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diff --git a/crates/hir_ty/src/diagnostics/match_check.rs b/crates/hir_ty/src/diagnostics/match_check.rs
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+//! This module implements match statement exhaustiveness checking and usefulness checking
+//! for match arms.
+//!
+//! It is modeled on the rustc module `librustc_mir_build::hair::pattern::_match`, which
+//! contains very detailed documentation about the algorithms used here. I've duplicated
+//! most of that documentation below.
+//!
+//! This file includes the logic for exhaustiveness and usefulness checking for
+//! pattern-matching. Specifically, given a list of patterns for a type, we can
+//! tell whether:
+//! - (a) the patterns cover every possible constructor for the type (exhaustiveness).
+//! - (b) each pattern is necessary (usefulness).
+//!
+//! The algorithm implemented here is a modified version of the one described in
+//! <http://moscova.inria.fr/~maranget/papers/warn/index.html>.
+//! However, to save future implementors from reading the original paper, we
+//! summarise the algorithm here to hopefully save time and be a little clearer
+//! (without being so rigorous).
+//!
+//! The core of the algorithm revolves about a "usefulness" check. In particular, we
+//! are trying to compute a predicate `U(P, p)` where `P` is a list of patterns (we refer to this as
+//! a matrix). `U(P, p)` represents whether, given an existing list of patterns
+//! `P_1 ..= P_m`, adding a new pattern `p` will be "useful" (that is, cover previously-
+//! uncovered values of the type).
+//!
+//! If we have this predicate, then we can easily compute both exhaustiveness of an
+//! entire set of patterns and the individual usefulness of each one.
+//! (a) the set of patterns is exhaustive iff `U(P, _)` is false (i.e., adding a wildcard
+//! match doesn't increase the number of values we're matching)
+//! (b) a pattern `P_i` is not useful if `U(P[0..=(i-1), P_i)` is false (i.e., adding a
+//! pattern to those that have come before it doesn't increase the number of values
+//! we're matching).
+//!
+//! During the course of the algorithm, the rows of the matrix won't just be individual patterns,
+//! but rather partially-deconstructed patterns in the form of a list of patterns. The paper
+//! calls those pattern-vectors, and we will call them pattern-stacks. The same holds for the
+//! new pattern `p`.
+//!
+//! For example, say we have the following:
+//!
+//! ```ignore
+//! // x: (Option<bool>, Result<()>)
+//! match x {
+//!     (Some(true), _) => (),
+//!     (None, Err(())) => (),
+//!     (None, Err(_)) => (),
+//! }
+//! ```
+//!
+//! Here, the matrix `P` starts as:
+//!
+//! ```text
+//! [
+//!     [(Some(true), _)],
+//!     [(None, Err(()))],
+//!     [(None, Err(_))],
+//! ]
+//! ```
+//!
+//! We can tell it's not exhaustive, because `U(P, _)` is true (we're not covering
+//! `[(Some(false), _)]`, for instance). In addition, row 3 is not useful, because
+//! all the values it covers are already covered by row 2.
+//!
+//! A list of patterns can be thought of as a stack, because we are mainly interested in the top of
+//! the stack at any given point, and we can pop or apply constructors to get new pattern-stacks.
+//! To match the paper, the top of the stack is at the beginning / on the left.
+//!
+//! There are two important operations on pattern-stacks necessary to understand the algorithm:
+//!
+//! 1. We can pop a given constructor off the top of a stack. This operation is called
+//!    `specialize`, and is denoted `S(c, p)` where `c` is a constructor (like `Some` or
+//!    `None`) and `p` a pattern-stack.
+//!    If the pattern on top of the stack can cover `c`, this removes the constructor and
+//!    pushes its arguments onto the stack. It also expands OR-patterns into distinct patterns.
+//!    Otherwise the pattern-stack is discarded.
+//!    This essentially filters those pattern-stacks whose top covers the constructor `c` and
+//!    discards the others.
+//!
+//!    For example, the first pattern above initially gives a stack `[(Some(true), _)]`. If we
+//!    pop the tuple constructor, we are left with `[Some(true), _]`, and if we then pop the
+//!    `Some` constructor we get `[true, _]`. If we had popped `None` instead, we would get
+//!    nothing back.
+//!
+//!    This returns zero or more new pattern-stacks, as follows. We look at the pattern `p_1`
+//!    on top of the stack, and we have four cases:
+//!
+//!    * 1.1. `p_1 = c(r_1, .., r_a)`, i.e. the top of the stack has constructor `c`. We push onto
+//!           the stack the arguments of this constructor, and return the result:
+//!
+//!          r_1, .., r_a, p_2, .., p_n
+//!
+//!    * 1.2. `p_1 = c'(r_1, .., r_a')` where `c ≠ c'`. We discard the current stack and return
+//!           nothing.
+//!    * 1.3. `p_1 = _`. We push onto the stack as many wildcards as the constructor `c` has
+//!           arguments (its arity), and return the resulting stack:
+//!
+//!          _, .., _, p_2, .., p_n
+//!
+//!    * 1.4. `p_1 = r_1 | r_2`. We expand the OR-pattern and then recurse on each resulting stack:
+//!
+//!          S(c, (r_1, p_2, .., p_n))
+//!          S(c, (r_2, p_2, .., p_n))
+//!
+//! 2. We can pop a wildcard off the top of the stack. This is called `D(p)`, where `p` is
+//!    a pattern-stack.
+//!    This is used when we know there are missing constructor cases, but there might be
+//!    existing wildcard patterns, so to check the usefulness of the matrix, we have to check
+//!    all its *other* components.
+//!
+//!    It is computed as follows. We look at the pattern `p_1` on top of the stack,
+//!    and we have three cases:
+//!    * 1.1. `p_1 = c(r_1, .., r_a)`. We discard the current stack and return nothing.
+//!    * 1.2. `p_1 = _`. We return the rest of the stack:
+//!
+//!          p_2, .., p_n
+//!
+//!    * 1.3. `p_1 = r_1 | r_2`. We expand the OR-pattern and then recurse on each resulting stack:
+//!
+//!          D((r_1, p_2, .., p_n))
+//!          D((r_2, p_2, .., p_n))
+//!
+//!    Note that the OR-patterns are not always used directly in Rust, but are used to derive the
+//!    exhaustive integer matching rules, so they're written here for posterity.
+//!
+//! Both those operations extend straightforwardly to a list or pattern-stacks, i.e. a matrix, by
+//! working row-by-row. Popping a constructor ends up keeping only the matrix rows that start with
+//! the given constructor, and popping a wildcard keeps those rows that start with a wildcard.
+//!
+//!
+//! The algorithm for computing `U`
+//! -------------------------------
+//! The algorithm is inductive (on the number of columns: i.e., components of tuple patterns).
+//! That means we're going to check the components from left-to-right, so the algorithm
+//! operates principally on the first component of the matrix and new pattern-stack `p`.
+//! This algorithm is realised in the `is_useful` function.
+//!
+//! Base case (`n = 0`, i.e., an empty tuple pattern):
+//! - If `P` already contains an empty pattern (i.e., if the number of patterns `m > 0`), then
+//!   `U(P, p)` is false.
+//! - Otherwise, `P` must be empty, so `U(P, p)` is true.
+//!
+//! Inductive step (`n > 0`, i.e., whether there's at least one column [which may then be expanded
+//! into further columns later]). We're going to match on the top of the new pattern-stack, `p_1`:
+//!
+//! - If `p_1 == c(r_1, .., r_a)`, i.e. we have a constructor pattern.
+//!   Then, the usefulness of `p_1` can be reduced to whether it is useful when
+//!   we ignore all the patterns in the first column of `P` that involve other constructors.
+//!   This is where `S(c, P)` comes in:
+//!
+//!   ```text
+//!   U(P, p) := U(S(c, P), S(c, p))
+//!   ```
+//!
+//!   This special case is handled in `is_useful_specialized`.
+//!
+//!   For example, if `P` is:
+//!
+//!   ```text
+//!   [
+//!       [Some(true), _],
+//!       [None, 0],
+//!   ]
+//!   ```
+//!
+//!   and `p` is `[Some(false), 0]`, then we don't care about row 2 since we know `p` only
+//!   matches values that row 2 doesn't. For row 1 however, we need to dig into the
+//!   arguments of `Some` to know whether some new value is covered. So we compute
+//!   `U([[true, _]], [false, 0])`.
+//!
+//! - If `p_1 == _`, then we look at the list of constructors that appear in the first component of
+//!   the rows of `P`:
+//!     - If there are some constructors that aren't present, then we might think that the
+//!       wildcard `_` is useful, since it covers those constructors that weren't covered
+//!       before.
+//!       That's almost correct, but only works if there were no wildcards in those first
+//!       components. So we need to check that `p` is useful with respect to the rows that
+//!       start with a wildcard, if there are any. This is where `D` comes in:
+//!       `U(P, p) := U(D(P), D(p))`
+//!
+//!       For example, if `P` is:
+//!       ```text
+//!       [
+//!           [_, true, _],
+//!           [None, false, 1],
+//!       ]
+//!       ```
+//!       and `p` is `[_, false, _]`, the `Some` constructor doesn't appear in `P`. So if we
+//!       only had row 2, we'd know that `p` is useful. However row 1 starts with a
+//!       wildcard, so we need to check whether `U([[true, _]], [false, 1])`.
+//!
+//!     - Otherwise, all possible constructors (for the relevant type) are present. In this
+//!       case we must check whether the wildcard pattern covers any unmatched value. For
+//!       that, we can think of the `_` pattern as a big OR-pattern that covers all
+//!       possible constructors. For `Option`, that would mean `_ = None | Some(_)` for
+//!       example. The wildcard pattern is useful in this case if it is useful when
+//!       specialized to one of the possible constructors. So we compute:
+//!       `U(P, p) := ∃(k ϵ constructors) U(S(k, P), S(k, p))`
+//!
+//!       For example, if `P` is:
+//!       ```text
+//!       [
+//!           [Some(true), _],
+//!           [None, false],
+//!       ]
+//!       ```
+//!       and `p` is `[_, false]`, both `None` and `Some` constructors appear in the first
+//!       components of `P`. We will therefore try popping both constructors in turn: we
+//!       compute `U([[true, _]], [_, false])` for the `Some` constructor, and `U([[false]],
+//!       [false])` for the `None` constructor. The first case returns true, so we know that
+//!       `p` is useful for `P`. Indeed, it matches `[Some(false), _]` that wasn't matched
+//!       before.
+//!
+//! - If `p_1 == r_1 | r_2`, then the usefulness depends on each `r_i` separately:
+//!
+//!   ```text
+//!   U(P, p) := U(P, (r_1, p_2, .., p_n))
+//!            || U(P, (r_2, p_2, .., p_n))
+//!   ```
+use std::sync::Arc;
+use arena::Idx;
+use hir_def::{
+    adt::VariantData,
+    body::Body,
+    expr::{Expr, Literal, Pat, PatId},
+    AdtId, EnumVariantId, VariantId,
+};
+use smallvec::{smallvec, SmallVec};
+use crate::{db::HirDatabase, ApplicationTy, InferenceResult, Ty, TypeCtor};
+#[derive(Debug, Clone, Copy)]
+/// Either a pattern from the source code being analyzed, represented as
+/// as `PatId`, or a `Wild` pattern which is created as an intermediate
+/// step in the match checking algorithm and thus is not backed by a
+/// real `PatId`.
+///
+/// Note that it is totally valid for the `PatId` variant to contain
+/// a `PatId` which resolves to a `Wild` pattern, if that wild pattern
+/// exists in the source code being analyzed.
+enum PatIdOrWild {
+    PatId(PatId),
+    Wild,
+}
+impl PatIdOrWild {
+    fn as_pat(self, cx: &MatchCheckCtx) -> Pat {
+        match self {
+            PatIdOrWild::PatId(id) => cx.body.pats[id].clone(),
+            PatIdOrWild::Wild => Pat::Wild,
+        }
+    }
+    fn as_id(self) -> Option<PatId> {
+        match self {
+            PatIdOrWild::PatId(id) => Some(id),
+            PatIdOrWild::Wild => None,
+        }
+    }
+}
+impl From<PatId> for PatIdOrWild {
+    fn from(pat_id: PatId) -> Self {
+        Self::PatId(pat_id)
+    }
+}
+impl From<&PatId> for PatIdOrWild {
+    fn from(pat_id: &PatId) -> Self {
+        Self::PatId(*pat_id)
+    }
+}
+#[derive(Debug, Clone, Copy, PartialEq)]
+pub(super) enum MatchCheckErr {
+    NotImplemented,
+    MalformedMatchArm,
+    /// Used when type inference cannot resolve the type of
+    /// a pattern or expression.
+    Unknown,
+}
+/// The return type of `is_useful` is either an indication of usefulness
+/// of the match arm, or an error in the case the match statement
+/// is made up of types for which exhaustiveness checking is currently
+/// not completely implemented.
+///
+/// The `std::result::Result` type is used here rather than a custom enum
+/// to allow the use of `?`.
+pub(super) type MatchCheckResult<T> = Result<T, MatchCheckErr>;
+#[derive(Debug)]
+/// A row in a Matrix.
+///
+/// This type is modeled from the struct of the same name in `rustc`.
+pub(super) struct PatStack(PatStackInner);
+type PatStackInner = SmallVec<[PatIdOrWild; 2]>;
+impl PatStack {
+    pub(super) fn from_pattern(pat_id: PatId) -> PatStack {
+        Self(smallvec!(pat_id.into()))
+    }
+    pub(super) fn from_wild() -> PatStack {
+        Self(smallvec!(PatIdOrWild::Wild))
+    }
+    fn from_slice(slice: &[PatIdOrWild]) -> PatStack {
+        Self(SmallVec::from_slice(slice))
+    }
+    fn from_vec(v: PatStackInner) -> PatStack {
+        Self(v)
+    }
+    fn get_head(&self) -> Option<PatIdOrWild> {
+        self.0.first().copied()
+    }
+    fn tail(&self) -> &[PatIdOrWild] {
+        self.0.get(1..).unwrap_or(&[])
+    }
+    fn to_tail(&self) -> PatStack {
+        Self::from_slice(self.tail())
+    }
+    fn replace_head_with<I, T>(&self, pats: I) -> PatStack
+    where
+        I: Iterator<Item = T>,
+        T: Into<PatIdOrWild>,
+    {
+        let mut patterns: PatStackInner = smallvec![];
+        for pat in pats {
+            patterns.push(pat.into());
+        }
+        for pat in &self.0[1..] {
+            patterns.push(*pat);
+        }
+        PatStack::from_vec(patterns)
+    }
+    /// Computes `D(self)`.
+    ///
+    /// See the module docs and the associated documentation in rustc for details.
+    fn specialize_wildcard(&self, cx: &MatchCheckCtx) -> Option<PatStack> {
+        if matches!(self.get_head()?.as_pat(cx), Pat::Wild) {
+            Some(self.to_tail())
+        } else {
+            None
+        }
+    }
+    /// Computes `S(constructor, self)`.
+    ///
+    /// See the module docs and the associated documentation in rustc for details.
+    fn specialize_constructor(
+        &self,
+        cx: &MatchCheckCtx,
+        constructor: &Constructor,
+    ) -> MatchCheckResult<Option<PatStack>> {
+        let head = match self.get_head() {
+            Some(head) => head,
+            None => return Ok(None),
+        };
+        let head_pat = head.as_pat(cx);
+        let result = match (head_pat, constructor) {
+            (Pat::Tuple { args: ref pat_ids, ellipsis }, Constructor::Tuple { arity: _ }) => {
+                if ellipsis.is_some() {
+                    // If there are ellipsis here, we should add the correct number of
+                    // Pat::Wild patterns to `pat_ids`. We should be able to use the
+                    // constructors arity for this, but at the time of writing we aren't
+                    // correctly calculating this arity when ellipsis are present.
+                    return Err(MatchCheckErr::NotImplemented);
+                }
+                Some(self.replace_head_with(pat_ids.iter()))
+            }
+            (Pat::Lit(lit_expr), Constructor::Bool(constructor_val)) => {
+                match cx.body.exprs[lit_expr] {
+                    Expr::Literal(Literal::Bool(pat_val)) if *constructor_val == pat_val => {
+                        Some(self.to_tail())
+                    }
+                    // it was a bool but the value doesn't match
+                    Expr::Literal(Literal::Bool(_)) => None,
+                    // perhaps this is actually unreachable given we have
+                    // already checked that these match arms have the appropriate type?
+                    _ => return Err(MatchCheckErr::NotImplemented),
+                }
+            }
+            (Pat::Wild, constructor) => Some(self.expand_wildcard(cx, constructor)?),
+            (Pat::Path(_), Constructor::Enum(constructor)) => {
+                // unit enum variants become `Pat::Path`
+                let pat_id = head.as_id().expect("we know this isn't a wild");
+                if !enum_variant_matches(cx, pat_id, *constructor) {
+                    None
+                } else {
+                    Some(self.to_tail())
+                }
+            }
+            (
+                Pat::TupleStruct { args: ref pat_ids, ellipsis, .. },
+                Constructor::Enum(enum_constructor),
+            ) => {
+                let pat_id = head.as_id().expect("we know this isn't a wild");
+                if !enum_variant_matches(cx, pat_id, *enum_constructor) {
+                    None
+                } else {
+                    let constructor_arity = constructor.arity(cx)?;
+                    if let Some(ellipsis_position) = ellipsis {
+                        // If there are ellipsis in the pattern, the ellipsis must take the place
+                        // of at least one sub-pattern, so `pat_ids` should be smaller than the
+                        // constructor arity.
+                        if pat_ids.len() < constructor_arity {
+                            let mut new_patterns: Vec<PatIdOrWild> = vec![];
+                            for pat_id in &pat_ids[0..ellipsis_position] {
+                                new_patterns.push((*pat_id).into());
+                            }
+                            for _ in 0..(constructor_arity - pat_ids.len()) {
+                                new_patterns.push(PatIdOrWild::Wild);
+                            }
+                            for pat_id in &pat_ids[ellipsis_position..pat_ids.len()] {
+                                new_patterns.push((*pat_id).into());
+                            }
+                            Some(self.replace_head_with(new_patterns.into_iter()))
+                        } else {
+                            return Err(MatchCheckErr::MalformedMatchArm);
+                        }
+                    } else {
+                        // If there is no ellipsis in the tuple pattern, the number
+                        // of patterns must equal the constructor arity.
+                        if pat_ids.len() == constructor_arity {
+                            Some(self.replace_head_with(pat_ids.into_iter()))
+                        } else {
+                            return Err(MatchCheckErr::MalformedMatchArm);
+                        }
+                    }
+                }
+            }
+            (Pat::Record { args: ref arg_patterns, .. }, Constructor::Enum(e)) => {
+                let pat_id = head.as_id().expect("we know this isn't a wild");
+                if !enum_variant_matches(cx, pat_id, *e) {
+                    None
+                } else {
+                    match cx.db.enum_data(e.parent).variants[e.local_id].variant_data.as_ref() {
+                        VariantData::Record(struct_field_arena) => {
+                            // Here we treat any missing fields in the record as the wild pattern, as
+                            // if the record has ellipsis. We want to do this here even if the
+                            // record does not contain ellipsis, because it allows us to continue
+                            // enforcing exhaustiveness for the rest of the match statement.
+                            //
+                            // Creating the diagnostic for the missing field in the pattern
+                            // should be done in a different diagnostic.
+                            let patterns = struct_field_arena.iter().map(|(_, struct_field)| {
+                                arg_patterns
+                                    .iter()
+                                    .find(|pat| pat.name == struct_field.name)
+                                    .map(|pat| PatIdOrWild::from(pat.pat))
+                                    .unwrap_or(PatIdOrWild::Wild)
+                            });
+                            Some(self.replace_head_with(patterns))
+                        }
+                        _ => return Err(MatchCheckErr::Unknown),
+                    }
+                }
+            }
+            (Pat::Or(_), _) => return Err(MatchCheckErr::NotImplemented),
+            (_, _) => return Err(MatchCheckErr::NotImplemented),
+        };
+        Ok(result)
+    }
+    /// A special case of `specialize_constructor` where the head of the pattern stack
+    /// is a Wild pattern.
+    ///
+    /// Replaces the Wild pattern at the head of the pattern stack with N Wild patterns
+    /// (N >= 0), where N is the arity of the given constructor.
+    fn expand_wildcard(
+        &self,
+        cx: &MatchCheckCtx,
+        constructor: &Constructor,
+    ) -> MatchCheckResult<PatStack> {
+        assert_eq!(
+            Pat::Wild,
+            self.get_head().expect("expand_wildcard called on empty PatStack").as_pat(cx),
+            "expand_wildcard must only be called on PatStack with wild at head",
+        );
+        let mut patterns: PatStackInner = smallvec![];
+        for _ in 0..constructor.arity(cx)? {
+            patterns.push(PatIdOrWild::Wild);
+        }
+        for pat in &self.0[1..] {
+            patterns.push(*pat);
+        }
+        Ok(PatStack::from_vec(patterns))
+    }
+}
+/// A collection of PatStack.
+///
+/// This type is modeled from the struct of the same name in `rustc`.
+pub(super) struct Matrix(Vec<PatStack>);
+impl Matrix {
+    pub(super) fn empty() -> Self {
+        Self(vec![])
+    }
+    pub(super) fn push(&mut self, cx: &MatchCheckCtx, row: PatStack) {
+        if let Some(Pat::Or(pat_ids)) = row.get_head().map(|pat_id| pat_id.as_pat(cx)) {
+            // Or patterns are expanded here
+            for pat_id in pat_ids {
+                self.0.push(PatStack::from_pattern(pat_id));
+            }
+        } else {
+            self.0.push(row);
+        }
+    }
+    fn is_empty(&self) -> bool {
+        self.0.is_empty()
+    }
+    fn heads(&self) -> Vec<PatIdOrWild> {
+        self.0.iter().flat_map(|p| p.get_head()).collect()
+    }
+    /// Computes `D(self)` for each contained PatStack.
+    ///
+    /// See the module docs and the associated documentation in rustc for details.
+    fn specialize_wildcard(&self, cx: &MatchCheckCtx) -> Self {
+        Self::collect(cx, self.0.iter().filter_map(|r| r.specialize_wildcard(cx)))
+    }
+    /// Computes `S(constructor, self)` for each contained PatStack.
+    ///
+    /// See the module docs and the associated documentation in rustc for details.
+    fn specialize_constructor(
+        &self,
+        cx: &MatchCheckCtx,
+        constructor: &Constructor,
+    ) -> MatchCheckResult<Self> {
+        let mut new_matrix = Matrix::empty();
+        for pat in &self.0 {
+            if let Some(pat) = pat.specialize_constructor(cx, constructor)? {
+                new_matrix.push(cx, pat);
+            }
+        }
+        Ok(new_matrix)
+    }
+    fn collect<T: IntoIterator<Item = PatStack>>(cx: &MatchCheckCtx, iter: T) -> Self {
+        let mut matrix = Matrix::empty();
+        for pat in iter {
+            // using push ensures we expand or-patterns
+            matrix.push(cx, pat);
+        }
+        matrix
+    }
+}
+#[derive(Clone, Debug, PartialEq)]
+/// An indication of the usefulness of a given match arm, where
+/// usefulness is defined as matching some patterns which were
+/// not matched by an prior match arms.
+///
+/// We may eventually need an `Unknown` variant here.
+pub(super) enum Usefulness {
+    Useful,
+    NotUseful,
+}
+pub(super) struct MatchCheckCtx<'a> {
+    pub(super) match_expr: Idx<Expr>,
+    pub(super) body: Arc<Body>,
+    pub(super) infer: Arc<InferenceResult>,
+    pub(super) db: &'a dyn HirDatabase,
+}
+/// Given a set of patterns `matrix`, and pattern to consider `v`, determines
+/// whether `v` is useful. A pattern is useful if it covers cases which were
+/// not previously covered.
+///
+/// When calling this function externally (that is, not the recursive calls) it
+/// expected that you have already type checked the match arms. All patterns in
+/// matrix should be the same type as v, as well as they should all be the same
+/// type as the match expression.
+pub(super) fn is_useful(
+    cx: &MatchCheckCtx,
+    matrix: &Matrix,
+    v: &PatStack,
+) -> MatchCheckResult<Usefulness> {
+    // Handle two special cases:
+    // - enum with no variants
+    // - `!` type
+    // In those cases, no match arm is useful.
+    match cx.infer[cx.match_expr].strip_references() {
+        Ty::Apply(ApplicationTy { ctor: TypeCtor::Adt(AdtId::EnumId(enum_id)), .. }) => {
+            if cx.db.enum_data(*enum_id).variants.is_empty() {
+                return Ok(Usefulness::NotUseful);
+            }
+        }
+        Ty::Apply(ApplicationTy { ctor: TypeCtor::Never, .. }) => {
+            return Ok(Usefulness::NotUseful);
+        }
+        _ => (),
+    }
+    let head = match v.get_head() {
+        Some(head) => head,
+        None => {
+            let result = if matrix.is_empty() { Usefulness::Useful } else { Usefulness::NotUseful };
+            return Ok(result);
+        }
+    };
+    if let Pat::Or(pat_ids) = head.as_pat(cx) {
+        let mut found_unimplemented = false;
+        let any_useful = pat_ids.iter().any(|&pat_id| {
+            let v = PatStack::from_pattern(pat_id);
+            match is_useful(cx, matrix, &v) {
+                Ok(Usefulness::Useful) => true,
+                Ok(Usefulness::NotUseful) => false,
+                _ => {
+                    found_unimplemented = true;
+                    false
+                }
+            }
+        });
+        return if any_useful {
+            Ok(Usefulness::Useful)
+        } else if found_unimplemented {
+            Err(MatchCheckErr::NotImplemented)
+        } else {
+            Ok(Usefulness::NotUseful)
+        };
+    }
+    if let Some(constructor) = pat_constructor(cx, head)? {
+        let matrix = matrix.specialize_constructor(&cx, &constructor)?;
+        let v = v
+            .specialize_constructor(&cx, &constructor)?
+            .expect("we know this can't fail because we get the constructor from `v.head()` above");
+        is_useful(&cx, &matrix, &v)
+    } else {
+        // expanding wildcard
+        let mut used_constructors: Vec<Constructor> = vec![];
+        for pat in matrix.heads() {
+            if let Some(constructor) = pat_constructor(cx, pat)? {
+                used_constructors.push(constructor);
+            }
+        }
+        // We assume here that the first constructor is the "correct" type. Since we
+        // only care about the "type" of the constructor (i.e. if it is a bool we
+        // don't care about the value), this assumption should be valid as long as
+        // the match statement is well formed. We currently uphold this invariant by
+        // filtering match arms before calling `is_useful`, only passing in match arms
+        // whose type matches the type of the match expression.
+        match &used_constructors.first() {
+            Some(constructor) if all_constructors_covered(&cx, constructor, &used_constructors) => {
+                // If all constructors are covered, then we need to consider whether
+                // any values are covered by this wildcard.
+                //
+                // For example, with matrix '[[Some(true)], [None]]', all
+                // constructors are covered (`Some`/`None`), so we need
+                // to perform specialization to see that our wildcard will cover
+                // the `Some(false)` case.
+                //
+                // Here we create a constructor for each variant and then check
+                // usefulness after specializing for that constructor.
+                let mut found_unimplemented = false;
+                for constructor in constructor.all_constructors(cx) {
+                    let matrix = matrix.specialize_constructor(&cx, &constructor)?;
+                    let v = v.expand_wildcard(&cx, &constructor)?;
+                    match is_useful(&cx, &matrix, &v) {
+                        Ok(Usefulness::Useful) => return Ok(Usefulness::Useful),
+                        Ok(Usefulness::NotUseful) => continue,
+                        _ => found_unimplemented = true,
+                    };
+                }
+                if found_unimplemented {
+                    Err(MatchCheckErr::NotImplemented)
+                } else {
+                    Ok(Usefulness::NotUseful)
+                }
+            }
+            _ => {
+                // Either not all constructors are covered, or the only other arms
+                // are wildcards. Either way, this pattern is useful if it is useful
+                // when compared to those arms with wildcards.
+                let matrix = matrix.specialize_wildcard(&cx);
+                let v = v.to_tail();
+                is_useful(&cx, &matrix, &v)
+            }
+        }
+    }
+}
+#[derive(Debug, Clone, Copy)]
+/// Similar to TypeCtor, but includes additional information about the specific
+/// value being instantiated. For example, TypeCtor::Bool doesn't contain the
+/// boolean value.
+enum Constructor {
+    Bool(bool),
+    Tuple { arity: usize },
+    Enum(EnumVariantId),
+}
+impl Constructor {
+    fn arity(&self, cx: &MatchCheckCtx) -> MatchCheckResult<usize> {
+        let arity = match self {
+            Constructor::Bool(_) => 0,
+            Constructor::Tuple { arity } => *arity,
+            Constructor::Enum(e) => {
+                match cx.db.enum_data(e.parent).variants[e.local_id].variant_data.as_ref() {
+                    VariantData::Tuple(struct_field_data) => struct_field_data.len(),
+                    VariantData::Record(struct_field_data) => struct_field_data.len(),
+                    VariantData::Unit => 0,
+                }
+            }
+        };
+        Ok(arity)
+    }
+    fn all_constructors(&self, cx: &MatchCheckCtx) -> Vec<Constructor> {
+        match self {
+            Constructor::Bool(_) => vec![Constructor::Bool(true), Constructor::Bool(false)],
+            Constructor::Tuple { .. } => vec![*self],
+            Constructor::Enum(e) => cx
+                .db
+                .enum_data(e.parent)
+                .variants
+                .iter()
+                .map(|(local_id, _)| {
+                    Constructor::Enum(EnumVariantId { parent: e.parent, local_id })
+                })
+                .collect(),
+        }
+    }
+}
+/// Returns the constructor for the given pattern. Should only return None
+/// in the case of a Wild pattern.
+fn pat_constructor(cx: &MatchCheckCtx, pat: PatIdOrWild) -> MatchCheckResult<Option<Constructor>> {
+    let res = match pat.as_pat(cx) {
+        Pat::Wild => None,
+        // FIXME somehow create the Tuple constructor with the proper arity. If there are
+        // ellipsis, the arity is not equal to the number of patterns.
+        Pat::Tuple { args: pats, ellipsis } if ellipsis.is_none() => {
+            Some(Constructor::Tuple { arity: pats.len() })
+        }
+        Pat::Lit(lit_expr) => match cx.body.exprs[lit_expr] {
+            Expr::Literal(Literal::Bool(val)) => Some(Constructor::Bool(val)),
+            _ => return Err(MatchCheckErr::NotImplemented),
+        },
+        Pat::TupleStruct { .. } | Pat::Path(_) | Pat::Record { .. } => {
+            let pat_id = pat.as_id().expect("we already know this pattern is not a wild");
+            let variant_id =
+                cx.infer.variant_resolution_for_pat(pat_id).ok_or(MatchCheckErr::Unknown)?;
+            match variant_id {
+                VariantId::EnumVariantId(enum_variant_id) => {
+                    Some(Constructor::Enum(enum_variant_id))
+                }
+                _ => return Err(MatchCheckErr::NotImplemented),
+            }
+        }
+        _ => return Err(MatchCheckErr::NotImplemented),
+    };
+    Ok(res)
+}
+fn all_constructors_covered(
+    cx: &MatchCheckCtx,
+    constructor: &Constructor,
+    used_constructors: &[Constructor],
+) -> bool {
+    match constructor {
+        Constructor::Tuple { arity } => {
+            used_constructors.iter().any(|constructor| match constructor {
+                Constructor::Tuple { arity: used_arity } => arity == used_arity,
+                _ => false,
+            })
+        }
+        Constructor::Bool(_) => {
+            if used_constructors.is_empty() {
+                return false;
+            }
+            let covers_true =
+                used_constructors.iter().any(|c| matches!(c, Constructor::Bool(true)));
+            let covers_false =
+                used_constructors.iter().any(|c| matches!(c, Constructor::Bool(false)));
+            covers_true && covers_false
+        }
+        Constructor::Enum(e) => cx.db.enum_data(e.parent).variants.iter().all(|(id, _)| {
+            for constructor in used_constructors {
+                if let Constructor::Enum(e) = constructor {
+                    if id == e.local_id {
+                        return true;
+                    }
+                }
+            }
+            false
+        }),
+    }
+}
+fn enum_variant_matches(cx: &MatchCheckCtx, pat_id: PatId, enum_variant_id: EnumVariantId) -> bool {
+    Some(enum_variant_id.into()) == cx.infer.variant_resolution_for_pat(pat_id)
+}
+#[cfg(test)]
+mod tests {
+    use crate::diagnostics::tests::check_diagnostics;
+    #[test]
+    fn empty_tuple() {
+        check_diagnostics(
+            r#"
+fn main() {
+    match () { }
+        //^^ Missing match arm
+   match (()) { }
+       //^^^^ Missing match arm
+    match () { _ => (), }
+    match () { () => (), }
+    match (()) { (()) => (), }
+}
+"#,
+        );
+    }
+    #[test]
+    fn tuple_of_two_empty_tuple() {
+        check_diagnostics(
+            r#"
+fn main() {
+    match ((), ()) { }
+        //^^^^^^^^ Missing match arm
+    match ((), ()) { ((), ()) => (), }
+}
+"#,
+        );
+    }
+    #[test]
+    fn boolean() {
+        check_diagnostics(
+            r#"
+fn test_main() {
+    match false { }
+        //^^^^^ Missing match arm
+    match false { true => (), }
+        //^^^^^ Missing match arm
+    match (false, true) {}
+        //^^^^^^^^^^^^^ Missing match arm
+    match (false, true) { (true, true) => (), }
+        //^^^^^^^^^^^^^ Missing match arm
+    match (false, true) {
+        //^^^^^^^^^^^^^ Missing match arm
+        (false, true) => (),
+        (false, false) => (),
+        (true, false) => (),
+    }
+    match (false, true) { (true, _x) => (), }
+        //^^^^^^^^^^^^^ Missing match arm
+    match false { true => (), false => (), }
+    match (false, true) {
+        (false, _) => (),
+        (true, false) => (),
+        (_, true) => (),
+    }
+    match (false, true) {
+        (true, true) => (),
+        (true, false) => (),
+        (false, true) => (),
+        (false, false) => (),
+    }
+    match (false, true) {
+        (true, _x) => (),
+        (false, true) => (),
+        (false, false) => (),
+    }
+    match (false, true, false) {
+        (false, ..) => (),
+        (true, ..) => (),
+    }
+    match (false, true, false) {
+        (.., false) => (),
+        (.., true) => (),
+    }
+    match (false, true, false) { (..) => (), }
+}
+"#,
+        );
+    }
+    #[test]
+    fn tuple_of_tuple_and_bools() {
+        check_diagnostics(
+            r#"
+fn main() {
+    match (false, ((), false)) {}
+        //^^^^^^^^^^^^^^^^^^^^ Missing match arm
+    match (false, ((), false)) { (true, ((), true)) => (), }
+        //^^^^^^^^^^^^^^^^^^^^ Missing match arm
+    match (false, ((), false)) { (true, _) => (), }
+        //^^^^^^^^^^^^^^^^^^^^ Missing match arm
+    match (false, ((), false)) {
+        (true, ((), true)) => (),
+        (true, ((), false)) => (),
+        (false, ((), true)) => (),
+        (false, ((), false)) => (),
+    }
+    match (false, ((), false)) {
+        (true, ((), true)) => (),
+        (true, ((), false)) => (),
+        (false, _) => (),
+    }
+}
+"#,
+        );
+    }
+    #[test]
+    fn enums() {
+        check_diagnostics(
+            r#"
+enum Either { A, B, }
+fn main() {
+    match Either::A { }
+        //^^^^^^^^^ Missing match arm
+    match Either::B { Either::A => (), }
+        //^^^^^^^^^ Missing match arm
+    match &Either::B {
+        //^^^^^^^^^^ Missing match arm
+        Either::A => (),
+    }
+    match Either::B {
+        Either::A => (), Either::B => (),
+    }
+    match &Either::B {
+        Either::A => (), Either::B => (),
+    }
+}
+"#,
+        );
+    }
+    #[test]
+    fn enum_containing_bool() {
+        check_diagnostics(
+            r#"
+enum Either { A(bool), B }
+fn main() {
+    match Either::B { }
+        //^^^^^^^^^ Missing match arm
+    match Either::B {
+        //^^^^^^^^^ Missing match arm
+        Either::A(true) => (), Either::B => ()
+    }
+    match Either::B {
+        Either::A(true) => (),
+        Either::A(false) => (),
+        Either::B => (),
+    }
+    match Either::B {
+        Either::B => (),
+        _ => (),
+    }
+    match Either::B {
+        Either::A(_) => (),
+        Either::B => (),
+    }
+}
+        "#,
+        );
+    }
+    #[test]
+    fn enum_different_sizes() {
+        check_diagnostics(
+            r#"
+enum Either { A(bool), B(bool, bool) }
+fn main() {
+    match Either::A(false) {
+        //^^^^^^^^^^^^^^^^ Missing match arm
+        Either::A(_) => (),
+        Either::B(false, _) => (),
+    }
+    match Either::A(false) {
+        Either::A(_) => (),
+        Either::B(true, _) => (),
+        Either::B(false, _) => (),
+    }
+    match Either::A(false) {
+        Either::A(true) | Either::A(false) => (),
+        Either::B(true, _) => (),
+        Either::B(false, _) => (),
+    }
+}
+"#,
+        );
+    }
+    #[test]
+    fn tuple_of_enum_no_diagnostic() {
+        check_diagnostics(
+            r#"
+enum Either { A(bool), B(bool, bool) }
+enum Either2 { C, D }
+fn main() {
+    match (Either::A(false), Either2::C) {
+        (Either::A(true), _) | (Either::A(false), _) => (),
+        (Either::B(true, _), Either2::C) => (),
+        (Either::B(false, _), Either2::C) => (),
+        (Either::B(_, _), Either2::D) => (),
+    }
+}
+"#,
+        );
+    }
+    #[test]
+    fn mismatched_types() {
+        // Match statements with arms that don't match the
+        // expression pattern do not fire this diagnostic.
+        check_diagnostics(
+            r#"
+enum Either { A, B }
+enum Either2 { C, D }
+fn main() {
+    match Either::A {
+        Either2::C => (),
+        Either2::D => (),
+    }
+    match (true, false) {
+        (true, false, true) => (),
+        (true) => (),
+    }
+    match (0) { () => () }
+    match Unresolved::Bar { Unresolved::Baz => () }
+}
+        "#,
+        );
+    }
+    #[test]
+    fn malformed_match_arm_tuple_enum_missing_pattern() {
+        // We are testing to be sure we don't panic here when the match
+        // arm `Either::B` is missing its pattern.
+        check_diagnostics(
+            r#"
+enum Either { A, B(u32) }
+fn main() {
+    match Either::A {
+        Either::A => (),
+        Either::B() => (),
+    }
+}
+"#,
+        );
+    }
+    #[test]
+    fn expr_diverges() {
+        check_diagnostics(
+            r#"
+enum Either { A, B }
+fn main() {
+    match loop {} {
+        Either::A => (),
+        Either::B => (),
+    }
+    match loop {} {
+        Either::A => (),
+    }
+    match loop { break Foo::A } {
+        //^^^^^^^^^^^^^^^^^^^^^ Missing match arm
+        Either::A => (),
+    }
+    match loop { break Foo::A } {
+        Either::A => (),
+        Either::B => (),
+    }
+}
+"#,
+        );
+    }
+    #[test]
+    fn expr_partially_diverges() {
+        check_diagnostics(
+            r#"
+enum Either<T> { A(T), B }
+fn foo() -> Either<!> { Either::B }
+fn main() -> u32 {
+    match foo() {
+        Either::A(val) => val,
+        Either::B => 0,
+    }
+}
+"#,
+        );
+    }
+    #[test]
+    fn enum_record() {
+        check_diagnostics(
+            r#"
+enum Either { A { foo: bool }, B }
+fn main() {
+    let a = Either::A { foo: true };
+    match a { }
+        //^ Missing match arm
+    match a { Either::A { foo: true } => () }
+        //^ Missing match arm
+    match a {
+        Either::A { } => (),
+      //^^^^^^^^^ Missing structure fields:
+      //        | - foo
+        Either::B => (),
+    }
+    match a {
+        //^ Missing match arm
+        Either::A { } => (),
+    } //^^^^^^^^^ Missing structure fields:
+      //        | - foo
+    match a {
+        Either::A { foo: true } => (),
+        Either::A { foo: false } => (),
+        Either::B => (),
+    }
+    match a {
+        Either::A { foo: _ } => (),
+        Either::B => (),
+    }
+}
+"#,
+        );
+    }
+    #[test]
+    fn enum_record_fields_out_of_order() {
+        check_diagnostics(
+            r#"
+enum Either {
+    A { foo: bool, bar: () },
+    B,
+}
+fn main() {
+    let a = Either::A { foo: true, bar: () };
+    match a {
+        //^ Missing match arm
+        Either::A { bar: (), foo: false } => (),
+        Either::A { foo: true, bar: () } => (),
+    }
+    match a {
+        Either::A { bar: (), foo: false } => (),
+        Either::A { foo: true, bar: () } => (),
+        Either::B => (),
+    }
+}
+"#,
+        );
+    }
+    #[test]
+    fn enum_record_ellipsis() {
+        check_diagnostics(
+            r#"
+enum Either {
+    A { foo: bool, bar: bool },
+    B,
+}
+fn main() {
+    let a = Either::B;
+    match a {
+        //^ Missing match arm
+        Either::A { foo: true, .. } => (),
+        Either::B => (),
+    }
+    match a {
+        //^ Missing match arm
+        Either::A { .. } => (),
+    }
+    match a {
+        Either::A { foo: true, .. } => (),
+        Either::A { foo: false, .. } => (),
+        Either::B => (),
+    }
+    match a {
+        Either::A { .. } => (),
+        Either::B => (),
+    }
+}
+"#,
+        );
+    }
+    #[test]
+    fn enum_tuple_partial_ellipsis() {
+        check_diagnostics(
+            r#"
+enum Either {
+    A(bool, bool, bool, bool),
+    B,
+}
+fn main() {
+    match Either::B {
+        //^^^^^^^^^ Missing match arm
+        Either::A(true, .., true) => (),
+        Either::A(true, .., false) => (),
+        Either::A(false, .., false) => (),
+        Either::B => (),
+    }
+    match Either::B {
+        //^^^^^^^^^ Missing match arm
+        Either::A(true, .., true) => (),
+        Either::A(true, .., false) => (),
+        Either::A(.., true) => (),
+        Either::B => (),
+    }
+    match Either::B {
+        Either::A(true, .., true) => (),
+        Either::A(true, .., false) => (),
+        Either::A(false, .., true) => (),
+        Either::A(false, .., false) => (),
+        Either::B => (),
+    }
+    match Either::B {
+        Either::A(true, .., true) => (),
+        Either::A(true, .., false) => (),
+        Either::A(.., true) => (),
+        Either::A(.., false) => (),
+        Either::B => (),
+    }
+}
+"#,
+        );
+    }
+    #[test]
+    fn never() {
+        check_diagnostics(
+            r#"
+enum Never {}
+fn enum_(never: Never) {
+    match never {}
+}
+fn enum_ref(never: &Never) {
+    match never {}
+}
+fn bang(never: !) {
+    match never {}
+}
+"#,
+        );
+    }
+    #[test]
+    fn or_pattern_panic() {
+        check_diagnostics(
+            r#"
+pub enum Category { Infinity, Zero }
+fn panic(a: Category, b: Category) {
+    match (a, b) {
+        (Category::Zero | Category::Infinity, _) => (),
+        (_, Category::Zero | Category::Infinity) => (),
+    }
+    // FIXME: This is a false positive, but the code used to cause a panic in the match checker,
+    // so this acts as a regression test for that.
+    match (a, b) {
+        //^^^^^^ Missing match arm
+        (Category::Infinity, Category::Infinity) | (Category::Zero, Category::Zero) => (),
+        (Category::Infinity | Category::Zero, _) => (),
+    }
+}
+"#,
+        );
+    }
+    mod false_negatives {
+        //! The implementation of match checking here is a work in progress. As we roll this out, we
+        //! prefer false negatives to false positives (ideally there would be no false positives). This
+        //! test module should document known false negatives. Eventually we will have a complete
+        //! implementation of match checking and this module will be empty.
+        //!
+        //! The reasons for documenting known false negatives:
+        //!
+        //!   1. It acts as a backlog of work that can be done to improve the behavior of the system.
+        //!   2. It ensures the code doesn't panic when handling these cases.
+        use super::*;
+        #[test]
+        fn integers() {
+            // We don't currently check integer exhaustiveness.
+            check_diagnostics(
+                r#"
+fn main() {
+    match 5 {
+        10 => (),
+        11..20 => (),
+    }
+}
+"#,
+            );
+        }
+        #[test]
+        fn internal_or() {
+            // We do not currently handle patterns with internal `or`s.
+            check_diagnostics(
+                r#"
+fn main() {
+    enum Either { A(bool), B }
+    match Either::B {
+        Either::A(true | false) => (),
+    }
+}
+"#,
+            );
+        }
+        #[test]
+        fn tuple_of_bools_with_ellipsis_at_end_missing_arm() {
+            // We don't currently handle tuple patterns with ellipsis.
+            check_diagnostics(
+                r#"
+fn main() {
+    match (false, true, false) {
+        (false, ..) => (),
+    }
+}
+"#,
+            );
+        }
+        #[test]
+        fn tuple_of_bools_with_ellipsis_at_beginning_missing_arm() {
+            // We don't currently handle tuple patterns with ellipsis.
+            check_diagnostics(
+                r#"
+fn main() {
+    match (false, true, false) {
+        (.., false) => (),
+    }
+}
+"#,
+            );
+        }
+        #[test]
+        fn struct_missing_arm() {
+            // We don't currently handle structs.
+            check_diagnostics(
+                r#"
+struct Foo { a: bool }
+fn main(f: Foo) {
+    match f { Foo { a: true } => () }
+}
+"#,
+            );
+        }
+    }
+}