Expand description

Note: tests specific to this file can be found in:

  • ui/pattern/usefulness
  • ui/or-patterns
  • ui/consts/const_in_pattern
  • ui/rfc-2008-non-exhaustive
  • ui/half-open-range-patterns
  • probably many others

I (Nadrieril) prefer to put new tests in ui/pattern/usefulness unless there’s a specific reason not to, for example if they depend on a particular feature like or_patterns.

This file includes the logic for exhaustiveness and reachability checking for pattern-matching. Specifically, given a list of patterns for a type, we can tell whether: (a) each pattern is reachable (reachability) (b) the patterns cover every possible value for the type (exhaustiveness)

The algorithm implemented here is a modified version of the one described in this paper. We have however generalized it to accommodate the variety of patterns that Rust supports. We thus explain our version here, without being as rigorous.


The core of the algorithm is the notion of “usefulness”. A pattern q is said to be useful relative to another pattern p of the same type if there is a value that is matched by q and not matched by p. This generalizes to many ps: q is useful w.r.t. a list of patterns p_1 .. p_n if there is a value that is matched by q and by none of the p_i. We write usefulness(p_1 .. p_n, q) for a function that returns a list of such values. The aim of this file is to compute it efficiently.

This is enough to compute reachability: a pattern in a match expression is reachable iff it is useful w.r.t. the patterns above it:

match x {
    Some(_) => {},
    None => {},    // reachable: `None` is matched by this but not the branch above
    Some(0) => {}, // unreachable: all the values this matches are already matched by
                   // `Some(_)` above

This is also enough to compute exhaustiveness: a match is exhaustive iff the wildcard _ pattern is not useful w.r.t. the patterns in the match. The values returned by usefulness are used to tell the user which values are missing.

match x {
    Some(0) => {},
    None => {},
    // not exhaustive: `_` is useful because it matches `Some(1)`

The entrypoint of this file is the compute_match_usefulness function, which computes reachability for each match branch and exhaustiveness for the whole match.

Constructors and fields

Note: we will often abbreviate “constructor” as “ctor”.

The idea that powers everything that is done in this file is the following: a (matchable) value is made from a constructor applied to a number of subvalues. Examples of constructors are Some, None, (,) (the 2-tuple constructor), Foo {..} (the constructor for a struct Foo), and 2 (the constructor for the number 2). This is natural when we think of pattern-matching, and this is the basis for what follows.

Some of the ctors listed above might feel weird: None and 2 don’t take any arguments. That’s ok: those are ctors that take a list of 0 arguments; they are the simplest case of ctors. We treat 2 as a ctor because u64 and other number types behave exactly like a huge enum, with one variant for each number. This allows us to see any matchable value as made up from a tree of ctors, each having a set number of children. For example: Foo { bar: None, baz: Ok(0) } is made from 4 different ctors, namely Foo{..}, None, Ok and 0.

This idea can be extended to patterns: they are also made from constructors applied to fields. A pattern for a given type is allowed to use all the ctors for values of that type (which we call “value constructors”), but there are also pattern-only ctors. The most important one is the wildcard (_), and the others are integer ranges (0..=10), variable-length slices ([x, ..]), and or-patterns (Ok(0) | Err(_)). Examples of valid patterns are 42, Some(_), Foo { bar: Some(0) | None, baz: _ }. Note that a binder in a pattern (e.g. Some(x)) matches the same values as a wildcard (e.g. Some(_)), so we treat both as wildcards.

From this deconstruction we can compute whether a given value matches a given pattern; we simply look at ctors one at a time. Given a pattern p and a value v, we want to compute matches!(v, p). It’s mostly straightforward: we compare the head ctors and when they match we compare their fields recursively. A few representative examples:

  • matches!(v, _) := true
  • matches!((v0, v1), (p0, p1)) := matches!(v0, p0) && matches!(v1, p1)
  • matches!(Foo { bar: v0, baz: v1 }, Foo { bar: p0, baz: p1 }) := matches!(v0, p0) && matches!(v1, p1)
  • matches!(Ok(v0), Ok(p0)) := matches!(v0, p0)
  • matches!(Ok(v0), Err(p0)) := false (incompatible variants)
  • matches!(v, 1..=100) := matches!(v, 1) || ... || matches!(v, 100)
  • matches!([v0], [p0, .., p1]) := false (incompatible lengths)
  • matches!([v0, v1, v2], [p0, .., p1]) := matches!(v0, p0) && matches!(v2, p1)
  • matches!(v, p0 | p1) := matches!(v, p0) || matches!(v, p1)

Constructors, fields and relevant operations are defined in the super::deconstruct_pat module.

Note: this constructors/fields distinction may not straightforwardly apply to every Rust type. For example a value of type Rc<u64> can’t be deconstructed that way, and &str has an infinitude of constructors. There are also subtleties with visibility of fields and uninhabitedness and various other things. The constructors idea can be extended to handle most of these subtleties though; caveats are documented where relevant throughout the code.

Whether constructors cover each other is computed by Constructor::is_covered_by.


Recall that we wish to compute usefulness(p_1 .. p_n, q): given a list of patterns p_1 .. p_n and a pattern q, all of the same type, we want to find a list of values (called “witnesses”) that are matched by q and by none of the p_i. We obviously don’t just enumerate all possible values. From the discussion above we see that we can proceed ctor-by-ctor: for each value ctor of the given type, we ask “is there a value that starts with this constructor and matches q and none of the p_i?”. As we saw above, there’s a lot we can say from knowing only the first constructor of our candidate value.

Let’s take the following example:

match x {
    Enum::Variant1(_) => {} // `p1`
    Enum::Variant2(None, 0) => {} // `p2`
    Enum::Variant2(Some(_), 0) => {} // `q`

We can easily see that if our candidate value v starts with Variant1 it will not match q. If v = Variant2(v0, v1) however, whether or not it matches p2 and q will depend on v0 and v1. In fact, such a v will be a witness of usefulness of q exactly when the tuple (v0, v1) is a witness of usefulness of q' in the following reduced match:

match x {
    (None, 0) => {} // `p2'`
    (Some(_), 0) => {} // `q'`

This motivates a new step in computing usefulness, that we call specialization. Specialization consist of filtering a list of patterns for those that match a constructor, and then looking into the constructor’s fields. This enables usefulness to be computed recursively.

Instead of acting on a single pattern in each row, we will consider a list of patterns for each row, and we call such a list a pattern-stack. The idea is that we will specialize the leftmost pattern, which amounts to popping the constructor and pushing its fields, which feels like a stack. We note a pattern-stack simply with [p_1 ... p_n]. Here’s a sequence of specializations of a list of pattern-stacks, to illustrate what’s happening:

[Enum::Variant2(None, 0)]
[Enum::Variant2(Some(_), 0)]
//==>> specialize with `Variant2`
[None, 0]
[Some(_), 0]
//==>> specialize with `Some`
[_, 0]
//==>> specialize with `true` (say the type was `bool`)
//==>> specialize with `0`

The function specialize(c, p) takes a value constructor c and a pattern p, and returns 0 or more pattern-stacks. If c does not match the head constructor of p, it returns nothing; otherwise if returns the fields of the constructor. This only returns more than one pattern-stack if p has a pattern-only constructor.

  • Specializing for the wrong constructor returns nothing

    specialize(None, Some(p0)) := []

  • Specializing for the correct constructor returns a single row with the fields

    specialize(Variant1, Variant1(p0, p1, p2)) := [[p0, p1, p2]]

    specialize(Foo{..}, Foo { bar: p0, baz: p1 }) := [[p0, p1]]

  • For or-patterns, we specialize each branch and concatenate the results

    specialize(c, p0 | p1) := specialize(c, p0) ++ specialize(c, p1)

  • We treat the other pattern constructors as if they were a large or-pattern of all the possibilities:

    specialize(c, _) := specialize(c, Variant1(_) | Variant2(_, _) | ...)

    specialize(c, 1..=100) := specialize(c, 1 | ... | 100)

    specialize(c, [p0, .., p1]) := specialize(c, [p0, p1] | [p0, _, p1] | [p0, _, _, p1] | ...)

  • If c is a pattern-only constructor, specialize is defined on a case-by-case basis. See the discussion about constructor splitting in super::deconstruct_pat.

We then extend this function to work with pattern-stacks as input, by acting on the first column and keeping the other columns untouched.

Specialization for the whole matrix is done in Matrix::specialize_constructor. Note that or-patterns in the first column are expanded before being stored in the matrix. Specialization for a single patstack is done from a combination of Constructor::is_covered_by and PatStack::pop_head_constructor. The internals of how it’s done mostly live in the Fields struct.

Computing usefulness

We now have all we need to compute usefulness. The inputs to usefulness are a list of pattern-stacks p_1 ... p_n (one per row), and a new pattern_stack q. The paper and this file calls the list of patstacks a matrix. They must all have the same number of columns and the patterns in a given column must all have the same type. usefulness returns a (possibly empty) list of witnesses of usefulness. These witnesses will also be pattern-stacks.

  • base case: n_columns == 0. Since a pattern-stack functions like a tuple of patterns, an empty one functions like the unit type. Thus q is useful iff there are no rows above it, i.e. if n == 0.

  • inductive case: n_columns > 0. We need a way to list the constructors we want to try. We will be more clever in the next section but for now assume we list all value constructors for the type of the first column.

    • for each such ctor c:

      • for each q' returned by specialize(c, q):

        • we compute usefulness(specialize(c, p_1) ... specialize(c, p_n), q')
      • for each witness found, we revert specialization by pushing the constructor c on top.

    • We return the concatenation of all the witnesses found, if any.


[Some(true)] // p_1
[None] // p_2
[Some(_)] // q
//==>> try `None`: `specialize(None, q)` returns nothing
//==>> try `Some`: `specialize(Some, q)` returns a single row
[true] // p_1'
[_] // q'
//==>> try `true`: `specialize(true, q')` returns a single row
[] // p_1''
[] // q''
//==>> base case; `n != 0` so `q''` is not useful.
//==>> go back up a step
[true] // p_1'
[_] // q'
//==>> try `false`: `specialize(false, q')` returns a single row
[] // q''
//==>> base case; `n == 0` so `q''` is useful. We return the single witness `[]`
//==>> undo the specialization with `false`
//==>> undo the specialization with `Some`
//==>> we have tried all the constructors. The output is the single witness `[Some(false)]`.

This computation is done in is_useful. In practice we don’t care about the list of witnesses when computing reachability; we only need to know whether any exist. We do keep the witnesses when computing exhaustiveness to report them to the user.

Making usefulness tractable: constructor splitting

We’re missing one last detail: which constructors do we list? Naively listing all value constructors cannot work for types like u64 or &str, so we need to be more clever. The first obvious insight is that we only want to list constructors that are covered by the head constructor of q. If it’s a value constructor, we only try that one. If it’s a pattern-only constructor, we use the final clever idea for this algorithm: constructor splitting, where we group together constructors that behave the same.

The details are not necessary to understand this file, so we explain them in super::deconstruct_pat. Splitting is done by the Constructor::split function.

Constants in patterns

There are two kinds of constants in patterns:

  • literals (1, true, "foo")
  • named or inline consts (FOO, const { 5 + 6 })

The latter are converted into other patterns with literals at the leaves. For example const_to_pat(const { [1, 2, 3] }) becomes an Array(vec![Const(1), Const(2), Const(3)]) pattern. This gets problematic when comparing the constant via == would behave differently from matching on the constant converted to a pattern. Situations like that can occur, when the user implements PartialEq manually, and thus could make == behave arbitrarily different. In order to honor the == implementation, constants of types that implement PartialEq manually stay as a full constant and become an Opaque pattern. These Opaque patterns do not participate in exhaustiveness, specialization or overlap checking.


  • MatchArm 🔒
    The arm of a match expression.
  • Matrix 🔒
    A 2D matrix.
  • PatCtxt 🔒
  • PatStack 🔒
    A row of a matrix. Rows of len 1 are very common, which is why SmallVec[_; 2] works well.
  • The output of checking a match for exhaustiveness and arm reachability.
  • Witness 🔒
    A witness of non-exhaustiveness for error reporting, represented as a list of patterns (in reverse order of construction) with wildcards inside to represent elements that can take any inhabitant of the type as a value.


  • ArmType 🔒
  • Indicates whether or not a given arm is reachable.
  • Usefulness 🔒
    This carries the results of computing usefulness, as described at the top of the file. When checking usefulness of a match branch, we use the NoWitnesses variant, which also keeps track of potential unreachable sub-patterns (in the presence of or-patterns). When checking exhaustiveness of a whole match, we use the WithWitnesses variant, which carries a list of witnesses of non-exhaustiveness when there are any. Which variant to use is dictated by ArmType.


  • The entrypoint for the usefulness algorithm. Computes whether a match is exhaustive and which of its arms are reachable.
  • is_useful 🔒
    Algorithm from http://moscova.inria.fr/~maranget/papers/warn/index.html. The algorithm from the paper has been modified to correctly handle empty types. The changes are: (0) We don’t exit early if the pattern matrix has zero rows. We just continue to recurse over columns. (1) all_constructors will only return constructors that are statically possible. E.g., it will only return Ok for Result<T, !>.