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+//! # Match exhaustiveness and redundancy algorithm
+//!
+//! This file contains the logic for exhaustiveness and usefulness checking for pattern-matching.
+//! Specifically, given a list of patterns in a match, we can tell whether:
+//! (a) a given pattern is redundant
+//! (b) the patterns cover every possible value for the type (exhaustiveness)
+//!
+//! The algorithm implemented here is inspired from the one described in [this
+//! paper](http://moscova.inria.fr/~maranget/papers/warn/index.html). We have however changed it in
+//! various ways to accommodate the variety of patterns that Rust supports. We thus explain our
+//! version here, without being as precise.
+//!
+//! Fun fact: computing exhaustiveness is NP-complete, because we can encode a SAT problem as an
+//! exhaustiveness problem. See [here](https://niedzejkob.p4.team/rust-np) for the fun details.
+//!
+//!
+//! # Summary
+//!
+//! The algorithm is given as input a list of patterns, one for each arm of a match, and computes
+//! the following:
+//! - a set of values that match none of the patterns (if any),
+//! - for each subpattern (taking into account or-patterns), whether removing it would change
+//! anything about how the match executes, i.e. whether it is useful/not redundant.
+//!
+//! To a first approximation, the algorithm works by exploring all possible values for the type
+//! being matched on, and determining which arm(s) catch which value. To make this tractable we
+//! cleverly group together values, as we'll see below.
+//!
+//! The entrypoint of this file is the [`compute_match_usefulness`] function, which computes
+//! usefulness for each subpattern and exhaustiveness for the whole match.
+//!
+//! In this page we explain the necessary concepts to understand how the algorithm works.
+//!
+//!
+//! # Usefulness
+//!
+//! The central concept of this file is the notion of "usefulness". Given some patterns `p_1 ..
+//! p_n`, a pattern `q` is said to be *useful* 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 usefulness: a pattern in a `match` expression is redundant iff it is
+//! not useful w.r.t. the patterns above it:
+//! ```compile_fail,E0004
+//! # #![feature(exclusive_range_pattern)]
+//! # fn foo() {
+//! match Some(0u32) {
+//! Some(0..100) => {},
+//! Some(90..190) => {}, // useful: `Some(150)` is matched by this but not the branch above
+//! Some(50..150) => {}, // redundant: all the values this matches are already matched by
+//! // the branches above
+//! None => {}, // useful: `None` is matched by this but not the branches 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.
+//! ```compile_fail,E0004
+//! # fn foo(x: Option<u32>) {
+//! match x {
+//! None => {},
+//! Some(0) => {},
+//! // not exhaustive: `_` is useful because it matches `Some(1)`
+//! }
+//! # }
+//! ```
+//!
+//!
+//! # Constructors and fields
+//!
+//! In the value `Pair(Some(0), true)`, `Pair` is called the constructor of the value, and `Some(0)`
+//! and `true` are its fields. Every matcheable value can be decomposed in this way. 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`).
+//!
+//! Each constructor takes a fixed number of fields; this is called its arity. `Pair` and `(,)` have
+//! arity 2, `Some` has arity 1, `None` and `42` have arity 0. Each type has a known set of
+//! constructors. Some types have many constructors (like `u64`) or even an infinitely many (like
+//! `&str` and `&[T]`).
+//!
+//! Patterns are similar: `Pair(Some(_), _)` has constructor `Pair` and two fields. The difference
+//! is that we get some extra pattern-only constructors, namely: the wildcard `_`, variable
+//! bindings, integer ranges like `0..=10`, and variable-length slices like `[_, .., _]`. We treat
+//! or-patterns separately, see the dedicated section below.
+//!
+//! Now to check if a value `v` matches a pattern `p`, we check if `v`'s constructor matches `p`'s
+//! constructor, then recursively compare their fields if necessary. 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)`
+//!
+//! Constructors and relevant operations are defined in the [`crate::constructor`] module. A
+//! representation of patterns that uses constructors is available in [`crate::pat`]. The question
+//! of whether a constructor is matched by another one is answered by
+//! [`Constructor::is_covered_by`].
+//!
+//! Note 1: variable bindings (like the `x` in `Some(x)`) match anything, so we treat them as wildcards.
+//! Note 2: this only applies to matcheable values. For example a value of type `Rc<u64>` can't be
+//! deconstructed that way.
+//!
+//!
+//!
+//! # Specialization
+//!
+//! The examples in the previous section motivate the operation at the heart of the algorithm:
+//! "specialization". It captures this idea of "removing one layer of constructor".
+//!
+//! `specialize(c, p)` takes a value-only constructor `c` and a pattern `p`, and returns a
+//! pattern-tuple or nothing. It works as follows:
+//!
+//! - Specializing for the wrong constructor returns nothing
+//!
+//! - `specialize(None, Some(p0)) := <nothing>`
+//! - `specialize([,,,], [p0]) := <nothing>`
+//!
+//! - Specializing for the correct constructor returns a tuple of the fields
+//!
+//! - `specialize(Variant1, Variant1(p0, p1, p2)) := (p0, p1, p2)`
+//! - `specialize(Foo{ bar, baz, quz }, Foo { bar: p0, baz: p1, .. }) := (p0, p1, _)`
+//! - `specialize([,,,], [p0, .., p1]) := (p0, _, _, p1)`
+//!
+//! We get the following property: for any values `v_1, .., v_n` of appropriate types, we have:
+//! ```text
+//! matches!(c(v_1, .., v_n), p)
+//! <=> specialize(c, p) returns something
+//! && matches!((v_1, .., v_n), specialize(c, p))
+//! ```
+//!
+//! We also extend specialization to pattern-tuples by applying it to the first pattern:
+//! `specialize(c, (p_0, .., p_n)) := specialize(c, p_0) ++ (p_1, .., p_m)`
+//! where `++` is concatenation of tuples.
+//!
+//!
+//! The previous property extends to pattern-tuples:
+//! ```text
+//! matches!((c(v_1, .., v_n), w_1, .., w_m), (p_0, p_1, .., p_m))
+//! <=> specialize(c, p_0) does not error
+//! && matches!((v_1, .., v_n, w_1, .., w_m), specialize(c, (p_0, p_1, .., p_m)))
+//! ```
+//!
+//! Whether specialization returns something or not is given by [`Constructor::is_covered_by`].
+//! Specialization of a pattern is computed in [`DeconstructedPat::specialize`]. Specialization for
+//! a pattern-tuple is computed in [`PatStack::pop_head_constructor`]. Finally, specialization for a
+//! set of pattern-tuples is computed in [`Matrix::specialize_constructor`].
+//!
+//!
+//!
+//! # Undoing specialization
+//!
+//! To construct witnesses we will need an inverse of specialization. If `c` is a constructor of
+//! arity `n`, we define `unspecialize` as:
+//! `unspecialize(c, (p_1, .., p_n, q_1, .., q_m)) := (c(p_1, .., p_n), q_1, .., q_m)`.
+//!
+//! This is done for a single witness-tuple in [`WitnessStack::apply_constructor`], and for a set of
+//! witness-tuples in [`WitnessMatrix::apply_constructor`].
+//!
+//!
+//!
+//! # Computing usefulness
+//!
+//! We now present a naive version of the algorithm for computing usefulness. From now on we operate
+//! on pattern-tuples.
+//!
+//! Let `pt_1, .., pt_n` and `qt` be length-m tuples of patterns for the same type `(T_1, .., T_m)`.
+//! We compute `usefulness(tp_1, .., tp_n, tq)` as follows:
+//!
+//! - Base case: `m == 0`.
+//! The pattern-tuples are all empty, i.e. they're all `()`. Thus `tq` is useful iff there are
+//! no rows above it, i.e. if `n == 0`. In that case we return `()` as a witness-tuple of
+//! usefulness of `tq`.
+//!
+//! - Inductive case: `m > 0`.
+//! In this naive version, we list all the possible constructors for values of type `T1` (we
+//! will be more clever in the next section).
+//!
+//! - For each such constructor `c` for which `specialize(c, tq)` is not nothing:
+//! - We recursively compute `usefulness(specialize(c, tp_1) ... specialize(c, tp_n), specialize(c, tq))`,
+//! where we discard any `specialize(c, p_i)` that returns nothing.
+//! - For each witness-tuple `w` found, we apply `unspecialize(c, w)` to it.
+//!
+//! - We return the all the witnesses found, if any.
+//!
+//!
+//! Let's take the following example:
+//! ```compile_fail,E0004
+//! # enum Enum { Variant1(()), Variant2(Option<bool>, u32)}
+//! # use Enum::*;
+//! # fn foo(x: Enum) {
+//! match x {
+//! Variant1(_) => {} // `p1`
+//! Variant2(None, 0) => {} // `p2`
+//! Variant2(Some(_), 0) => {} // `q`
+//! }
+//! # }
+//! ```
+//!
+//! To compute the usefulness of `q`, we would proceed as follows:
+//! ```text
+//! Start:
+//! `tp1 = [Variant1(_)]`
+//! `tp2 = [Variant2(None, 0)]`
+//! `tq = [Variant2(Some(true), 0)]`
+//!
+//! Constructors are `Variant1` and `Variant2`. Only `Variant2` can specialize `tq`.
+//! Specialize with `Variant2`:
+//! `tp2 = [None, 0]`
+//! `tq = [Some(true), 0]`
+//!
+//! Constructors are `None` and `Some`. Only `Some` can specialize `tq`.
+//! Specialize with `Some`:
+//! `tq = [true, 0]`
+//!
+//! Constructors are `false` and `true`. Only `true` can specialize `tq`.
+//! Specialize with `true`:
+//! `tq = [0]`
+//!
+//! Constructors are `0`, `1`, .. up to infinity. Only `0` can specialize `tq`.
+//! Specialize with `0`:
+//! `tq = []`
+//!
+//! m == 0 and n == 0, so `tq` is useful with witness `[]`.
+//! `witness = []`
+//!
+//! Unspecialize with `0`:
+//! `witness = [0]`
+//! Unspecialize with `true`:
+//! `witness = [true, 0]`
+//! Unspecialize with `Some`:
+//! `witness = [Some(true), 0]`
+//! Unspecialize with `Variant2`:
+//! `witness = [Variant2(Some(true), 0)]`
+//! ```
+//!
+//! Therefore `usefulness(tp_1, tp_2, tq)` returns the single witness-tuple `[Variant2(Some(true), 0)]`.
+//!
+//!
+//! Computing the set of constructors for a type is done in [`TypeCx::ctors_for_ty`]. See
+//! the following sections for more accurate versions of the algorithm and corresponding links.
+//!
+//!
+//!
+//! # Computing usefulness and exhaustiveness in one go
+//!
+//! The algorithm we have described so far computes usefulness of each pattern in turn, and ends by
+//! checking if `_` is useful to determine exhaustiveness of the whole match. In practice, instead
+//! of doing "for each pattern { for each constructor { ... } }", we do "for each constructor { for
+//! each pattern { ... } }". This allows us to compute everything in one go.
+//!
+//! [`Matrix`] stores the set of pattern-tuples under consideration. We track usefulness of each
+//! row mutably in the matrix as we go along. We ignore witnesses of usefulness of the match rows.
+//! We gather witnesses of the usefulness of `_` in [`WitnessMatrix`]. The algorithm that computes
+//! all this is in [`compute_exhaustiveness_and_usefulness`].
+//!
+//! See the full example at the bottom of this documentation.
+//!
+//!
+//!
+//! # 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 final
+//! clever idea for this algorithm is that we can group together constructors that behave the same.
+//!
+//! Examples:
+//! ```compile_fail,E0004
+//! match (0, false) {
+//! (0 ..=100, true) => {}
+//! (50..=150, false) => {}
+//! (0 ..=200, _) => {}
+//! }
+//! ```
+//!
+//! In this example, trying any of `0`, `1`, .., `49` will give the same specialized matrix, and
+//! thus the same usefulness/exhaustiveness results. We can thus accelerate the algorithm by
+//! trying them all at once. Here in fact, the only cases we need to consider are: `0..50`,
+//! `50..=100`, `101..=150`,`151..=200` and `201..`.
+//!
+//! ```
+//! enum Direction { North, South, East, West }
+//! # let wind = (Direction::North, 0u8);
+//! match wind {
+//! (Direction::North, 50..) => {}
+//! (_, _) => {}
+//! }
+//! ```
+//!
+//! In this example, trying any of `South`, `East`, `West` will give the same specialized matrix. By
+//! the same reasoning, we only need to try two cases: `North`, and "everything else".
+//!
+//! We call _constructor splitting_ the operation that computes such a minimal set of cases to try.
+//! This is done in [`ConstructorSet::split`] and explained in [`crate::constructor`].
+//!
+//!
+//!
+//! # `Missing` and relevancy
+//!
+//! ## Relevant values
+//!
+//! Take the following example:
+//!
+//! ```compile_fail,E0004
+//! # let foo = (true, true);
+//! match foo {
+//! (true, _) => 1,
+//! (_, true) => 2,
+//! };
+//! ```
+//!
+//! Consider the value `(true, true)`:
+//! - Row 2 does not distinguish `(true, true)` and `(false, true)`;
+//! - `false` does not show up in the first column of the match, so without knowing anything else we
+//! can deduce that `(false, true)` matches the same or fewer rows than `(true, true)`.
+//!
+//! Using those two facts together, we deduce that `(true, true)` will not give us more usefulness
+//! information about row 2 than `(false, true)` would. We say that "`(true, true)` is made
+//! irrelevant for row 2 by `(false, true)`". We will use this idea to prune the search tree.
+//!
+//!
+//! ## Computing relevancy
+//!
+//! We now generalize from the above example to approximate relevancy in a simple way. Note that we
+//! will only compute an approximation: we can sometimes determine when a case is irrelevant, but
+//! computing this precisely is at least as hard as computing usefulness.
+//!
+//! Our computation of relevancy relies on the `Missing` constructor. As explained in
+//! [`crate::constructor`], `Missing` represents the constructors not present in a given column. For
+//! example in the following:
+//!
+//! ```compile_fail,E0004
+//! enum Direction { North, South, East, West }
+//! # let wind = (Direction::North, 0u8);
+//! match wind {
+//! (Direction::North, _) => 1,
+//! (_, 50..) => 2,
+//! };
+//! ```
+//!
+//! Here `South`, `East` and `West` are missing in the first column, and `0..50` is missing in the
+//! second. Both of these sets are represented by `Constructor::Missing` in their corresponding
+//! column.
+//!
+//! We then compute relevancy as follows: during the course of the algorithm, for a row `r`:
+//! - if `r` has a wildcard in the first column;
+//! - and some constructors are missing in that column;
+//! - then any `c != Missing` is considered irrelevant for row `r`.
+//!
+//! By this we mean that continuing the algorithm by specializing with `c` is guaranteed not to
+//! contribute more information about the usefulness of row `r` than what we would get by
+//! specializing with `Missing`. The argument is the same as in the previous subsection.
+//!
+//! Once we've specialized by a constructor `c` that is irrelevant for row `r`, we're guaranteed to
+//! only explore values irrelevant for `r`. If we then ever reach a point where we're only exploring
+//! values that are irrelevant to all of the rows (including the virtual wildcard row used for
+//! exhaustiveness), we skip that case entirely.
+//!
+//!
+//! ## Example
+//!
+//! Let's go through a variation on the first example:
+//!
+//! ```compile_fail,E0004
+//! # let foo = (true, true, true);
+//! match foo {
+//! (true, _, true) => 1,
+//! (_, true, _) => 2,
+//! };
+//! ```
+//!
+//! ```text
+//! ┐ Patterns:
+//! │ 1. `[(true, _, true)]`
+//! │ 2. `[(_, true, _)]`
+//! │ 3. `[_]` // virtual extra wildcard row
+//! │
+//! │ Specialize with `(,,)`:
+//! ├─┐ Patterns:
+//! │ │ 1. `[true, _, true]`
+//! │ │ 2. `[_, true, _]`
+//! │ │ 3. `[_, _, _]`
+//! │ │
+//! │ │ There are missing constructors in the first column (namely `false`), hence
+//! │ │ `true` is irrelevant for rows 2 and 3.
+//! │ │
+//! │ │ Specialize with `true`:
+//! │ ├─┐ Patterns:
+//! │ │ │ 1. `[_, true]`
+//! │ │ │ 2. `[true, _]` // now exploring irrelevant cases
+//! │ │ │ 3. `[_, _]` // now exploring irrelevant cases
+//! │ │ │
+//! │ │ │ There are missing constructors in the first column (namely `false`), hence
+//! │ │ │ `true` is irrelevant for rows 1 and 3.
+//! │ │ │
+//! │ │ │ Specialize with `true`:
+//! │ │ ├─┐ Patterns:
+//! │ │ │ │ 1. `[true]` // now exploring irrelevant cases
+//! │ │ │ │ 2. `[_]` // now exploring irrelevant cases
+//! │ │ │ │ 3. `[_]` // now exploring irrelevant cases
+//! │ │ │ │
+//! │ │ │ │ The current case is irrelevant for all rows: we backtrack immediately.
+//! │ │ ├─┘
+//! │ │ │
+//! │ │ │ Specialize with `false`:
+//! │ │ ├─┐ Patterns:
+//! │ │ │ │ 1. `[true]`
+//! │ │ │ │ 3. `[_]` // now exploring irrelevant cases
+//! │ │ │ │
+//! │ │ │ │ Specialize with `true`:
+//! │ │ │ ├─┐ Patterns:
+//! │ │ │ │ │ 1. `[]`
+//! │ │ │ │ │ 3. `[]` // now exploring irrelevant cases
+//! │ │ │ │ │
+//! │ │ │ │ │ Row 1 is therefore useful.
+//! │ │ │ ├─┘
+//! <etc...>
+//! ```
+//!
+//! Relevancy allowed us to skip the case `(true, true, _)` entirely. In some cases this pruning can
+//! give drastic speedups. The case this was built for is the following (#118437):
+//!
+//! ```ignore(illustrative)
+//! match foo {
+//! (true, _, _, _, ..) => 1,
+//! (_, true, _, _, ..) => 2,
+//! (_, _, true, _, ..) => 3,
+//! (_, _, _, true, ..) => 4,
+//! ...
+//! }
+//! ```
+//!
+//! Without considering relevancy, we would explore all 2^n combinations of the `true` and `Missing`
+//! constructors. Relevancy tells us that e.g. `(true, true, false, false, false, ...)` is
+//! irrelevant for all the rows. This allows us to skip all cases with more than one `true`
+//! constructor, changing the runtime from exponential to linear.
+//!
+//!
+//! ## Relevancy and exhaustiveness
+//!
+//! For exhaustiveness, we do something slightly different w.r.t relevancy: we do not report
+//! witnesses of non-exhaustiveness that are irrelevant for the virtual wildcard row. For example,
+//! in:
+//!
+//! ```ignore(illustrative)
+//! match foo {
+//! (true, true) => {}
+//! }
+//! ```
+//!
+//! we only report `(false, _)` as missing. This was a deliberate choice made early in the
+//! development of rust, for diagnostic and performance purposes. As showed in the previous section,
+//! ignoring irrelevant cases preserves usefulness, so this choice still correctly computes whether
+//! a match is exhaustive.
+//!
+//!
+//!
+//! # Or-patterns
+//!
+//! What we have described so far works well if there are no or-patterns. To handle them, if the
+//! first pattern of a row in the matrix is an or-pattern, we expand it by duplicating the rest of
+//! the row as necessary. This is handled automatically in [`Matrix`].
+//!
+//! This makes usefulness tracking subtle, because we also want to compute whether an alternative
+//! of an or-pattern is redundant, e.g. in `Some(_) | Some(0)`. We track usefulness of each
+//! subpattern by interior mutability in [`DeconstructedPat`] with `set_useful`/`is_useful`.
+//!
+//! It's unfortunate that we have to use interior mutability, but believe me (Nadrieril), I have
+//! tried [other](https://github.com/rust-lang/rust/pull/80104)
+//! [solutions](https://github.com/rust-lang/rust/pull/80632) and nothing is remotely as simple.
+//!
+//!
+//!
+//! # Constants and opaques
+//!
+//! 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 the corresponding patterns by a previous phase. 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. The situation around this is currently
+//! unclear and the lang team is working on clarifying what we want to do there. In any case, there
+//! are constants we will not turn into patterns. We capture these with `Constructor::Opaque`. These
+//! `Opaque` patterns do not participate in exhaustiveness, specialization or overlap checking.
+//!
+//!
+//!
+//! # Usefulness vs reachability, validity, and empty patterns
+//!
+//! This is likely the subtlest aspect of the algorithm. To be fully precise, a match doesn't
+//! operate on a value, it operates on a place. In certain unsafe circumstances, it is possible for
+//! a place to not contain valid data for its type. This has subtle consequences for empty types.
+//! Take the following:
+//!
+//! ```rust
+//! enum Void {}
+//! let x: u8 = 0;
+//! let ptr: *const Void = &x as *const u8 as *const Void;
+//! unsafe {
+//! match *ptr {
+//! _ => println!("Reachable!"),
+//! }
+//! }
+//! ```
+//!
+//! In this example, `ptr` is a valid pointer pointing to a place with invalid data. The `_` pattern
+//! does not look at the contents of `*ptr`, so this is ok and the arm is taken. In other words,
+//! despite the place we are inspecting being of type `Void`, there is a reachable arm. If the
+//! arm had a binding however:
+//!
+//! ```rust
+//! # #[derive(Copy, Clone)]
+//! # enum Void {}
+//! # let x: u8 = 0;
+//! # let ptr: *const Void = &x as *const u8 as *const Void;
+//! # unsafe {
+//! match *ptr {
+//! _a => println!("Unreachable!"),
+//! }
+//! # }
+//! ```
+//!
+//! Here the binding loads the value of type `Void` from the `*ptr` place. In this example, this
+//! causes UB since the data is not valid. In the general case, this asserts validity of the data at
+//! `*ptr`. Either way, this arm will never be taken.
+//!
+//! Finally, let's consider the empty match `match *ptr {}`. If we consider this exhaustive, then
+//! having invalid data at `*ptr` is invalid. In other words, the empty match is semantically
+//! equivalent to the `_a => ...` match. In the interest of explicitness, we prefer the case with an
+//! arm, hence we won't tell the user to remove the `_a` arm. In other words, the `_a` arm is
+//! unreachable yet not redundant. This is why we lint on redundant arms rather than unreachable
+//! arms, despite the fact that the lint says "unreachable".
+//!
+//! These considerations only affects certain places, namely those that can contain non-valid data
+//! without UB. These are: pointer dereferences, reference dereferences, and union field accesses.
+//! We track in the algorithm whether a given place is known to contain valid data. This is done
+//! first by inspecting the scrutinee syntactically (which gives us `cx.known_valid_scrutinee`), and
+//! then by tracking validity of each column of the matrix (which correspond to places) as we
+//! recurse into subpatterns. That second part is done through [`ValidityConstraint`], most notably
+//! [`ValidityConstraint::specialize`].
+//!
+//! Having said all that, in practice we don't fully follow what's been presented in this section.
+//! Under `exhaustive_patterns`, we allow omitting empty arms even in `!known_valid` places, for
+//! backwards-compatibility until we have a better alternative. Without `exhaustive_patterns`, we
+//! mostly treat empty types as inhabited, except specifically a non-nested `!` or empty enum. In
+//! this specific case we also allow the empty match regardless of place validity, for
+//! backwards-compatibility. Hopefully we can eventually deprecate this.
+//!
+//!
+//!
+//! # Full example
+//!
+//! We illustrate a full run of the algorithm on the following match.
+//!
+//! ```compile_fail,E0004
+//! # struct Pair(Option<u32>, bool);
+//! # fn foo(x: Pair) -> u32 {
+//! match x {
+//! Pair(Some(0), _) => 1,
+//! Pair(_, false) => 2,
+//! Pair(Some(0), false) => 3,
+//! }
+//! # }
+//! ```
+//!
+//! We keep track of the original row for illustration purposes, this is not what the algorithm
+//! actually does (it tracks usefulness as a boolean on each row).
+//!
+//! ```text
+//! ┐ Patterns:
+//! │ 1. `[Pair(Some(0), _)]`
+//! │ 2. `[Pair(_, false)]`
+//! │ 3. `[Pair(Some(0), false)]`
+//! │
+//! │ Specialize with `Pair`:
+//! ├─┐ Patterns:
+//! │ │ 1. `[Some(0), _]`
+//! │ │ 2. `[_, false]`
+//! │ │ 3. `[Some(0), false]`
+//! │ │
+//! │ │ Specialize with `Some`:
+//! │ ├─┐ Patterns:
+//! │ │ │ 1. `[0, _]`
+//! │ │ │ 2. `[_, false]`
+//! │ │ │ 3. `[0, false]`
+//! │ │ │
+//! │ │ │ Specialize with `0`:
+//! │ │ ├─┐ Patterns:
+//! │ │ │ │ 1. `[_]`
+//! │ │ │ │ 3. `[false]`
+//! │ │ │ │
+//! │ │ │ │ Specialize with `true`:
+//! │ │ │ ├─┐ Patterns:
+//! │ │ │ │ │ 1. `[]`
+//! │ │ │ │ │
+//! │ │ │ │ │ We note arm 1 is useful (by `Pair(Some(0), true)`).
+//! │ │ │ ├─┘
+//! │ │ │ │
+//! │ │ │ │ Specialize with `false`:
+//! │ │ │ ├─┐ Patterns:
+//! │ │ │ │ │ 1. `[]`
+//! │ │ │ │ │ 3. `[]`
+//! │ │ │ │ │
+//! │ │ │ │ │ We note arm 1 is useful (by `Pair(Some(0), false)`).
+//! │ │ │ ├─┘
+//! │ │ ├─┘
+//! │ │ │
+//! │ │ │ Specialize with `1..`:
+//! │ │ ├─┐ Patterns:
+//! │ │ │ │ 2. `[false]`
+//! │ │ │ │
+//! │ │ │ │ Specialize with `true`:
+//! │ │ │ ├─┐ Patterns:
+//! │ │ │ │ │ // no rows left
+//! │ │ │ │ │
+//! │ │ │ │ │ We have found an unmatched value (`Pair(Some(1..), true)`)! This gives us a witness.
+//! │ │ │ │ │ New witnesses:
+//! │ │ │ │ │ `[]`
+//! │ │ │ ├─┘
+//! │ │ │ │ Unspecialize new witnesses with `true`:
+//! │ │ │ │ `[true]`
+//! │ │ │ │
+//! │ │ │ │ Specialize with `false`:
+//! │ │ │ ├─┐ Patterns:
+//! │ │ │ │ │ 2. `[]`
+//! │ │ │ │ │
+//! │ │ │ │ │ We note arm 2 is useful (by `Pair(Some(1..), false)`).
+//! │ │ │ ├─┘
+//! │ │ │ │
+//! │ │ │ │ Total witnesses for `1..`:
+//! │ │ │ │ `[true]`
+//! │ │ ├─┘
+//! │ │ │ Unspecialize new witnesses with `1..`:
+//! │ │ │ `[1.., true]`
+//! │ │ │
+//! │ │ │ Total witnesses for `Some`:
+//! │ │ │ `[1.., true]`
+//! │ ├─┘
+//! │ │ Unspecialize new witnesses with `Some`:
+//! │ │ `[Some(1..), true]`
+//! │ │
+//! │ │ Specialize with `None`:
+//! │ ├─┐ Patterns:
+//! │ │ │ 2. `[false]`
+//! │ │ │
+//! │ │ │ Specialize with `true`:
+//! │ │ ├─┐ Patterns:
+//! │ │ │ │ // no rows left
+//! │ │ │ │
+//! │ │ │ │ We have found an unmatched value (`Pair(None, true)`)! This gives us a witness.
+//! │ │ │ │ New witnesses:
+//! │ │ │ │ `[]`
+//! │ │ ├─┘
+//! │ │ │ Unspecialize new witnesses with `true`:
+//! │ │ │ `[true]`
+//! │ │ │
+//! │ │ │ Specialize with `false`:
+//! │ │ ├─┐ Patterns:
+//! │ │ │ │ 2. `[]`
+//! │ │ │ │
+//! │ │ │ │ We note arm 2 is useful (by `Pair(None, false)`).
+//! │ │ ├─┘
+//! │ │ │
+//! │ │ │ Total witnesses for `None`:
+//! │ │ │ `[true]`
+//! │ ├─┘
+//! │ │ Unspecialize new witnesses with `None`:
+//! │ │ `[None, true]`
+//! │ │
+//! │ │ Total witnesses for `Pair`:
+//! │ │ `[Some(1..), true]`
+//! │ │ `[None, true]`
+//! ├─┘
+//! │ Unspecialize new witnesses with `Pair`:
+//! │ `[Pair(Some(1..), true)]`
+//! │ `[Pair(None, true)]`
+//! │
+//! │ Final witnesses:
+//! │ `[Pair(Some(1..), true)]`
+//! │ `[Pair(None, true)]`
+//! ┘
+//! ```
+//!
+//! We conclude:
+//! - Arm 3 is redundant (it was never marked as useful);
+//! - The match is not exhaustive;
+//! - Adding arms with `Pair(Some(1..), true)` and `Pair(None, true)` would make the match exhaustive.
+//!
+//! Note that when we're deep in the algorithm, we don't know what specialization steps got us here.
+//! We can only figure out what our witnesses correspond to by unspecializing back up the stack.
+//!
+//!
+//! # Tests
+//!
+//! 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 crucially depend on a particular feature like `or_patterns`.
+
+use smallvec::{smallvec, SmallVec};
+use std::fmt;
+
+use crate::constructor::{Constructor, ConstructorSet};
+use crate::pat::{DeconstructedPat, WitnessPat};
+use crate::{Captures, MatchArm, MatchCtxt, TypeCx, TypedArena};
+
+use self::ValidityConstraint::*;
+
+#[cfg(feature = "rustc")]
+use rustc_data_structures::stack::ensure_sufficient_stack;
+#[cfg(not(feature = "rustc"))]
+pub fn ensure_sufficient_stack<R>(f: impl FnOnce() -> R) -> R {
+ f()
+}
+
+/// Context that provides information local to a place under investigation.
+#[derive(Clone)]
+pub(crate) struct PlaceCtxt<'a, 'p, Cx: TypeCx> {
+ pub(crate) mcx: MatchCtxt<'a, 'p, Cx>,
+ /// Type of the place under investigation.
+ pub(crate) ty: Cx::Ty,
+ /// Whether the place is the original scrutinee place, as opposed to a subplace of it.
+ pub(crate) is_scrutinee: bool,
+}
+
+impl<'a, 'p, Cx: TypeCx> PlaceCtxt<'a, 'p, Cx> {
+ /// A `PlaceCtxt` when code other than `is_useful` needs one.
+ #[cfg_attr(not(feature = "rustc"), allow(dead_code))]
+ pub(crate) fn new_dummy(mcx: MatchCtxt<'a, 'p, Cx>, ty: Cx::Ty) -> Self {
+ PlaceCtxt { mcx, ty, is_scrutinee: false }
+ }
+
+ pub(crate) fn ctor_arity(&self, ctor: &Constructor<Cx>) -> usize {
+ self.mcx.tycx.ctor_arity(ctor, self.ty)
+ }
+ pub(crate) fn ctor_sub_tys(&self, ctor: &Constructor<Cx>) -> &[Cx::Ty] {
+ self.mcx.tycx.ctor_sub_tys(ctor, self.ty)
+ }
+ pub(crate) fn ctors_for_ty(&self) -> ConstructorSet<Cx> {
+ self.mcx.tycx.ctors_for_ty(self.ty)
+ }
+}
+
+impl<'a, 'p, Cx: TypeCx> Copy for PlaceCtxt<'a, 'p, Cx> {}
+
+impl<'a, 'p, Cx: TypeCx> fmt::Debug for PlaceCtxt<'a, 'p, Cx> {
+ fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+ f.debug_struct("PlaceCtxt").field("ty", &self.ty).finish()
+ }
+}
+
+/// Serves two purposes:
+/// - in a wildcard, tracks whether the wildcard matches only valid values (i.e. is a binding `_a`)
+/// or also invalid values (i.e. is a true `_` pattern).
+/// - in the matrix, track whether a given place (aka column) is known to contain a valid value or
+/// not.
+#[derive(Debug, Copy, Clone, PartialEq, Eq)]
+pub enum ValidityConstraint {
+ ValidOnly,
+ MaybeInvalid,
+ /// Option for backwards compatibility: the place is not known to be valid but we allow omitting
+ /// `useful && !reachable` arms anyway.
+ MaybeInvalidButAllowOmittingArms,
+}
+
+impl ValidityConstraint {
+ pub fn from_bool(is_valid_only: bool) -> Self {
+ if is_valid_only { ValidOnly } else { MaybeInvalid }
+ }
+
+ fn allow_omitting_side_effecting_arms(self) -> Self {
+ match self {
+ MaybeInvalid | MaybeInvalidButAllowOmittingArms => MaybeInvalidButAllowOmittingArms,
+ // There are no side-effecting empty arms here, nothing to do.
+ ValidOnly => ValidOnly,
+ }
+ }
+
+ fn is_known_valid(self) -> bool {
+ matches!(self, ValidOnly)
+ }
+ fn allows_omitting_empty_arms(self) -> bool {
+ matches!(self, ValidOnly | MaybeInvalidButAllowOmittingArms)
+ }
+
+ /// If the place has validity given by `self` and we read that the value at the place has
+ /// constructor `ctor`, this computes what we can assume about the validity of the constructor
+ /// fields.
+ ///
+ /// Pending further opsem decisions, the current behavior is: validity is preserved, except
+ /// inside `&` and union fields where validity is reset to `MaybeInvalid`.
+ fn specialize<Cx: TypeCx>(self, ctor: &Constructor<Cx>) -> Self {
+ // We preserve validity except when we go inside a reference or a union field.
+ if matches!(ctor, Constructor::Ref | Constructor::UnionField) {
+ // Validity of `x: &T` does not imply validity of `*x: T`.
+ MaybeInvalid
+ } else {
+ self
+ }
+ }
+}
+
+impl fmt::Display for ValidityConstraint {
+ fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+ let s = match self {
+ ValidOnly => "✓",
+ MaybeInvalid | MaybeInvalidButAllowOmittingArms => "?",
+ };
+ write!(f, "{s}")
+ }
+}
+
+/// Represents a pattern-tuple under investigation.
+// The three lifetimes are:
+// - 'a allocated by us
+// - 'p coming from the input
+// - Cx global compilation context
+#[derive(Clone)]
+struct PatStack<'a, 'p, Cx: TypeCx> {
+ // Rows of len 1 are very common, which is why `SmallVec[_; 2]` works well.
+ pats: SmallVec<[&'a DeconstructedPat<'p, Cx>; 2]>,
+ /// Sometimes we know that as far as this row is concerned, the current case is already handled
+ /// by a different, more general, case. When the case is irrelevant for all rows this allows us
+ /// to skip a case entirely. This is purely an optimization. See at the top for details.
+ relevant: bool,
+}
+
+impl<'a, 'p, Cx: TypeCx> PatStack<'a, 'p, Cx> {
+ fn from_pattern(pat: &'a DeconstructedPat<'p, Cx>) -> Self {
+ PatStack { pats: smallvec![pat], relevant: true }
+ }
+
+ fn is_empty(&self) -> bool {
+ self.pats.is_empty()
+ }
+
+ fn len(&self) -> usize {
+ self.pats.len()
+ }
+
+ fn head(&self) -> &'a DeconstructedPat<'p, Cx> {
+ self.pats[0]
+ }
+
+ fn iter<'b>(&'b self) -> impl Iterator<Item = &'a DeconstructedPat<'p, Cx>> + Captures<'b> {
+ self.pats.iter().copied()
+ }
+
+ // Recursively expand the first or-pattern into its subpatterns. Only useful if the pattern is
+ // an or-pattern. Panics if `self` is empty.
+ fn expand_or_pat<'b>(&'b self) -> impl Iterator<Item = PatStack<'a, 'p, Cx>> + Captures<'b> {
+ self.head().flatten_or_pat().into_iter().map(move |pat| {
+ let mut new = self.clone();
+ new.pats[0] = pat;
+ new
+ })
+ }
+
+ /// This computes `specialize(ctor, self)`. See top of the file for explanations.
+ /// Only call if `ctor.is_covered_by(self.head().ctor())` is true.
+ fn pop_head_constructor(
+ &self,
+ pcx: &PlaceCtxt<'a, 'p, Cx>,
+ ctor: &Constructor<Cx>,
+ ctor_is_relevant: bool,
+ ) -> PatStack<'a, 'p, Cx> {
+ // We pop the head pattern and push the new fields extracted from the arguments of
+ // `self.head()`.
+ let mut new_pats = self.head().specialize(pcx, ctor);
+ new_pats.extend_from_slice(&self.pats[1..]);
+ // `ctor` is relevant for this row if it is the actual constructor of this row, or if the
+ // row has a wildcard and `ctor` is relevant for wildcards.
+ let ctor_is_relevant =
+ !matches!(self.head().ctor(), Constructor::Wildcard) || ctor_is_relevant;
+ PatStack { pats: new_pats, relevant: self.relevant && ctor_is_relevant }
+ }
+}
+
+impl<'a, 'p, Cx: TypeCx> fmt::Debug for PatStack<'a, 'p, Cx> {
+ fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+ // We pretty-print similarly to the `Debug` impl of `Matrix`.
+ write!(f, "+")?;
+ for pat in self.iter() {
+ write!(f, " {pat:?} +")?;
+ }
+ Ok(())
+ }
+}
+
+/// A row of the matrix.
+#[derive(Clone)]
+struct MatrixRow<'a, 'p, Cx: TypeCx> {
+ // The patterns in the row.
+ pats: PatStack<'a, 'p, Cx>,
+ /// Whether the original arm had a guard. This is inherited when specializing.
+ is_under_guard: bool,
+ /// When we specialize, we remember which row of the original matrix produced a given row of the
+ /// specialized matrix. When we unspecialize, we use this to propagate usefulness back up the
+ /// callstack.
+ parent_row: usize,
+ /// False when the matrix is just built. This is set to `true` by
+ /// [`compute_exhaustiveness_and_usefulness`] if the arm is found to be useful.
+ /// This is reset to `false` when specializing.
+ useful: bool,
+}
+
+impl<'a, 'p, Cx: TypeCx> MatrixRow<'a, 'p, Cx> {
+ fn is_empty(&self) -> bool {
+ self.pats.is_empty()
+ }
+
+ fn len(&self) -> usize {
+ self.pats.len()
+ }
+
+ fn head(&self) -> &'a DeconstructedPat<'p, Cx> {
+ self.pats.head()
+ }
+
+ fn iter<'b>(&'b self) -> impl Iterator<Item = &'a DeconstructedPat<'p, Cx>> + Captures<'b> {
+ self.pats.iter()
+ }
+
+ // Recursively expand the first or-pattern into its subpatterns. Only useful if the pattern is
+ // an or-pattern. Panics if `self` is empty.
+ fn expand_or_pat<'b>(&'b self) -> impl Iterator<Item = MatrixRow<'a, 'p, Cx>> + Captures<'b> {
+ self.pats.expand_or_pat().map(|patstack| MatrixRow {
+ pats: patstack,
+ parent_row: self.parent_row,
+ is_under_guard: self.is_under_guard,
+ useful: false,
+ })
+ }
+
+ /// This computes `specialize(ctor, self)`. See top of the file for explanations.
+ /// Only call if `ctor.is_covered_by(self.head().ctor())` is true.
+ fn pop_head_constructor(
+ &self,
+ pcx: &PlaceCtxt<'a, 'p, Cx>,
+ ctor: &Constructor<Cx>,
+ ctor_is_relevant: bool,
+ parent_row: usize,
+ ) -> MatrixRow<'a, 'p, Cx> {
+ MatrixRow {
+ pats: self.pats.pop_head_constructor(pcx, ctor, ctor_is_relevant),
+ parent_row,
+ is_under_guard: self.is_under_guard,
+ useful: false,
+ }
+ }
+}
+
+impl<'a, 'p, Cx: TypeCx> fmt::Debug for MatrixRow<'a, 'p, Cx> {
+ fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+ self.pats.fmt(f)
+ }
+}
+
+/// A 2D matrix. Represents a list of pattern-tuples under investigation.
+///
+/// Invariant: each row must have the same length, and each column must have the same type.
+///
+/// Invariant: the first column must not contain or-patterns. This is handled by
+/// [`Matrix::expand_and_push`].
+///
+/// In fact each column corresponds to a place inside the scrutinee of the match. E.g. after
+/// specializing `(,)` and `Some` on a pattern of type `(Option<u32>, bool)`, the first column of
+/// the matrix will correspond to `scrutinee.0.Some.0` and the second column to `scrutinee.1`.
+#[derive(Clone)]
+struct Matrix<'a, 'p, Cx: TypeCx> {
+ /// Vector of rows. The rows must form a rectangular 2D array. Moreover, all the patterns of
+ /// each column must have the same type. Each column corresponds to a place within the
+ /// scrutinee.
+ rows: Vec<MatrixRow<'a, 'p, Cx>>,
+ /// Stores an extra fictitious row full of wildcards. Mostly used to keep track of the type of
+ /// each column. This must obey the same invariants as the real rows.
+ wildcard_row: PatStack<'a, 'p, Cx>,
+ /// Track for each column/place whether it contains a known valid value.
+ place_validity: SmallVec<[ValidityConstraint; 2]>,
+}
+
+impl<'a, 'p, Cx: TypeCx> Matrix<'a, 'p, Cx> {
+ /// Pushes a new row to the matrix. If the row starts with an or-pattern, this recursively
+ /// expands it. Internal method, prefer [`Matrix::new`].
+ fn expand_and_push(&mut self, row: MatrixRow<'a, 'p, Cx>) {
+ if !row.is_empty() && row.head().is_or_pat() {
+ // Expand nested or-patterns.
+ for new_row in row.expand_or_pat() {
+ self.rows.push(new_row);
+ }
+ } else {
+ self.rows.push(row);
+ }
+ }
+
+ /// Build a new matrix from an iterator of `MatchArm`s.
+ fn new(
+ wildcard_arena: &'a TypedArena<DeconstructedPat<'p, Cx>>,
+ arms: &'a [MatchArm<'p, Cx>],
+ scrut_ty: Cx::Ty,
+ scrut_validity: ValidityConstraint,
+ ) -> Self {
+ let wild_pattern =
+ wildcard_arena.alloc(DeconstructedPat::wildcard(scrut_ty, Default::default()));
+ let wildcard_row = PatStack::from_pattern(wild_pattern);
+ let mut matrix = Matrix {
+ rows: Vec::with_capacity(arms.len()),
+ wildcard_row,
+ place_validity: smallvec![scrut_validity],
+ };
+ for (row_id, arm) in arms.iter().enumerate() {
+ let v = MatrixRow {
+ pats: PatStack::from_pattern(arm.pat),
+ parent_row: row_id, // dummy, we won't read it
+ is_under_guard: arm.has_guard,
+ useful: false,
+ };
+ matrix.expand_and_push(v);
+ }
+ matrix
+ }
+
+ fn head_ty(&self) -> Option<Cx::Ty> {
+ if self.column_count() == 0 {
+ return None;
+ }
+
+ let mut ty = self.wildcard_row.head().ty();
+ // If the type is opaque and it is revealed anywhere in the column, we take the revealed
+ // version. Otherwise we could encounter constructors for the revealed type and crash.
+ if Cx::is_opaque_ty(ty) {
+ for pat in self.heads() {
+ let pat_ty = pat.ty();
+ if !Cx::is_opaque_ty(pat_ty) {
+ ty = pat_ty;
+ break;
+ }
+ }
+ }
+ Some(ty)
+ }
+ fn column_count(&self) -> usize {
+ self.wildcard_row.len()
+ }
+
+ fn rows<'b>(
+ &'b self,
+ ) -> impl Iterator<Item = &'b MatrixRow<'a, 'p, Cx>> + Clone + DoubleEndedIterator + ExactSizeIterator
+ {
+ self.rows.iter()
+ }
+ fn rows_mut<'b>(
+ &'b mut self,
+ ) -> impl Iterator<Item = &'b mut MatrixRow<'a, 'p, Cx>> + DoubleEndedIterator + ExactSizeIterator
+ {
+ self.rows.iter_mut()
+ }
+
+ /// Iterate over the first pattern of each row.
+ fn heads<'b>(
+ &'b self,
+ ) -> impl Iterator<Item = &'b DeconstructedPat<'p, Cx>> + Clone + Captures<'a> {
+ self.rows().map(|r| r.head())
+ }
+
+ /// This computes `specialize(ctor, self)`. See top of the file for explanations.
+ fn specialize_constructor(
+ &self,
+ pcx: &PlaceCtxt<'a, 'p, Cx>,
+ ctor: &Constructor<Cx>,
+ ctor_is_relevant: bool,
+ ) -> Matrix<'a, 'p, Cx> {
+ let wildcard_row = self.wildcard_row.pop_head_constructor(pcx, ctor, ctor_is_relevant);
+ let new_validity = self.place_validity[0].specialize(ctor);
+ let new_place_validity = std::iter::repeat(new_validity)
+ .take(ctor.arity(pcx))
+ .chain(self.place_validity[1..].iter().copied())
+ .collect();
+ let mut matrix =
+ Matrix { rows: Vec::new(), wildcard_row, place_validity: new_place_validity };
+ for (i, row) in self.rows().enumerate() {
+ if ctor.is_covered_by(pcx, row.head().ctor()) {
+ let new_row = row.pop_head_constructor(pcx, ctor, ctor_is_relevant, i);
+ matrix.expand_and_push(new_row);
+ }
+ }
+ matrix
+ }
+}
+
+/// Pretty-printer for matrices of patterns, example:
+///
+/// ```text
+/// + _ + [] +
+/// + true + [First] +
+/// + true + [Second(true)] +
+/// + false + [_] +
+/// + _ + [_, _, tail @ ..] +
+/// | ✓ | ? | // column validity
+/// ```
+impl<'a, 'p, Cx: TypeCx> fmt::Debug for Matrix<'a, 'p, Cx> {
+ fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+ write!(f, "\n")?;
+
+ let mut pretty_printed_matrix: Vec<Vec<String>> = self
+ .rows
+ .iter()
+ .map(|row| row.iter().map(|pat| format!("{pat:?}")).collect())
+ .collect();
+ pretty_printed_matrix
+ .push(self.place_validity.iter().map(|validity| format!("{validity}")).collect());
+
+ let column_count = self.column_count();
+ assert!(self.rows.iter().all(|row| row.len() == column_count));
+ assert!(self.place_validity.len() == column_count);
+ let column_widths: Vec<usize> = (0..column_count)
+ .map(|col| pretty_printed_matrix.iter().map(|row| row[col].len()).max().unwrap_or(0))
+ .collect();
+
+ for (row_i, row) in pretty_printed_matrix.into_iter().enumerate() {
+ let is_validity_row = row_i == self.rows.len();
+ let sep = if is_validity_row { "|" } else { "+" };
+ write!(f, "{sep}")?;
+ for (column, pat_str) in row.into_iter().enumerate() {
+ write!(f, " ")?;
+ write!(f, "{:1$}", pat_str, column_widths[column])?;
+ write!(f, " {sep}")?;
+ }
+ if is_validity_row {
+ write!(f, " // column validity")?;
+ }
+ write!(f, "\n")?;
+ }
+ Ok(())
+ }
+}
+
+/// A witness-tuple of non-exhaustiveness for error reporting, represented as a list of patterns (in
+/// reverse order of construction).
+///
+/// This mirrors `PatStack`: they function similarly, except `PatStack` contains user patterns we
+/// are inspecting, and `WitnessStack` contains witnesses we are constructing.
+/// FIXME(Nadrieril): use the same order of patterns for both.
+///
+/// A `WitnessStack` should have the same types and length as the `PatStack`s we are inspecting
+/// (except we store the patterns in reverse order). The same way `PatStack` starts with length 1,
+/// at the end of the algorithm this will have length 1. In the middle of the algorithm, it can
+/// contain multiple patterns.
+///
+/// For example, if we are constructing a witness for the match against
+///
+/// ```compile_fail,E0004
+/// struct Pair(Option<(u32, u32)>, bool);
+/// # fn foo(p: Pair) {
+/// match p {
+/// Pair(None, _) => {}
+/// Pair(_, false) => {}
+/// }
+/// # }
+/// ```
+///
+/// We'll perform the following steps (among others):
+/// ```text
+/// - Start with a matrix representing the match
+/// `PatStack(vec![Pair(None, _)])`
+/// `PatStack(vec![Pair(_, false)])`
+/// - Specialize with `Pair`
+/// `PatStack(vec![None, _])`
+/// `PatStack(vec![_, false])`
+/// - Specialize with `Some`
+/// `PatStack(vec![_, false])`
+/// - Specialize with `_`
+/// `PatStack(vec![false])`
+/// - Specialize with `true`
+/// // no patstacks left
+/// - This is a non-exhaustive match: we have the empty witness stack as a witness.
+/// `WitnessStack(vec![])`
+/// - Apply `true`
+/// `WitnessStack(vec![true])`
+/// - Apply `_`
+/// `WitnessStack(vec![true, _])`
+/// - Apply `Some`
+/// `WitnessStack(vec![true, Some(_)])`
+/// - Apply `Pair`
+/// `WitnessStack(vec![Pair(Some(_), true)])`
+/// ```
+///
+/// The final `Pair(Some(_), true)` is then the resulting witness.
+///
+/// See the top of the file for more detailed explanations and examples.
+#[derive(Debug, Clone)]
+struct WitnessStack<Cx: TypeCx>(Vec<WitnessPat<Cx>>);
+
+impl<Cx: TypeCx> WitnessStack<Cx> {
+ /// Asserts that the witness contains a single pattern, and returns it.
+ fn single_pattern(self) -> WitnessPat<Cx> {
+ assert_eq!(self.0.len(), 1);
+ self.0.into_iter().next().unwrap()
+ }
+
+ /// Reverses specialization by the `Missing` constructor by pushing a whole new pattern.
+ fn push_pattern(&mut self, pat: WitnessPat<Cx>) {
+ self.0.push(pat);
+ }
+
+ /// Reverses specialization. Given a witness obtained after specialization, this constructs a
+ /// new witness valid for before specialization. See the section on `unspecialize` at the top of
+ /// the file.
+ ///
+ /// Examples:
+ /// ```text
+ /// ctor: tuple of 2 elements
+ /// pats: [false, "foo", _, true]
+ /// result: [(false, "foo"), _, true]
+ ///
+ /// ctor: Enum::Variant { a: (bool, &'static str), b: usize}
+ /// pats: [(false, "foo"), _, true]
+ /// result: [Enum::Variant { a: (false, "foo"), b: _ }, true]
+ /// ```
+ fn apply_constructor(&mut self, pcx: &PlaceCtxt<'_, '_, Cx>, ctor: &Constructor<Cx>) {
+ let len = self.0.len();
+ let arity = ctor.arity(pcx);
+ let fields = self.0.drain((len - arity)..).rev().collect();
+ let pat = WitnessPat::new(ctor.clone(), fields, pcx.ty);
+ self.0.push(pat);
+ }
+}
+
+/// Represents a set of pattern-tuples that are witnesses of non-exhaustiveness for error
+/// reporting. This has similar invariants as `Matrix` does.
+///
+/// The `WitnessMatrix` returned by [`compute_exhaustiveness_and_usefulness`] obeys the invariant
+/// that the union of the input `Matrix` and the output `WitnessMatrix` together matches the type
+/// exhaustively.
+///
+/// Just as the `Matrix` starts with a single column, by the end of the algorithm, this has a single
+/// column, which contains the patterns that are missing for the match to be exhaustive.
+#[derive(Debug, Clone)]
+struct WitnessMatrix<Cx: TypeCx>(Vec<WitnessStack<Cx>>);
+
+impl<Cx: TypeCx> WitnessMatrix<Cx> {
+ /// New matrix with no witnesses.
+ fn empty() -> Self {
+ WitnessMatrix(vec![])
+ }
+ /// New matrix with one `()` witness, i.e. with no columns.
+ fn unit_witness() -> Self {
+ WitnessMatrix(vec![WitnessStack(vec![])])
+ }
+
+ /// Whether this has any witnesses.
+ fn is_empty(&self) -> bool {
+ self.0.is_empty()
+ }
+ /// Asserts that there is a single column and returns the patterns in it.
+ fn single_column(self) -> Vec<WitnessPat<Cx>> {
+ self.0.into_iter().map(|w| w.single_pattern()).collect()
+ }
+
+ /// Reverses specialization by the `Missing` constructor by pushing a whole new pattern.
+ fn push_pattern(&mut self, pat: WitnessPat<Cx>) {
+ for witness in self.0.iter_mut() {
+ witness.push_pattern(pat.clone())
+ }
+ }
+
+ /// Reverses specialization by `ctor`. See the section on `unspecialize` at the top of the file.
+ fn apply_constructor(
+ &mut self,
+ pcx: &PlaceCtxt<'_, '_, Cx>,
+ missing_ctors: &[Constructor<Cx>],
+ ctor: &Constructor<Cx>,
+ report_individual_missing_ctors: bool,
+ ) {
+ if self.is_empty() {
+ return;
+ }
+ if matches!(ctor, Constructor::Missing) {
+ // We got the special `Missing` constructor that stands for the constructors not present
+ // in the match.
+ if missing_ctors.is_empty() {
+ // Nothing to report.
+ *self = Self::empty();
+ } else if !report_individual_missing_ctors {
+ // Report `_` as missing.
+ let pat = WitnessPat::wild_from_ctor(pcx, Constructor::Wildcard);
+ self.push_pattern(pat);
+ } else if missing_ctors.iter().any(|c| c.is_non_exhaustive()) {
+ // We need to report a `_` anyway, so listing other constructors would be redundant.
+ // `NonExhaustive` is displayed as `_` just like `Wildcard`, but it will be picked
+ // up by diagnostics to add a note about why `_` is required here.
+ let pat = WitnessPat::wild_from_ctor(pcx, Constructor::NonExhaustive);
+ self.push_pattern(pat);
+ } else {
+ // For each missing constructor `c`, we add a `c(_, _, _)` witness appropriately
+ // filled with wildcards.
+ let mut ret = Self::empty();
+ for ctor in missing_ctors {
+ let pat = WitnessPat::wild_from_ctor(pcx, ctor.clone());
+ // Clone `self` and add `c(_, _, _)` to each of its witnesses.
+ let mut wit_matrix = self.clone();
+ wit_matrix.push_pattern(pat);
+ ret.extend(wit_matrix);
+ }
+ *self = ret;
+ }
+ } else {
+ // Any other constructor we unspecialize as expected.
+ for witness in self.0.iter_mut() {
+ witness.apply_constructor(pcx, ctor)
+ }
+ }
+ }
+
+ /// Merges the witnesses of two matrices. Their column types must match.
+ fn extend(&mut self, other: Self) {
+ self.0.extend(other.0)
+ }
+}
+
+/// The core of the algorithm.
+///
+/// This recursively computes witnesses of the non-exhaustiveness of `matrix` (if any). Also tracks
+/// usefulness of each row in the matrix (in `row.useful`). We track usefulness of each
+/// subpattern using interior mutability in `DeconstructedPat`.
+///
+/// The input `Matrix` and the output `WitnessMatrix` together match the type exhaustively.
+///
+/// The key steps are:
+/// - specialization, where we dig into the rows that have a specific constructor and call ourselves
+/// recursively;
+/// - unspecialization, where we lift the results from the previous step into results for this step
+/// (using `apply_constructor` and by updating `row.useful` for each parent row).
+/// This is all explained at the top of the file.
+#[instrument(level = "debug", skip(mcx, is_top_level), ret)]
+fn compute_exhaustiveness_and_usefulness<'a, 'p, Cx: TypeCx>(
+ mcx: MatchCtxt<'a, 'p, Cx>,
+ matrix: &mut Matrix<'a, 'p, Cx>,
+ is_top_level: bool,
+) -> WitnessMatrix<Cx> {
+ debug_assert!(matrix.rows().all(|r| r.len() == matrix.column_count()));
+
+ if !matrix.wildcard_row.relevant && matrix.rows().all(|r| !r.pats.relevant) {
+ // Here we know that nothing will contribute further to exhaustiveness or usefulness. This
+ // is purely an optimization: skipping this check doesn't affect correctness. See the top of
+ // the file for details.
+ return WitnessMatrix::empty();
+ }
+
+ let Some(ty) = matrix.head_ty() else {
+ // The base case: there are no columns in the matrix. We are morally pattern-matching on ().
+ // A row is useful iff it has no (unguarded) rows above it.
+ for row in matrix.rows_mut() {
+ // All rows are useful until they're not.
+ row.useful = true;
+ // When there's an unguarded row, the match is exhaustive and any subsequent row is not
+ // useful.
+ if !row.is_under_guard {
+ return WitnessMatrix::empty();
+ }
+ }
+ // No (unguarded) rows, so the match is not exhaustive. We return a new witness unless
+ // irrelevant.
+ return if matrix.wildcard_row.relevant {
+ WitnessMatrix::unit_witness()
+ } else {
+ // We choose to not report anything here; see at the top for details.
+ WitnessMatrix::empty()
+ };
+ };
+
+ debug!("ty: {ty:?}");
+ let pcx = &PlaceCtxt { mcx, ty, is_scrutinee: is_top_level };
+
+ // Whether the place/column we are inspecting is known to contain valid data.
+ let place_validity = matrix.place_validity[0];
+ // For backwards compability we allow omitting some empty arms that we ideally shouldn't.
+ let place_validity = place_validity.allow_omitting_side_effecting_arms();
+
+ // Analyze the constructors present in this column.
+ let ctors = matrix.heads().map(|p| p.ctor());
+ let ctors_for_ty = pcx.ctors_for_ty();
+ let is_integers = matches!(ctors_for_ty, ConstructorSet::Integers { .. }); // For diagnostics.
+ let split_set = ctors_for_ty.split(pcx, ctors);
+ let all_missing = split_set.present.is_empty();
+
+ // Build the set of constructors we will specialize with. It must cover the whole type.
+ let mut split_ctors = split_set.present;
+ if !split_set.missing.is_empty() {
+ // We need to iterate over a full set of constructors, so we add `Missing` to represent the
+ // missing ones. This is explained under "Constructor Splitting" at the top of this file.
+ split_ctors.push(Constructor::Missing);
+ } else if !split_set.missing_empty.is_empty() && !place_validity.is_known_valid() {
+ // The missing empty constructors are reachable if the place can contain invalid data.
+ split_ctors.push(Constructor::Missing);
+ }
+
+ // Decide what constructors to report.
+ let always_report_all = is_top_level && !is_integers;
+ // Whether we should report "Enum::A and Enum::C are missing" or "_ is missing".
+ let report_individual_missing_ctors = always_report_all || !all_missing;
+ // Which constructors are considered missing. We ensure that `!missing_ctors.is_empty() =>
+ // split_ctors.contains(Missing)`. The converse usually holds except in the
+ // `MaybeInvalidButAllowOmittingArms` backwards-compatibility case.
+ let mut missing_ctors = split_set.missing;
+ if !place_validity.allows_omitting_empty_arms() {
+ missing_ctors.extend(split_set.missing_empty);
+ }
+
+ let mut ret = WitnessMatrix::empty();
+ for ctor in split_ctors {
+ // Dig into rows that match `ctor`.
+ debug!("specialize({:?})", ctor);
+ // `ctor` is *irrelevant* if there's another constructor in `split_ctors` that matches
+ // strictly fewer rows. In that case we can sometimes skip it. See the top of the file for
+ // details.
+ let ctor_is_relevant = matches!(ctor, Constructor::Missing) || missing_ctors.is_empty();
+ let mut spec_matrix = matrix.specialize_constructor(pcx, &ctor, ctor_is_relevant);
+ let mut witnesses = ensure_sufficient_stack(|| {
+ compute_exhaustiveness_and_usefulness(mcx, &mut spec_matrix, false)
+ });
+
+ // Transform witnesses for `spec_matrix` into witnesses for `matrix`.
+ witnesses.apply_constructor(pcx, &missing_ctors, &ctor, report_individual_missing_ctors);
+ // Accumulate the found witnesses.
+ ret.extend(witnesses);
+
+ // A parent row is useful if any of its children is.
+ for child_row in spec_matrix.rows() {
+ let parent_row = &mut matrix.rows[child_row.parent_row];
+ parent_row.useful = parent_row.useful || child_row.useful;
+ }
+ }
+
+ // Record usefulness in the patterns.
+ for row in matrix.rows() {
+ if row.useful {
+ row.head().set_useful();
+ }
+ }
+
+ ret
+}
+
+/// Indicates whether or not a given arm is useful.
+#[derive(Clone, Debug)]
+pub enum Usefulness<'p, Cx: TypeCx> {
+ /// The arm is useful. This additionally carries a set of or-pattern branches that have been
+ /// found to be redundant despite the overall arm being useful. Used only in the presence of
+ /// or-patterns, otherwise it stays empty.
+ Useful(Vec<&'p DeconstructedPat<'p, Cx>>),
+ /// The arm is redundant and can be removed without changing the behavior of the match
+ /// expression.
+ Redundant,
+}
+
+/// The output of checking a match for exhaustiveness and arm usefulness.
+pub struct UsefulnessReport<'p, Cx: TypeCx> {
+ /// For each arm of the input, whether that arm is useful after the arms above it.
+ pub arm_usefulness: Vec<(MatchArm<'p, Cx>, Usefulness<'p, Cx>)>,
+ /// If the match is exhaustive, this is empty. If not, this contains witnesses for the lack of
+ /// exhaustiveness.
+ pub non_exhaustiveness_witnesses: Vec<WitnessPat<Cx>>,
+}
+
+/// Computes whether a match is exhaustive and which of its arms are useful.
+#[instrument(skip(cx, arms), level = "debug")]
+pub fn compute_match_usefulness<'p, Cx: TypeCx>(
+ cx: MatchCtxt<'_, 'p, Cx>,
+ arms: &[MatchArm<'p, Cx>],
+ scrut_ty: Cx::Ty,
+ scrut_validity: ValidityConstraint,
+) -> UsefulnessReport<'p, Cx> {
+ let mut matrix = Matrix::new(cx.wildcard_arena, arms, scrut_ty, scrut_validity);
+ let non_exhaustiveness_witnesses = compute_exhaustiveness_and_usefulness(cx, &mut matrix, true);
+
+ let non_exhaustiveness_witnesses: Vec<_> = non_exhaustiveness_witnesses.single_column();
+ let arm_usefulness: Vec<_> = arms
+ .iter()
+ .copied()
+ .map(|arm| {
+ debug!(?arm);
+ // We warn when a pattern is not useful.
+ let usefulness = if arm.pat.is_useful() {
+ Usefulness::Useful(arm.pat.redundant_subpatterns())
+ } else {
+ Usefulness::Redundant
+ };
+ (arm, usefulness)
+ })
+ .collect();
+ UsefulnessReport { arm_usefulness, non_exhaustiveness_witnesses }
+}