate this new variable with the original bound:

&'?b i32 <: &'a i32

This will result in a region constraint (see below) of '?b: 'a.

One final interesting case is relating two unbound type variables, like ?T <: ?U. In that case, we can't make progress, so we enqueue an obligation Subtype(?T, ?U) and return it via the InferOk mechanism. You'll have to try again when more details about ?T or ?U are known.

Region constraints

Regions are inferenced somewhat differently from types. Rather than eagerly unifying things, we simply collect constraints as we go, but make (almost) no attempt to solve regions. These constraints have the form of an "outlives" constraint:

'a: 'b

Actually the code tends to view them as a subregion relation, but it's the same idea:

'b <= 'a

(There are various other kinds of constraints, such as "verifys"; see the region_constraints module for details.)

There is one case where we do some amount of eager unification. If you have an equality constraint between two regions

'a = 'b

we will record that fact in a unification table. You can then use opportunistic_resolve_var to convert 'b to 'a (or vice versa). This is sometimes needed to ensure termination of fixed-point algorithms.

Solving region constraints

Region constraints are only solved at the very end of typechecking, once all other constraints are known and all other obligations have been proven. There are two ways to solve region constraints right now: lexical and non-lexical. Eventually there will only be one.

An exception here is the leak-check which is used during trait solving and relies on region constraints containing higher-ranked regions. Region constraints in the root universe (i.e. not arising from a for<'a>) must not influence the trait system, as these regions are all erased during codegen.

To solve lexical region constraints, you invoke resolve_regions_and_report_errors. This "closes" the region constraint process and invokes the lexical_region_resolve code. Once this is done, any further attempt to equate or create a subtyping relationship will yield an ICE.

The NLL solver (actually, the MIR type-checker) does things slightly differently. It uses canonical queries for trait solving which use take_and_reset_region_constraints at the end. This extracts all of the outlives constraints added during the canonical query. This is required as the NLL solver must not only know what regions outlive each other, but also where. Finally, the NLL solver invokes take_region_var_origins, providing all region variables to the solver.

Lexical region resolution

Lexical region resolution is done by initially assigning each region variable to an empty value. We then process each outlives constraint repeatedly, growing region variables until a fixed-point is reached. Region variables can be grown using a least-upper-bound relation on the region lattice in a fairly straightforward fashion.