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diff --git a/crates/hir_ty/src/diagnostics/match_check/deconstruct_pat.rs b/crates/hir_ty/src/diagnostics/match_check/deconstruct_pat.rs
new file mode 100644
index 000000000..9fa82a952
--- /dev/null
+++ b/crates/hir_ty/src/diagnostics/match_check/deconstruct_pat.rs
@@ -0,0 +1,894 @@
+//! [`super::usefulness`] explains most of what is happening in this file. As explained there,
+//! values and patterns are made from constructors applied to fields. This file defines a
+//! `Constructor` enum, a `Fields` struct, and various operations to manipulate them and convert
+//! them from/to patterns.
+//!
+//! There's one idea that is not detailed in [`super::usefulness`] because the details are not
+//! needed there: _constructor splitting_.
+//!
+//! # Constructor splitting
+//!
+//! The idea is as follows: given a constructor `c` and a matrix, we want to specialize in turn
+//! with all the value constructors that are covered by `c`, and compute usefulness for each.
+//! Instead of listing all those constructors (which is intractable), we group those value
+//! constructors together as much as possible. Example:
+//!
+//! ```
+//! match (0, false) {
+//!     (0 ..=100, true) => {} // `p_1`
+//!     (50..=150, false) => {} // `p_2`
+//!     (0 ..=200, _) => {} // `q`
+//! }
+//! ```
+//!
+//! The naive approach would try all numbers in the range `0..=200`. But we can be a lot more
+//! clever: `0` and `1` for example will match the exact same rows, and return equivalent
+//! witnesses. In fact all of `0..50` would. We can thus restrict our exploration to 4
+//! constructors: `0..50`, `50..=100`, `101..=150` and `151..=200`. That is enough and infinitely
+//! more tractable.
+//!
+//! We capture this idea in a function `split(p_1 ... p_n, c)` which returns a list of constructors
+//! `c'` covered by `c`. Given such a `c'`, we require that all value ctors `c''` covered by `c'`
+//! return an equivalent set of witnesses after specializing and computing usefulness.
+//! In the example above, witnesses for specializing by `c''` covered by `0..50` will only differ
+//! in their first element.
+//!
+//! We usually also ask that the `c'` together cover all of the original `c`. However we allow
+//! skipping some constructors as long as it doesn't change whether the resulting list of witnesses
+//! is empty of not. We use this in the wildcard `_` case.
+//!
+//! Splitting is implemented in the [`Constructor::split`] function. We don't do splitting for
+//! or-patterns; instead we just try the alternatives one-by-one. For details on splitting
+//! wildcards, see [`SplitWildcard`]; for integer ranges, see [`SplitIntRange`]; for slices, see
+//! [`SplitVarLenSlice`].
+
+use std::{
+    cmp::{max, min},
+    iter::once,
+    ops::RangeInclusive,
+};
+
+use hir_def::{EnumVariantId, HasModule, LocalFieldId, VariantId};
+use smallvec::{smallvec, SmallVec};
+
+use crate::{AdtId, Interner, Scalar, Ty, TyExt, TyKind};
+
+use super::{
+    usefulness::{MatchCheckCtx, PatCtxt},
+    FieldPat, Pat, PatId, PatKind,
+};
+
+use self::Constructor::*;
+
+/// [Constructor] uses this in umimplemented variants.
+/// It allows porting match expressions from upstream algorithm without losing semantics.
+#[derive(Copy, Clone, Debug, PartialEq, Eq)]
+pub(super) enum Void {}
+
+/// An inclusive interval, used for precise integer exhaustiveness checking.
+/// `IntRange`s always store a contiguous range. This means that values are
+/// encoded such that `0` encodes the minimum value for the integer,
+/// regardless of the signedness.
+/// For example, the pattern `-128..=127i8` is encoded as `0..=255`.
+/// This makes comparisons and arithmetic on interval endpoints much more
+/// straightforward. See `signed_bias` for details.
+///
+/// `IntRange` is never used to encode an empty range or a "range" that wraps
+/// around the (offset) space: i.e., `range.lo <= range.hi`.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub(super) struct IntRange {
+    range: RangeInclusive<u128>,
+}
+
+impl IntRange {
+    #[inline]
+    fn is_integral(ty: &Ty) -> bool {
+        match ty.kind(&Interner) {
+            TyKind::Scalar(Scalar::Char)
+            | TyKind::Scalar(Scalar::Int(_))
+            | TyKind::Scalar(Scalar::Uint(_))
+            | TyKind::Scalar(Scalar::Bool) => true,
+            _ => false,
+        }
+    }
+
+    fn is_singleton(&self) -> bool {
+        self.range.start() == self.range.end()
+    }
+
+    fn boundaries(&self) -> (u128, u128) {
+        (*self.range.start(), *self.range.end())
+    }
+
+    #[inline]
+    fn from_bool(value: bool) -> IntRange {
+        let val = value as u128;
+        IntRange { range: val..=val }
+    }
+
+    #[inline]
+    fn from_range(lo: u128, hi: u128, scalar_ty: Scalar) -> IntRange {
+        if let Scalar::Bool = scalar_ty {
+            IntRange { range: lo..=hi }
+        } else {
+            unimplemented!()
+        }
+    }
+
+    fn is_subrange(&self, other: &Self) -> bool {
+        other.range.start() <= self.range.start() && self.range.end() <= other.range.end()
+    }
+
+    fn intersection(&self, other: &Self) -> Option<Self> {
+        let (lo, hi) = self.boundaries();
+        let (other_lo, other_hi) = other.boundaries();
+        if lo <= other_hi && other_lo <= hi {
+            Some(IntRange { range: max(lo, other_lo)..=min(hi, other_hi) })
+        } else {
+            None
+        }
+    }
+
+    /// See `Constructor::is_covered_by`
+    fn is_covered_by(&self, other: &Self) -> bool {
+        if self.intersection(other).is_some() {
+            // Constructor splitting should ensure that all intersections we encounter are actually
+            // inclusions.
+            assert!(self.is_subrange(other));
+            true
+        } else {
+            false
+        }
+    }
+}
+
+/// Represents a border between 2 integers. Because the intervals spanning borders must be able to
+/// cover every integer, we need to be able to represent 2^128 + 1 such borders.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord)]
+enum IntBorder {
+    JustBefore(u128),
+    AfterMax,
+}
+
+/// A range of integers that is partitioned into disjoint subranges. This does constructor
+/// splitting for integer ranges as explained at the top of the file.
+///
+/// This is fed multiple ranges, and returns an output that covers the input, but is split so that
+/// the only intersections between an output range and a seen range are inclusions. No output range
+/// straddles the boundary of one of the inputs.
+///
+/// The following input:
+/// ```
+///   |-------------------------| // `self`
+/// |------|  |----------|   |----|
+///    |-------| |-------|
+/// ```
+/// would be iterated over as follows:
+/// ```
+///   ||---|--||-|---|---|---|--|
+/// ```
+#[derive(Debug, Clone)]
+struct SplitIntRange {
+    /// The range we are splitting
+    range: IntRange,
+    /// The borders of ranges we have seen. They are all contained within `range`. This is kept
+    /// sorted.
+    borders: Vec<IntBorder>,
+}
+
+impl SplitIntRange {
+    fn new(range: IntRange) -> Self {
+        SplitIntRange { range, borders: Vec::new() }
+    }
+
+    /// Internal use
+    fn to_borders(r: IntRange) -> [IntBorder; 2] {
+        use IntBorder::*;
+        let (lo, hi) = r.boundaries();
+        let lo = JustBefore(lo);
+        let hi = match hi.checked_add(1) {
+            Some(m) => JustBefore(m),
+            None => AfterMax,
+        };
+        [lo, hi]
+    }
+
+    /// Add ranges relative to which we split.
+    fn split(&mut self, ranges: impl Iterator<Item = IntRange>) {
+        let this_range = &self.range;
+        let included_ranges = ranges.filter_map(|r| this_range.intersection(&r));
+        let included_borders = included_ranges.flat_map(|r| {
+            let borders = Self::to_borders(r);
+            once(borders[0]).chain(once(borders[1]))
+        });
+        self.borders.extend(included_borders);
+        self.borders.sort_unstable();
+    }
+
+    /// Iterate over the contained ranges.
+    fn iter(&self) -> impl Iterator<Item = IntRange> + '_ {
+        use IntBorder::*;
+
+        let self_range = Self::to_borders(self.range.clone());
+        // Start with the start of the range.
+        let mut prev_border = self_range[0];
+        self.borders
+            .iter()
+            .copied()
+            // End with the end of the range.
+            .chain(once(self_range[1]))
+            // List pairs of adjacent borders.
+            .map(move |border| {
+                let ret = (prev_border, border);
+                prev_border = border;
+                ret
+            })
+            // Skip duplicates.
+            .filter(|(prev_border, border)| prev_border != border)
+            // Finally, convert to ranges.
+            .map(|(prev_border, border)| {
+                let range = match (prev_border, border) {
+                    (JustBefore(n), JustBefore(m)) if n < m => n..=(m - 1),
+                    (JustBefore(n), AfterMax) => n..=u128::MAX,
+                    _ => unreachable!(), // Ruled out by the sorting and filtering we did
+                };
+                IntRange { range }
+            })
+    }
+}
+
+/// A constructor for array and slice patterns.
+#[derive(Copy, Clone, Debug, PartialEq, Eq)]
+pub(super) struct Slice {
+    _unimplemented: Void,
+}
+
+impl Slice {
+    /// See `Constructor::is_covered_by`
+    fn is_covered_by(self, _other: Self) -> bool {
+        unimplemented!() // never called as Slice contains Void
+    }
+}
+
+/// A value can be decomposed into a constructor applied to some fields. This struct represents
+/// the constructor. See also `Fields`.
+///
+/// `pat_constructor` retrieves the constructor corresponding to a pattern.
+/// `specialize_constructor` returns the list of fields corresponding to a pattern, given a
+/// constructor. `Constructor::apply` reconstructs the pattern from a pair of `Constructor` and
+/// `Fields`.
+#[allow(dead_code)]
+#[derive(Clone, Debug, PartialEq)]
+pub(super) enum Constructor {
+    /// The constructor for patterns that have a single constructor, like tuples, struct patterns
+    /// and fixed-length arrays.
+    Single,
+    /// Enum variants.
+    Variant(EnumVariantId),
+    /// Ranges of integer literal values (`2`, `2..=5` or `2..5`).
+    IntRange(IntRange),
+    /// Ranges of floating-point literal values (`2.0..=5.2`).
+    FloatRange(Void),
+    /// String literals. Strings are not quite the same as `&[u8]` so we treat them separately.
+    Str(Void),
+    /// Array and slice patterns.
+    Slice(Slice),
+    /// Constants that must not be matched structurally. They are treated as black
+    /// boxes for the purposes of exhaustiveness: we must not inspect them, and they
+    /// don't count towards making a match exhaustive.
+    Opaque,
+    /// Fake extra constructor for enums that aren't allowed to be matched exhaustively. Also used
+    /// for those types for which we cannot list constructors explicitly, like `f64` and `str`.
+    NonExhaustive,
+    /// Stands for constructors that are not seen in the matrix, as explained in the documentation
+    /// for [`SplitWildcard`].
+    Missing,
+    /// Wildcard pattern.
+    Wildcard,
+}
+
+impl Constructor {
+    pub(super) fn is_wildcard(&self) -> bool {
+        matches!(self, Wildcard)
+    }
+
+    fn as_int_range(&self) -> Option<&IntRange> {
+        match self {
+            IntRange(range) => Some(range),
+            _ => None,
+        }
+    }
+
+    fn as_slice(&self) -> Option<Slice> {
+        match self {
+            Slice(slice) => Some(*slice),
+            _ => None,
+        }
+    }
+
+    fn variant_id_for_adt(&self, adt: hir_def::AdtId) -> VariantId {
+        match *self {
+            Variant(id) => id.into(),
+            Single => {
+                assert!(!matches!(adt, hir_def::AdtId::EnumId(_)));
+                match adt {
+                    hir_def::AdtId::EnumId(_) => unreachable!(),
+                    hir_def::AdtId::StructId(id) => id.into(),
+                    hir_def::AdtId::UnionId(id) => id.into(),
+                }
+            }
+            _ => panic!("bad constructor {:?} for adt {:?}", self, adt),
+        }
+    }
+
+    /// Determines the constructor that the given pattern can be specialized to.
+    pub(super) fn from_pat(cx: &MatchCheckCtx<'_>, pat: PatId) -> Self {
+        match cx.pattern_arena.borrow()[pat].kind.as_ref() {
+            PatKind::Binding { .. } | PatKind::Wild => Wildcard,
+            PatKind::Leaf { .. } | PatKind::Deref { .. } => Single,
+            &PatKind::Variant { enum_variant, .. } => Variant(enum_variant),
+            &PatKind::LiteralBool { value } => IntRange(IntRange::from_bool(value)),
+            PatKind::Or { .. } => panic!("bug: Or-pattern should have been expanded earlier on."),
+        }
+    }
+
+    /// Some constructors (namely `Wildcard`, `IntRange` and `Slice`) actually stand for a set of actual
+    /// constructors (like variants, integers or fixed-sized slices). When specializing for these
+    /// constructors, we want to be specialising for the actual underlying constructors.
+    /// Naively, we would simply return the list of constructors they correspond to. We instead are
+    /// more clever: if there are constructors that we know will behave the same wrt the current
+    /// matrix, we keep them grouped. For example, all slices of a sufficiently large length
+    /// will either be all useful or all non-useful with a given matrix.
+    ///
+    /// See the branches for details on how the splitting is done.
+    ///
+    /// This function may discard some irrelevant constructors if this preserves behavior and
+    /// diagnostics. Eg. for the `_` case, we ignore the constructors already present in the
+    /// matrix, unless all of them are.
+    pub(super) fn split<'a>(
+        &self,
+        pcx: PatCtxt<'_>,
+        ctors: impl Iterator<Item = &'a Constructor> + Clone,
+    ) -> SmallVec<[Self; 1]> {
+        match self {
+            Wildcard => {
+                let mut split_wildcard = SplitWildcard::new(pcx);
+                split_wildcard.split(pcx, ctors);
+                split_wildcard.into_ctors(pcx)
+            }
+            // Fast-track if the range is trivial. In particular, we don't do the overlapping
+            // ranges check.
+            IntRange(ctor_range) if !ctor_range.is_singleton() => {
+                let mut split_range = SplitIntRange::new(ctor_range.clone());
+                let int_ranges = ctors.filter_map(|ctor| ctor.as_int_range());
+                split_range.split(int_ranges.cloned());
+                split_range.iter().map(IntRange).collect()
+            }
+            Slice(_) => unimplemented!(),
+            // Any other constructor can be used unchanged.
+            _ => smallvec![self.clone()],
+        }
+    }
+
+    /// Returns whether `self` is covered by `other`, i.e. whether `self` is a subset of `other`.
+    /// For the simple cases, this is simply checking for equality. For the "grouped" constructors,
+    /// this checks for inclusion.
+    // We inline because this has a single call site in `Matrix::specialize_constructor`.
+    #[inline]
+    pub(super) fn is_covered_by(&self, _pcx: PatCtxt<'_>, other: &Self) -> bool {
+        // This must be kept in sync with `is_covered_by_any`.
+        match (self, other) {
+            // Wildcards cover anything
+            (_, Wildcard) => true,
+            // The missing ctors are not covered by anything in the matrix except wildcards.
+            (Missing, _) | (Wildcard, _) => false,
+
+            (Single, Single) => true,
+            (Variant(self_id), Variant(other_id)) => self_id == other_id,
+
+            (IntRange(self_range), IntRange(other_range)) => self_range.is_covered_by(other_range),
+            (FloatRange(..), FloatRange(..)) => {
+                unimplemented!()
+            }
+            (Str(..), Str(..)) => {
+                unimplemented!()
+            }
+            (Slice(self_slice), Slice(other_slice)) => self_slice.is_covered_by(*other_slice),
+
+            // We are trying to inspect an opaque constant. Thus we skip the row.
+            (Opaque, _) | (_, Opaque) => false,
+            // Only a wildcard pattern can match the special extra constructor.
+            (NonExhaustive, _) => false,
+
+            _ => panic!(
+                "bug: trying to compare incompatible constructors {:?} and {:?}",
+                self, other
+            ),
+        }
+    }
+
+    /// Faster version of `is_covered_by` when applied to many constructors. `used_ctors` is
+    /// assumed to be built from `matrix.head_ctors()` with wildcards filtered out, and `self` is
+    /// assumed to have been split from a wildcard.
+    fn is_covered_by_any(&self, _pcx: PatCtxt<'_>, used_ctors: &[Constructor]) -> bool {
+        if used_ctors.is_empty() {
+            return false;
+        }
+
+        // This must be kept in sync with `is_covered_by`.
+        match self {
+            // If `self` is `Single`, `used_ctors` cannot contain anything else than `Single`s.
+            Single => !used_ctors.is_empty(),
+            Variant(_) => used_ctors.iter().any(|c| c == self),
+            IntRange(range) => used_ctors
+                .iter()
+                .filter_map(|c| c.as_int_range())
+                .any(|other| range.is_covered_by(other)),
+            Slice(slice) => used_ctors
+                .iter()
+                .filter_map(|c| c.as_slice())
+                .any(|other| slice.is_covered_by(other)),
+            // This constructor is never covered by anything else
+            NonExhaustive => false,
+            Str(..) | FloatRange(..) | Opaque | Missing | Wildcard => {
+                panic!("bug: found unexpected ctor in all_ctors: {:?}", self)
+            }
+        }
+    }
+}
+
+/// A wildcard constructor that we split relative to the constructors in the matrix, as explained
+/// at the top of the file.
+///
+/// A constructor that is not present in the matrix rows will only be covered by the rows that have
+/// wildcards. Thus we can group all of those constructors together; we call them "missing
+/// constructors". Splitting a wildcard would therefore list all present constructors individually
+/// (or grouped if they are integers or slices), and then all missing constructors together as a
+/// group.
+///
+/// However we can go further: since any constructor will match the wildcard rows, and having more
+/// rows can only reduce the amount of usefulness witnesses, we can skip the present constructors
+/// and only try the missing ones.
+/// This will not preserve the whole list of witnesses, but will preserve whether the list is empty
+/// or not. In fact this is quite natural from the point of view of diagnostics too. This is done
+/// in `to_ctors`: in some cases we only return `Missing`.
+#[derive(Debug)]
+pub(super) struct SplitWildcard {
+    /// Constructors seen in the matrix.
+    matrix_ctors: Vec<Constructor>,
+    /// All the constructors for this type
+    all_ctors: SmallVec<[Constructor; 1]>,
+}
+
+impl SplitWildcard {
+    pub(super) fn new(pcx: PatCtxt<'_>) -> Self {
+        let cx = pcx.cx;
+        let make_range = |start, end, scalar| IntRange(IntRange::from_range(start, end, scalar));
+
+        // Unhandled types are treated as non-exhaustive. Being explicit here instead of falling
+        // to catchall arm to ease further implementation.
+        let unhandled = || smallvec![NonExhaustive];
+
+        // This determines the set of all possible constructors for the type `pcx.ty`. For numbers,
+        // arrays and slices we use ranges and variable-length slices when appropriate.
+        //
+        // If the `exhaustive_patterns` feature is enabled, we make sure to omit constructors that
+        // are statically impossible. E.g., for `Option<!>`, we do not include `Some(_)` in the
+        // returned list of constructors.
+        // Invariant: this is empty if and only if the type is uninhabited (as determined by
+        // `cx.is_uninhabited()`).
+        let all_ctors = match pcx.ty.kind(&Interner) {
+            TyKind::Scalar(Scalar::Bool) => smallvec![make_range(0, 1, Scalar::Bool)],
+            // TyKind::Array(..) if ... => unhandled(),
+            TyKind::Array(..) | TyKind::Slice(..) => unhandled(),
+            &TyKind::Adt(AdtId(hir_def::AdtId::EnumId(enum_id)), ref _substs) => {
+                let enum_data = cx.db.enum_data(enum_id);
+
+                // If the enum is declared as `#[non_exhaustive]`, we treat it as if it had an
+                // additional "unknown" constructor.
+                // There is no point in enumerating all possible variants, because the user can't
+                // actually match against them all themselves. So we always return only the fictitious
+                // constructor.
+                // E.g., in an example like:
+                //
+                // ```
+                //     let err: io::ErrorKind = ...;
+                //     match err {
+                //         io::ErrorKind::NotFound => {},
+                //     }
+                // ```
+                //
+                // we don't want to show every possible IO error, but instead have only `_` as the
+                // witness.
+                let is_declared_nonexhaustive = cx.is_foreign_non_exhaustive_enum(enum_id);
+
+                // If `exhaustive_patterns` is disabled and our scrutinee is an empty enum, we treat it
+                // as though it had an "unknown" constructor to avoid exposing its emptiness. The
+                // exception is if the pattern is at the top level, because we want empty matches to be
+                // considered exhaustive.
+                let is_secretly_empty = enum_data.variants.is_empty()
+                    && !cx.feature_exhaustive_patterns()
+                    && !pcx.is_top_level;
+
+                if is_secretly_empty || is_declared_nonexhaustive {
+                    smallvec![NonExhaustive]
+                } else if cx.feature_exhaustive_patterns() {
+                    // If `exhaustive_patterns` is enabled, we exclude variants known to be
+                    // uninhabited.
+                    unhandled()
+                } else {
+                    enum_data
+                        .variants
+                        .iter()
+                        .map(|(local_id, ..)| Variant(EnumVariantId { parent: enum_id, local_id }))
+                        .collect()
+                }
+            }
+            TyKind::Scalar(Scalar::Char) => unhandled(),
+            TyKind::Scalar(Scalar::Int(..)) | TyKind::Scalar(Scalar::Uint(..)) => unhandled(),
+            TyKind::Never if !cx.feature_exhaustive_patterns() && !pcx.is_top_level => {
+                smallvec![NonExhaustive]
+            }
+            TyKind::Never => SmallVec::new(),
+            _ if cx.is_uninhabited(&pcx.ty) => SmallVec::new(),
+            TyKind::Adt(..) | TyKind::Tuple(..) | TyKind::Ref(..) => smallvec![Single],
+            // This type is one for which we cannot list constructors, like `str` or `f64`.
+            _ => smallvec![NonExhaustive],
+        };
+        SplitWildcard { matrix_ctors: Vec::new(), all_ctors }
+    }
+
+    /// Pass a set of constructors relative to which to split this one. Don't call twice, it won't
+    /// do what you want.
+    pub(super) fn split<'a>(
+        &mut self,
+        pcx: PatCtxt<'_>,
+        ctors: impl Iterator<Item = &'a Constructor> + Clone,
+    ) {
+        // Since `all_ctors` never contains wildcards, this won't recurse further.
+        self.all_ctors =
+            self.all_ctors.iter().flat_map(|ctor| ctor.split(pcx, ctors.clone())).collect();
+        self.matrix_ctors = ctors.filter(|c| !c.is_wildcard()).cloned().collect();
+    }
+
+    /// Whether there are any value constructors for this type that are not present in the matrix.
+    fn any_missing(&self, pcx: PatCtxt<'_>) -> bool {
+        self.iter_missing(pcx).next().is_some()
+    }
+
+    /// Iterate over the constructors for this type that are not present in the matrix.
+    pub(super) fn iter_missing<'a>(
+        &'a self,
+        pcx: PatCtxt<'a>,
+    ) -> impl Iterator<Item = &'a Constructor> {
+        self.all_ctors.iter().filter(move |ctor| !ctor.is_covered_by_any(pcx, &self.matrix_ctors))
+    }
+
+    /// Return the set of constructors resulting from splitting the wildcard. As explained at the
+    /// top of the file, if any constructors are missing we can ignore the present ones.
+    fn into_ctors(self, pcx: PatCtxt<'_>) -> SmallVec<[Constructor; 1]> {
+        if self.any_missing(pcx) {
+            // Some constructors are missing, thus we can specialize with the special `Missing`
+            // constructor, which stands for those constructors that are not seen in the matrix,
+            // and matches the same rows as any of them (namely the wildcard rows). See the top of
+            // the file for details.
+            // However, when all constructors are missing we can also specialize with the full
+            // `Wildcard` constructor. The difference will depend on what we want in diagnostics.
+
+            // If some constructors are missing, we typically want to report those constructors,
+            // e.g.:
+            // ```
+            //     enum Direction { N, S, E, W }
+            //     let Direction::N = ...;
+            // ```
+            // we can report 3 witnesses: `S`, `E`, and `W`.
+            //
+            // However, if the user didn't actually specify a constructor
+            // in this arm, e.g., in
+            // ```
+            //     let x: (Direction, Direction, bool) = ...;
+            //     let (_, _, false) = x;
+            // ```
+            // we don't want to show all 16 possible witnesses `(<direction-1>, <direction-2>,
+            // true)` - we are satisfied with `(_, _, true)`. So if all constructors are missing we
+            // prefer to report just a wildcard `_`.
+            //
+            // The exception is: if we are at the top-level, for example in an empty match, we
+            // sometimes prefer reporting the list of constructors instead of just `_`.
+            let report_when_all_missing = pcx.is_top_level && !IntRange::is_integral(pcx.ty);
+            let ctor = if !self.matrix_ctors.is_empty() || report_when_all_missing {
+                Missing
+            } else {
+                Wildcard
+            };
+            return smallvec![ctor];
+        }
+
+        // All the constructors are present in the matrix, so we just go through them all.
+        self.all_ctors
+    }
+}
+
+/// A value can be decomposed into a constructor applied to some fields. This struct represents
+/// those fields, generalized to allow patterns in each field. See also `Constructor`.
+/// This is constructed from a constructor using [`Fields::wildcards()`].
+///
+/// If a private or `non_exhaustive` field is uninhabited, the code mustn't observe that it is
+/// uninhabited. For that, we filter these fields out of the matrix. This is handled automatically
+/// in `Fields`. This filtering is uncommon in practice, because uninhabited fields are rarely used,
+/// so we avoid it when possible to preserve performance.
+#[derive(Debug, Clone)]
+pub(super) enum Fields {
+    /// Lists of patterns that don't contain any filtered fields.
+    /// `Slice` and `Vec` behave the same; the difference is only to avoid allocating and
+    /// triple-dereferences when possible. Frankly this is premature optimization, I (Nadrieril)
+    /// have not measured if it really made a difference.
+    Vec(SmallVec<[PatId; 2]>),
+}
+
+impl Fields {
+    /// Internal use. Use `Fields::wildcards()` instead.
+    /// Must not be used if the pattern is a field of a struct/tuple/variant.
+    fn from_single_pattern(pat: PatId) -> Self {
+        Fields::Vec(smallvec![pat])
+    }
+
+    /// Convenience; internal use.
+    fn wildcards_from_tys<'a>(
+        cx: &MatchCheckCtx<'_>,
+        tys: impl IntoIterator<Item = &'a Ty>,
+    ) -> Self {
+        let wilds = tys.into_iter().map(Pat::wildcard_from_ty);
+        let pats = wilds.map(|pat| cx.alloc_pat(pat)).collect();
+        Fields::Vec(pats)
+    }
+
+    pub(crate) fn wildcards(pcx: PatCtxt<'_>, constructor: &Constructor) -> Self {
+        let ty = pcx.ty;
+        let cx = pcx.cx;
+        let wildcard_from_ty = |ty| cx.alloc_pat(Pat::wildcard_from_ty(ty));
+
+        let ret = match constructor {
+            Single | Variant(_) => match ty.kind(&Interner) {
+                TyKind::Tuple(_, substs) => {
+                    let tys = substs.iter(&Interner).map(|ty| ty.assert_ty_ref(&Interner));
+                    Fields::wildcards_from_tys(cx, tys)
+                }
+                TyKind::Ref(.., rty) => Fields::from_single_pattern(wildcard_from_ty(rty)),
+                TyKind::Adt(AdtId(adt), substs) => {
+                    let adt_is_box = false; // TODO(iDawer): implement this
+                    if adt_is_box {
+                        // Use T as the sub pattern type of Box<T>.
+                        let subst_ty = substs.at(&Interner, 0).assert_ty_ref(&Interner);
+                        Fields::from_single_pattern(wildcard_from_ty(subst_ty))
+                    } else {
+                        let variant_id = constructor.variant_id_for_adt(*adt);
+                        let adt_is_local =
+                            variant_id.module(cx.db.upcast()).krate() == cx.module.krate();
+                        // Whether we must not match the fields of this variant exhaustively.
+                        let is_non_exhaustive =
+                            is_field_list_non_exhaustive(variant_id, cx) && !adt_is_local;
+                        let field_ty_arena = cx.db.field_types(variant_id);
+                        let field_tys =
+                            || field_ty_arena.iter().map(|(_, binders)| binders.skip_binders());
+                        // In the following cases, we don't need to filter out any fields. This is
+                        // the vast majority of real cases, since uninhabited fields are uncommon.
+                        let has_no_hidden_fields = (matches!(adt, hir_def::AdtId::EnumId(_))
+                            && !is_non_exhaustive)
+                            || !field_tys().any(|ty| cx.is_uninhabited(ty));
+
+                        if has_no_hidden_fields {
+                            Fields::wildcards_from_tys(cx, field_tys())
+                        } else {
+                            //FIXME(iDawer): see MatchCheckCtx::is_uninhabited
+                            unimplemented!("exhaustive_patterns feature")
+                        }
+                    }
+                }
+                _ => panic!("Unexpected type for `Single` constructor: {:?}", ty),
+            },
+            Slice(..) => {
+                unimplemented!()
+            }
+            Str(..) | FloatRange(..) | IntRange(..) | NonExhaustive | Opaque | Missing
+            | Wildcard => Fields::Vec(Default::default()),
+        };
+        ret
+    }
+
+    /// Apply a constructor to a list of patterns, yielding a new pattern. `self`
+    /// must have as many elements as this constructor's arity.
+    ///
+    /// This is roughly the inverse of `specialize_constructor`.
+    ///
+    /// Examples:
+    /// `ctor`: `Constructor::Single`
+    /// `ty`: `Foo(u32, u32, u32)`
+    /// `self`: `[10, 20, _]`
+    /// returns `Foo(10, 20, _)`
+    ///
+    /// `ctor`: `Constructor::Variant(Option::Some)`
+    /// `ty`: `Option<bool>`
+    /// `self`: `[false]`
+    /// returns `Some(false)`
+    pub(super) fn apply(self, pcx: PatCtxt<'_>, ctor: &Constructor) -> Pat {
+        let subpatterns_and_indices = self.patterns_and_indices();
+        let mut subpatterns =
+            subpatterns_and_indices.iter().map(|&(_, p)| pcx.cx.pattern_arena.borrow()[p].clone());
+        // FIXME(iDawer) witnesses are not yet used
+        const UNHANDLED: PatKind = PatKind::Wild;
+
+        let pat = match ctor {
+            Single | Variant(_) => match pcx.ty.kind(&Interner) {
+                TyKind::Adt(..) | TyKind::Tuple(..) => {
+                    // We want the real indices here.
+                    let subpatterns = subpatterns_and_indices
+                        .iter()
+                        .map(|&(field, pat)| FieldPat {
+                            field,
+                            pattern: pcx.cx.pattern_arena.borrow()[pat].clone(),
+                        })
+                        .collect();
+
+                    if let Some((adt, substs)) = pcx.ty.as_adt() {
+                        if let hir_def::AdtId::EnumId(_) = adt {
+                            let enum_variant = match ctor {
+                                &Variant(id) => id,
+                                _ => unreachable!(),
+                            };
+                            PatKind::Variant { substs: substs.clone(), enum_variant, subpatterns }
+                        } else {
+                            PatKind::Leaf { subpatterns }
+                        }
+                    } else {
+                        PatKind::Leaf { subpatterns }
+                    }
+                }
+                // Note: given the expansion of `&str` patterns done in `expand_pattern`, we should
+                // be careful to reconstruct the correct constant pattern here. However a string
+                // literal pattern will never be reported as a non-exhaustiveness witness, so we
+                // can ignore this issue.
+                TyKind::Ref(..) => PatKind::Deref { subpattern: subpatterns.next().unwrap() },
+                TyKind::Slice(..) | TyKind::Array(..) => {
+                    panic!("bug: bad slice pattern {:?} {:?}", ctor, pcx.ty)
+                }
+                _ => PatKind::Wild,
+            },
+            Constructor::Slice(_) => UNHANDLED,
+            Str(_) => UNHANDLED,
+            FloatRange(..) => UNHANDLED,
+            Constructor::IntRange(_) => UNHANDLED,
+            NonExhaustive => PatKind::Wild,
+            Wildcard => return Pat::wildcard_from_ty(pcx.ty),
+            Opaque => panic!("bug: we should not try to apply an opaque constructor"),
+            Missing => {
+                panic!("bug: trying to apply the `Missing` constructor; this should have been done in `apply_constructors`")
+            }
+        };
+
+        Pat { ty: pcx.ty.clone(), kind: Box::new(pat) }
+    }
+
+    /// Returns the number of patterns. This is the same as the arity of the constructor used to
+    /// construct `self`.
+    pub(super) fn len(&self) -> usize {
+        match self {
+            Fields::Vec(pats) => pats.len(),
+        }
+    }
+
+    /// Returns the list of patterns along with the corresponding field indices.
+    fn patterns_and_indices(&self) -> SmallVec<[(LocalFieldId, PatId); 2]> {
+        match self {
+            Fields::Vec(pats) => pats
+                .iter()
+                .copied()
+                .enumerate()
+                .map(|(i, p)| (LocalFieldId::from_raw((i as u32).into()), p))
+                .collect(),
+        }
+    }
+
+    pub(super) fn into_patterns(self) -> SmallVec<[PatId; 2]> {
+        match self {
+            Fields::Vec(pats) => pats,
+        }
+    }
+
+    /// Overrides some of the fields with the provided patterns. Exactly like
+    /// `replace_fields_indexed`, except that it takes `FieldPat`s as input.
+    fn replace_with_fieldpats(
+        &self,
+        new_pats: impl IntoIterator<Item = (LocalFieldId, PatId)>,
+    ) -> Self {
+        self.replace_fields_indexed(
+            new_pats.into_iter().map(|(field, pat)| (u32::from(field.into_raw()) as usize, pat)),
+        )
+    }
+
+    /// Overrides some of the fields with the provided patterns. This is used when a pattern
+    /// defines some fields but not all, for example `Foo { field1: Some(_), .. }`: here we start
+    /// with a `Fields` that is just one wildcard per field of the `Foo` struct, and override the
+    /// entry corresponding to `field1` with the pattern `Some(_)`. This is also used for slice
+    /// patterns for the same reason.
+    fn replace_fields_indexed(&self, new_pats: impl IntoIterator<Item = (usize, PatId)>) -> Self {
+        let mut fields = self.clone();
+
+        match &mut fields {
+            Fields::Vec(pats) => {
+                for (i, pat) in new_pats {
+                    if let Some(p) = pats.get_mut(i) {
+                        *p = pat;
+                    }
+                }
+            }
+        }
+        fields
+    }
+
+    /// Replaces contained fields with the given list of patterns. There must be `len()` patterns
+    /// in `pats`.
+    pub(super) fn replace_fields(
+        &self,
+        cx: &MatchCheckCtx<'_>,
+        pats: impl IntoIterator<Item = Pat>,
+    ) -> Self {
+        let pats = pats.into_iter().map(|pat| cx.alloc_pat(pat)).collect();
+
+        match self {
+            Fields::Vec(_) => Fields::Vec(pats),
+        }
+    }
+
+    /// Replaces contained fields with the arguments of the given pattern. Only use on a pattern
+    /// that is compatible with the constructor used to build `self`.
+    /// This is meant to be used on the result of `Fields::wildcards()`. The idea is that
+    /// `wildcards` constructs a list of fields where all entries are wildcards, and the pattern
+    /// provided to this function fills some of the fields with non-wildcards.
+    /// In the following example `Fields::wildcards` would return `[_, _, _, _]`. If we call
+    /// `replace_with_pattern_arguments` on it with the pattern, the result will be `[Some(0), _,
+    /// _, _]`.
+    /// ```rust
+    /// let x: [Option<u8>; 4] = foo();
+    /// match x {
+    ///     [Some(0), ..] => {}
+    /// }
+    /// ```
+    /// This is guaranteed to preserve the number of patterns in `self`.
+    pub(super) fn replace_with_pattern_arguments(
+        &self,
+        pat: PatId,
+        cx: &MatchCheckCtx<'_>,
+    ) -> Self {
+        // FIXME(iDawer): these alocations and clones are so unfortunate (+1 for switching to references)
+        let mut arena = cx.pattern_arena.borrow_mut();
+        match arena[pat].kind.as_ref() {
+            PatKind::Deref { subpattern } => {
+                assert_eq!(self.len(), 1);
+                let subpattern = subpattern.clone();
+                Fields::from_single_pattern(arena.alloc(subpattern))
+            }
+            PatKind::Leaf { subpatterns } | PatKind::Variant { subpatterns, .. } => {
+                let subpatterns = subpatterns.clone();
+                let subpatterns = subpatterns
+                    .iter()
+                    .map(|field_pat| (field_pat.field, arena.alloc(field_pat.pattern.clone())));
+                self.replace_with_fieldpats(subpatterns)
+            }
+
+            PatKind::Wild
+            | PatKind::Binding { .. }
+            | PatKind::LiteralBool { .. }
+            | PatKind::Or { .. } => self.clone(),
+        }
+    }
+}
+
+fn is_field_list_non_exhaustive(variant_id: VariantId, cx: &MatchCheckCtx<'_>) -> bool {
+    let attr_def_id = match variant_id {
+        VariantId::EnumVariantId(id) => id.into(),
+        VariantId::StructId(id) => id.into(),
+        VariantId::UnionId(id) => id.into(),
+    };
+    cx.db.attrs(attr_def_id).by_key("non_exhaustive").exists()
+}
diff --git a/crates/hir_ty/src/diagnostics/match_check/pat_util.rs b/crates/hir_ty/src/diagnostics/match_check/pat_util.rs
new file mode 100644
index 000000000..eb0b07a52
--- /dev/null
+++ b/crates/hir_ty/src/diagnostics/match_check/pat_util.rs
@@ -0,0 +1,52 @@
+use std::iter::{Enumerate, ExactSizeIterator};
+
+pub(crate) struct EnumerateAndAdjust<I> {
+    enumerate: Enumerate<I>,
+    gap_pos: usize,
+    gap_len: usize,
+}
+
+impl<I> Iterator for EnumerateAndAdjust<I>
+where
+    I: Iterator,
+{
+    type Item = (usize, <I as Iterator>::Item);
+
+    fn next(&mut self) -> Option<(usize, <I as Iterator>::Item)> {
+        self.enumerate
+            .next()
+            .map(|(i, elem)| (if i < self.gap_pos { i } else { i + self.gap_len }, elem))
+    }
+
+    fn size_hint(&self) -> (usize, Option<usize>) {
+        self.enumerate.size_hint()
+    }
+}
+
+pub(crate) trait EnumerateAndAdjustIterator {
+    fn enumerate_and_adjust(
+        self,
+        expected_len: usize,
+        gap_pos: Option<usize>,
+    ) -> EnumerateAndAdjust<Self>
+    where
+        Self: Sized;
+}
+
+impl<T: ExactSizeIterator> EnumerateAndAdjustIterator for T {
+    fn enumerate_and_adjust(
+        self,
+        expected_len: usize,
+        gap_pos: Option<usize>,
+    ) -> EnumerateAndAdjust<Self>
+    where
+        Self: Sized,
+    {
+        let actual_len = self.len();
+        EnumerateAndAdjust {
+            enumerate: self.enumerate(),
+            gap_pos: gap_pos.unwrap_or(expected_len),
+            gap_len: expected_len - actual_len,
+        }
+    }
+}
diff --git a/crates/hir_ty/src/diagnostics/match_check/usefulness.rs b/crates/hir_ty/src/diagnostics/match_check/usefulness.rs
new file mode 100644
index 000000000..b01e3557c
--- /dev/null
+++ b/crates/hir_ty/src/diagnostics/match_check/usefulness.rs
@@ -0,0 +1,1180 @@
+//! Based on rust-lang/rust 1.52.0-nightly (25c15cdbe 2021-04-22)
+//! https://github.com/rust-lang/rust/blob/25c15cdbe/compiler/rustc_mir_build/src/thir/pattern/usefulness.rs
+//!
+//! -----
+//!
+//! This file includes the logic for exhaustiveness and reachability checking for pattern-matching.
+//! Specifically, given a list of patterns for a type, we can tell whether:
+//! (a) each pattern is reachable (reachability)
+//! (b) the patterns cover every possible value for the type (exhaustiveness)
+//!
+//! The algorithm implemented here is a modified version of the one described in [this
+//! paper](http://moscova.inria.fr/~maranget/papers/warn/index.html). We have however generalized
+//! it to accommodate the variety of patterns that Rust supports. We thus explain our version here,
+//! without being as rigorous.
+//!
+//!
+//! # Summary
+//!
+//! The core of the algorithm is the notion of "usefulness". A pattern `q` is said to be *useful*
+//! relative to another pattern `p` of the same type if there is a value that is matched by `q` and
+//! not matched by `p`. This generalizes to many `p`s: `q` is useful w.r.t. a list of patterns
+//! `p_1 .. p_n` if there is a value that is matched by `q` and by none of the `p_i`. We write
+//! `usefulness(p_1 .. p_n, q)` for a function that returns a list of such values. The aim of this
+//! file is to compute it efficiently.
+//!
+//! This is enough to compute reachability: a pattern in a `match` expression is reachable iff it
+//! is useful w.r.t. the patterns above it:
+//! ```rust
+//! match x {
+//!     Some(_) => ...,
+//!     None => ..., // reachable: `None` is matched by this but not the branch above
+//!     Some(0) => ..., // unreachable: all the values this matches are already matched by
+//!                     // `Some(_)` above
+//! }
+//! ```
+//!
+//! This is also enough to compute exhaustiveness: a match is exhaustive iff the wildcard `_`
+//! pattern is _not_ useful w.r.t. the patterns in the match. The values returned by `usefulness`
+//! are used to tell the user which values are missing.
+//! ```rust
+//! match x {
+//!     Some(0) => ...,
+//!     None => ...,
+//!     // not exhaustive: `_` is useful because it matches `Some(1)`
+//! }
+//! ```
+//!
+//! The entrypoint of this file is the [`compute_match_usefulness`] function, which computes
+//! reachability for each match branch and exhaustiveness for the whole match.
+//!
+//!
+//! # Constructors and fields
+//!
+//! Note: we will often abbreviate "constructor" as "ctor".
+//!
+//! The idea that powers everything that is done in this file is the following: a (matcheable)
+//! value is made from a constructor applied to a number of subvalues. Examples of constructors are
+//! `Some`, `None`, `(,)` (the 2-tuple constructor), `Foo {..}` (the constructor for a struct
+//! `Foo`), and `2` (the constructor for the number `2`). This is natural when we think of
+//! pattern-matching, and this is the basis for what follows.
+//!
+//! Some of the ctors listed above might feel weird: `None` and `2` don't take any arguments.
+//! That's ok: those are ctors that take a list of 0 arguments; they are the simplest case of
+//! ctors. We treat `2` as a ctor because `u64` and other number types behave exactly like a huge
+//! `enum`, with one variant for each number. This allows us to see any matcheable value as made up
+//! from a tree of ctors, each having a set number of children. For example: `Foo { bar: None,
+//! baz: Ok(0) }` is made from 4 different ctors, namely `Foo{..}`, `None`, `Ok` and `0`.
+//!
+//! This idea can be extended to patterns: they are also made from constructors applied to fields.
+//! A pattern for a given type is allowed to use all the ctors for values of that type (which we
+//! call "value constructors"), but there are also pattern-only ctors. The most important one is
+//! the wildcard (`_`), and the others are integer ranges (`0..=10`), variable-length slices (`[x,
+//! ..]`), and or-patterns (`Ok(0) | Err(_)`). Examples of valid patterns are `42`, `Some(_)`, `Foo
+//! { bar: Some(0) | None, baz: _ }`. Note that a binder in a pattern (e.g. `Some(x)`) matches the
+//! same values as a wildcard (e.g. `Some(_)`), so we treat both as wildcards.
+//!
+//! From this deconstruction we can compute whether a given value matches a given pattern; we
+//! simply look at ctors one at a time. Given a pattern `p` and a value `v`, we want to compute
+//! `matches!(v, p)`. It's mostly straightforward: we compare the head ctors and when they match
+//! we compare their fields recursively. A few representative examples:
+//!
+//! - `matches!(v, _) := true`
+//! - `matches!((v0,  v1), (p0,  p1)) := matches!(v0, p0) && matches!(v1, p1)`
+//! - `matches!(Foo { bar: v0, baz: v1 }, Foo { bar: p0, baz: p1 }) := matches!(v0, p0) && matches!(v1, p1)`
+//! - `matches!(Ok(v0), Ok(p0)) := matches!(v0, p0)`
+//! - `matches!(Ok(v0), Err(p0)) := false` (incompatible variants)
+//! - `matches!(v, 1..=100) := matches!(v, 1) || ... || matches!(v, 100)`
+//! - `matches!([v0], [p0, .., p1]) := false` (incompatible lengths)
+//! - `matches!([v0, v1, v2], [p0, .., p1]) := matches!(v0, p0) && matches!(v2, p1)`
+//! - `matches!(v, p0 | p1) := matches!(v, p0) || matches!(v, p1)`
+//!
+//! Constructors, fields and relevant operations are defined in the [`super::deconstruct_pat`] module.
+//!
+//! Note: this constructors/fields distinction may not straightforwardly apply to every Rust type.
+//! For example a value of type `Rc<u64>` can't be deconstructed that way, and `&str` has an
+//! infinitude of constructors. There are also subtleties with visibility of fields and
+//! uninhabitedness and various other things. The constructors idea can be extended to handle most
+//! of these subtleties though; caveats are documented where relevant throughout the code.
+//!
+//! Whether constructors cover each other is computed by [`Constructor::is_covered_by`].
+//!
+//!
+//! # Specialization
+//!
+//! Recall that we wish to compute `usefulness(p_1 .. p_n, q)`: given a list of patterns `p_1 ..
+//! p_n` and a pattern `q`, all of the same type, we want to find a list of values (called
+//! "witnesses") that are matched by `q` and by none of the `p_i`. We obviously don't just
+//! enumerate all possible values. From the discussion above we see that we can proceed
+//! ctor-by-ctor: for each value ctor of the given type, we ask "is there a value that starts with
+//! this constructor and matches `q` and none of the `p_i`?". As we saw above, there's a lot we can
+//! say from knowing only the first constructor of our candidate value.
+//!
+//! Let's take the following example:
+//! ```
+//! match x {
+//!     Enum::Variant1(_) => {} // `p1`
+//!     Enum::Variant2(None, 0) => {} // `p2`
+//!     Enum::Variant2(Some(_), 0) => {} // `q`
+//! }
+//! ```
+//!
+//! We can easily see that if our candidate value `v` starts with `Variant1` it will not match `q`.
+//! If `v = Variant2(v0, v1)` however, whether or not it matches `p2` and `q` will depend on `v0`
+//! and `v1`. In fact, such a `v` will be a witness of usefulness of `q` exactly when the tuple
+//! `(v0, v1)` is a witness of usefulness of `q'` in the following reduced match:
+//!
+//! ```
+//! match x {
+//!     (None, 0) => {} // `p2'`
+//!     (Some(_), 0) => {} // `q'`
+//! }
+//! ```
+//!
+//! This motivates a new step in computing usefulness, that we call _specialization_.
+//! Specialization consist of filtering a list of patterns for those that match a constructor, and
+//! then looking into the constructor's fields. This enables usefulness to be computed recursively.
+//!
+//! Instead of acting on a single pattern in each row, we will consider a list of patterns for each
+//! row, and we call such a list a _pattern-stack_. The idea is that we will specialize the
+//! leftmost pattern, which amounts to popping the constructor and pushing its fields, which feels
+//! like a stack. We note a pattern-stack simply with `[p_1 ... p_n]`.
+//! Here's a sequence of specializations of a list of pattern-stacks, to illustrate what's
+//! happening:
+//! ```
+//! [Enum::Variant1(_)]
+//! [Enum::Variant2(None, 0)]
+//! [Enum::Variant2(Some(_), 0)]
+//! //==>> specialize with `Variant2`
+//! [None, 0]
+//! [Some(_), 0]
+//! //==>> specialize with `Some`
+//! [_, 0]
+//! //==>> specialize with `true` (say the type was `bool`)
+//! [0]
+//! //==>> specialize with `0`
+//! []
+//! ```
+//!
+//! The function `specialize(c, p)` takes a value constructor `c` and a pattern `p`, and returns 0
+//! or more pattern-stacks. If `c` does not match the head constructor of `p`, it returns nothing;
+//! otherwise if returns the fields of the constructor. This only returns more than one
+//! pattern-stack if `p` has a pattern-only constructor.
+//!
+//! - Specializing for the wrong constructor returns nothing
+//!
+//!   `specialize(None, Some(p0)) := []`
+//!
+//! - Specializing for the correct constructor returns a single row with the fields
+//!
+//!   `specialize(Variant1, Variant1(p0, p1, p2)) := [[p0, p1, p2]]`
+//!
+//!   `specialize(Foo{..}, Foo { bar: p0, baz: p1 }) := [[p0, p1]]`
+//!
+//! - For or-patterns, we specialize each branch and concatenate the results
+//!
+//!   `specialize(c, p0 | p1) := specialize(c, p0) ++ specialize(c, p1)`
+//!
+//! - We treat the other pattern constructors as if they were a large or-pattern of all the
+//!   possibilities:
+//!
+//!   `specialize(c, _) := specialize(c, Variant1(_) | Variant2(_, _) | ...)`
+//!
+//!   `specialize(c, 1..=100) := specialize(c, 1 | ... | 100)`
+//!
+//!   `specialize(c, [p0, .., p1]) := specialize(c, [p0, p1] | [p0, _, p1] | [p0, _, _, p1] | ...)`
+//!
+//! - If `c` is a pattern-only constructor, `specialize` is defined on a case-by-case basis. See
+//!   the discussion about constructor splitting in [`super::deconstruct_pat`].
+//!
+//!
+//! We then extend this function to work with pattern-stacks as input, by acting on the first
+//! column and keeping the other columns untouched.
+//!
+//! Specialization for the whole matrix is done in [`Matrix::specialize_constructor`]. Note that
+//! or-patterns in the first column are expanded before being stored in the matrix. Specialization
+//! for a single patstack is done from a combination of [`Constructor::is_covered_by`] and
+//! [`PatStack::pop_head_constructor`]. The internals of how it's done mostly live in the
+//! [`Fields`] struct.
+//!
+//!
+//! # Computing usefulness
+//!
+//! We now have all we need to compute usefulness. The inputs to usefulness are a list of
+//! pattern-stacks `p_1 ... p_n` (one per row), and a new pattern_stack `q`. The paper and this
+//! file calls the list of patstacks a _matrix_. They must all have the same number of columns and
+//! the patterns in a given column must all have the same type. `usefulness` returns a (possibly
+//! empty) list of witnesses of usefulness. These witnesses will also be pattern-stacks.
+//!
+//! - base case: `n_columns == 0`.
+//!     Since a pattern-stack functions like a tuple of patterns, an empty one functions like the
+//!     unit type. Thus `q` is useful iff there are no rows above it, i.e. if `n == 0`.
+//!
+//! - inductive case: `n_columns > 0`.
+//!     We need a way to list the constructors we want to try. We will be more clever in the next
+//!     section but for now assume we list all value constructors for the type of the first column.
+//!
+//!     - for each such ctor `c`:
+//!
+//!         - for each `q'` returned by `specialize(c, q)`:
+//!
+//!             - we compute `usefulness(specialize(c, p_1) ... specialize(c, p_n), q')`
+//!
+//!         - for each witness found, we revert specialization by pushing the constructor `c` on top.
+//!
+//!     - We return the concatenation of all the witnesses found, if any.
+//!
+//! Example:
+//! ```
+//! [Some(true)] // p_1
+//! [None] // p_2
+//! [Some(_)] // q
+//! //==>> try `None`: `specialize(None, q)` returns nothing
+//! //==>> try `Some`: `specialize(Some, q)` returns a single row
+//! [true] // p_1'
+//! [_] // q'
+//! //==>> try `true`: `specialize(true, q')` returns a single row
+//! [] // p_1''
+//! [] // q''
+//! //==>> base case; `n != 0` so `q''` is not useful.
+//! //==>> go back up a step
+//! [true] // p_1'
+//! [_] // q'
+//! //==>> try `false`: `specialize(false, q')` returns a single row
+//! [] // q''
+//! //==>> base case; `n == 0` so `q''` is useful. We return the single witness `[]`
+//! witnesses:
+//! []
+//! //==>> undo the specialization with `false`
+//! witnesses:
+//! [false]
+//! //==>> undo the specialization with `Some`
+//! witnesses:
+//! [Some(false)]
+//! //==>> we have tried all the constructors. The output is the single witness `[Some(false)]`.
+//! ```
+//!
+//! This computation is done in [`is_useful`]. In practice we don't care about the list of
+//! witnesses when computing reachability; we only need to know whether any exist. We do keep the
+//! witnesses when computing exhaustiveness to report them to the user.
+//!
+//!
+//! # Making usefulness tractable: constructor splitting
+//!
+//! We're missing one last detail: which constructors do we list? Naively listing all value
+//! constructors cannot work for types like `u64` or `&str`, so we need to be more clever. The
+//! first obvious insight is that we only want to list constructors that are covered by the head
+//! constructor of `q`. If it's a value constructor, we only try that one. If it's a pattern-only
+//! constructor, we use the final clever idea for this algorithm: _constructor splitting_, where we
+//! group together constructors that behave the same.
+//!
+//! The details are not necessary to understand this file, so we explain them in
+//! [`super::deconstruct_pat`]. Splitting is done by the [`Constructor::split`] function.
+
+use std::{cell::RefCell, iter::FromIterator};
+
+use hir_def::{expr::ExprId, HasModule, ModuleId};
+use la_arena::Arena;
+use once_cell::unsync::OnceCell;
+use rustc_hash::FxHashMap;
+use smallvec::{smallvec, SmallVec};
+
+use crate::{db::HirDatabase, InferenceResult, Interner, Ty};
+
+use super::{
+    deconstruct_pat::{Constructor, Fields, SplitWildcard},
+    Pat, PatId, PatKind, PatternFoldable, PatternFolder,
+};
+
+use self::{helper::PatIdExt, Usefulness::*, WitnessPreference::*};
+
+pub(crate) struct MatchCheckCtx<'a> {
+    pub(crate) module: ModuleId,
+    pub(crate) match_expr: ExprId,
+    pub(crate) infer: &'a InferenceResult,
+    pub(crate) db: &'a dyn HirDatabase,
+    /// Lowered patterns from self.body.pats plus generated by the check.
+    pub(crate) pattern_arena: &'a RefCell<PatternArena>,
+}
+
+impl<'a> MatchCheckCtx<'a> {
+    pub(super) fn is_uninhabited(&self, _ty: &Ty) -> bool {
+        // FIXME(iDawer) implement exhaustive_patterns feature. More info in:
+        // Tracking issue for RFC 1872: exhaustive_patterns feature https://github.com/rust-lang/rust/issues/51085
+        false
+    }
+
+    /// Returns whether the given type is an enum from another crate declared `#[non_exhaustive]`.
+    pub(super) fn is_foreign_non_exhaustive_enum(&self, enum_id: hir_def::EnumId) -> bool {
+        let has_non_exhaustive_attr =
+            self.db.attrs(enum_id.into()).by_key("non_exhaustive").exists();
+        let is_local =
+            hir_def::AdtId::from(enum_id).module(self.db.upcast()).krate() == self.module.krate();
+        has_non_exhaustive_attr && !is_local
+    }
+
+    // Rust feature described as "Allows exhaustive pattern matching on types that contain uninhabited types."
+    pub(super) fn feature_exhaustive_patterns(&self) -> bool {
+        // TODO
+        false
+    }
+
+    pub(super) fn alloc_pat(&self, pat: Pat) -> PatId {
+        self.pattern_arena.borrow_mut().alloc(pat)
+    }
+
+    /// Get type of a pattern. Handles expanded patterns.
+    pub(super) fn type_of(&self, pat: PatId) -> Ty {
+        self.pattern_arena.borrow()[pat].ty.clone()
+    }
+}
+
+#[derive(Copy, Clone)]
+pub(super) struct PatCtxt<'a> {
+    pub(super) cx: &'a MatchCheckCtx<'a>,
+    /// Type of the current column under investigation.
+    pub(super) ty: &'a Ty,
+    /// Whether the current pattern is the whole pattern as found in a match arm, or if it's a
+    /// subpattern.
+    pub(super) is_top_level: bool,
+}
+
+pub(crate) fn expand_pattern(pat: Pat) -> Pat {
+    LiteralExpander.fold_pattern(&pat)
+}
+
+struct LiteralExpander;
+
+impl PatternFolder for LiteralExpander {
+    fn fold_pattern(&mut self, pat: &Pat) -> Pat {
+        match (pat.ty.kind(&Interner), pat.kind.as_ref()) {
+            (_, PatKind::Binding { subpattern: Some(s), .. }) => s.fold_with(self),
+            _ => pat.super_fold_with(self),
+        }
+    }
+}
+
+impl Pat {
+    fn _is_wildcard(&self) -> bool {
+        matches!(*self.kind, PatKind::Binding { subpattern: None, .. } | PatKind::Wild)
+    }
+}
+
+impl PatIdExt for PatId {
+    fn is_or_pat(self, cx: &MatchCheckCtx<'_>) -> bool {
+        matches!(*cx.pattern_arena.borrow()[self].kind, PatKind::Or { .. })
+    }
+
+    /// Recursively expand this pattern into its subpatterns. Only useful for or-patterns.
+    fn expand_or_pat(self, cx: &MatchCheckCtx<'_>) -> Vec<Self> {
+        fn expand(pat: PatId, vec: &mut Vec<PatId>, pat_arena: &mut PatternArena) {
+            if let PatKind::Or { pats } = pat_arena[pat].kind.as_ref() {
+                let pats = pats.clone();
+                for pat in pats {
+                    // FIXME(iDawer): Ugh, I want to go back to references (PatId -> &Pat)
+                    let pat = pat_arena.alloc(pat.clone());
+                    expand(pat, vec, pat_arena);
+                }
+            } else {
+                vec.push(pat)
+            }
+        }
+
+        let mut pat_arena = cx.pattern_arena.borrow_mut();
+        let mut pats = Vec::new();
+        expand(self, &mut pats, &mut pat_arena);
+        pats
+    }
+}
+
+/// A row of a matrix. Rows of len 1 are very common, which is why `SmallVec[_; 2]`
+/// works well.
+#[derive(Clone)]
+pub(super) struct PatStack {
+    pats: SmallVec<[PatId; 2]>,
+    /// Cache for the constructor of the head
+    head_ctor: OnceCell<Constructor>,
+}
+
+impl PatStack {
+    fn from_pattern(pat: PatId) -> Self {
+        Self::from_vec(smallvec![pat])
+    }
+
+    fn from_vec(vec: SmallVec<[PatId; 2]>) -> Self {
+        PatStack { pats: vec, head_ctor: OnceCell::new() }
+    }
+
+    fn is_empty(&self) -> bool {
+        self.pats.is_empty()
+    }
+
+    fn len(&self) -> usize {
+        self.pats.len()
+    }
+
+    fn head(&self) -> PatId {
+        self.pats[0]
+    }
+
+    #[inline]
+    fn head_ctor(&self, cx: &MatchCheckCtx<'_>) -> &Constructor {
+        self.head_ctor.get_or_init(|| Constructor::from_pat(cx, self.head()))
+    }
+
+    // Recursively expand the first pattern into its subpatterns. Only useful if the pattern is an
+    // or-pattern. Panics if `self` is empty.
+    fn expand_or_pat(&self, cx: &MatchCheckCtx<'_>) -> impl Iterator<Item = PatStack> + '_ {
+        self.head().expand_or_pat(cx).into_iter().map(move |pat| {
+            let mut new_patstack = PatStack::from_pattern(pat);
+            new_patstack.pats.extend_from_slice(&self.pats[1..]);
+            new_patstack
+        })
+    }
+
+    /// This computes `S(self.head_ctor(), self)`. See top of the file for explanations.
+    ///
+    /// Structure patterns with a partial wild pattern (Foo { a: 42, .. }) have their missing
+    /// fields filled with wild patterns.
+    ///
+    /// This is roughly the inverse of `Constructor::apply`.
+    fn pop_head_constructor(
+        &self,
+        ctor_wild_subpatterns: &Fields,
+        cx: &MatchCheckCtx<'_>,
+    ) -> PatStack {
+        // We pop the head pattern and push the new fields extracted from the arguments of
+        // `self.head()`.
+        let mut new_fields =
+            ctor_wild_subpatterns.replace_with_pattern_arguments(self.head(), cx).into_patterns();
+        new_fields.extend_from_slice(&self.pats[1..]);
+        PatStack::from_vec(new_fields)
+    }
+}
+
+impl Default for PatStack {
+    fn default() -> Self {
+        Self::from_vec(smallvec![])
+    }
+}
+
+impl PartialEq for PatStack {
+    fn eq(&self, other: &Self) -> bool {
+        self.pats == other.pats
+    }
+}
+
+impl FromIterator<PatId> for PatStack {
+    fn from_iter<T>(iter: T) -> Self
+    where
+        T: IntoIterator<Item = PatId>,
+    {
+        Self::from_vec(iter.into_iter().collect())
+    }
+}
+
+/// A 2D matrix.
+#[derive(Clone)]
+pub(super) struct Matrix {
+    patterns: Vec<PatStack>,
+}
+
+impl Matrix {
+    fn empty() -> Self {
+        Matrix { patterns: vec![] }
+    }
+
+    /// Number of columns of this matrix. `None` is the matrix is empty.
+    pub(super) fn _column_count(&self) -> Option<usize> {
+        self.patterns.get(0).map(|r| r.len())
+    }
+
+    /// Pushes a new row to the matrix. If the row starts with an or-pattern, this recursively
+    /// expands it.
+    fn push(&mut self, row: PatStack, cx: &MatchCheckCtx<'_>) {
+        if !row.is_empty() && row.head().is_or_pat(cx) {
+            for row in row.expand_or_pat(cx) {
+                self.patterns.push(row);
+            }
+        } else {
+            self.patterns.push(row);
+        }
+    }
+
+    /// Iterate over the first component of each row
+    fn heads(&self) -> impl Iterator<Item = PatId> + '_ {
+        self.patterns.iter().map(|r| r.head())
+    }
+
+    /// Iterate over the first constructor of each row.
+    fn head_ctors<'a>(
+        &'a self,
+        cx: &'a MatchCheckCtx<'_>,
+    ) -> impl Iterator<Item = &'a Constructor> + Clone {
+        self.patterns.iter().map(move |r| r.head_ctor(cx))
+    }
+
+    /// This computes `S(constructor, self)`. See top of the file for explanations.
+    fn specialize_constructor(
+        &self,
+        pcx: PatCtxt<'_>,
+        ctor: &Constructor,
+        ctor_wild_subpatterns: &Fields,
+    ) -> Matrix {
+        let rows = self
+            .patterns
+            .iter()
+            .filter(|r| ctor.is_covered_by(pcx, r.head_ctor(pcx.cx)))
+            .map(|r| r.pop_head_constructor(ctor_wild_subpatterns, pcx.cx));
+        Matrix::from_iter(rows, pcx.cx)
+    }
+
+    fn from_iter(rows: impl IntoIterator<Item = PatStack>, cx: &MatchCheckCtx<'_>) -> Matrix {
+        let mut matrix = Matrix::empty();
+        for x in rows {
+            // Using `push` ensures we correctly expand or-patterns.
+            matrix.push(x, cx);
+        }
+        matrix
+    }
+}
+
+/// Given a pattern or a pattern-stack, this struct captures a set of its subpatterns. We use that
+/// to track reachable sub-patterns arising from or-patterns. In the absence of or-patterns this
+/// will always be either `Empty` (the whole pattern is unreachable) or `Full` (the whole pattern
+/// is reachable). When there are or-patterns, some subpatterns may be reachable while others
+/// aren't. In this case the whole pattern still counts as reachable, but we will lint the
+/// unreachable subpatterns.
+///
+/// This supports a limited set of operations, so not all possible sets of subpatterns can be
+/// represented. That's ok, we only want the ones that make sense for our usage.
+///
+/// What we're doing is illustrated by this:
+/// ```
+/// match (true, 0) {
+///     (true, 0) => {}
+///     (_, 1) => {}
+///     (true | false, 0 | 1) => {}
+/// }
+/// ```
+/// When we try the alternatives of the `true | false` or-pattern, the last `0` is reachable in the
+/// `false` alternative but not the `true`. So overall it is reachable. By contrast, the last `1`
+/// is not reachable in either alternative, so we want to signal this to the user.
+/// Therefore we take the union of sets of reachable patterns coming from different alternatives in
+/// order to figure out which subpatterns are overall reachable.
+///
+/// Invariant: we try to construct the smallest representation we can. In particular if
+/// `self.is_empty()` we ensure that `self` is `Empty`, and same with `Full`. This is not important
+/// for correctness currently.
+#[derive(Debug, Clone)]
+enum SubPatSet {
+    /// The empty set. This means the pattern is unreachable.
+    Empty,
+    /// The set containing the full pattern.
+    Full,
+    /// If the pattern is a pattern with a constructor or a pattern-stack, we store a set for each
+    /// of its subpatterns. Missing entries in the map are implicitly full, because that's the
+    /// common case.
+    Seq { subpats: FxHashMap<usize, SubPatSet> },
+    /// If the pattern is an or-pattern, we store a set for each of its alternatives. Missing
+    /// entries in the map are implicitly empty. Note: we always flatten nested or-patterns.
+    Alt {
+        subpats: FxHashMap<usize, SubPatSet>,
+        /// Counts the total number of alternatives in the pattern
+        alt_count: usize,
+        /// We keep the pattern around to retrieve spans.
+        pat: PatId,
+    },
+}
+
+impl SubPatSet {
+    fn full() -> Self {
+        SubPatSet::Full
+    }
+
+    fn empty() -> Self {
+        SubPatSet::Empty
+    }
+
+    fn is_empty(&self) -> bool {
+        match self {
+            SubPatSet::Empty => true,
+            SubPatSet::Full => false,
+            // If any subpattern in a sequence is unreachable, the whole pattern is unreachable.
+            SubPatSet::Seq { subpats } => subpats.values().any(|set| set.is_empty()),
+            // An or-pattern is reachable if any of its alternatives is.
+            SubPatSet::Alt { subpats, .. } => subpats.values().all(|set| set.is_empty()),
+        }
+    }
+
+    fn is_full(&self) -> bool {
+        match self {
+            SubPatSet::Empty => false,
+            SubPatSet::Full => true,
+            // The whole pattern is reachable only when all its alternatives are.
+            SubPatSet::Seq { subpats } => subpats.values().all(|sub_set| sub_set.is_full()),
+            // The whole or-pattern is reachable only when all its alternatives are.
+            SubPatSet::Alt { subpats, alt_count, .. } => {
+                subpats.len() == *alt_count && subpats.values().all(|set| set.is_full())
+            }
+        }
+    }
+
+    /// Union `self` with `other`, mutating `self`.
+    fn union(&mut self, other: Self) {
+        use SubPatSet::*;
+        // Union with full stays full; union with empty changes nothing.
+        if self.is_full() || other.is_empty() {
+            return;
+        } else if self.is_empty() {
+            *self = other;
+            return;
+        } else if other.is_full() {
+            *self = Full;
+            return;
+        }
+
+        match (&mut *self, other) {
+            (Seq { subpats: s_set }, Seq { subpats: mut o_set }) => {
+                s_set.retain(|i, s_sub_set| {
+                    // Missing entries count as full.
+                    let o_sub_set = o_set.remove(&i).unwrap_or(Full);
+                    s_sub_set.union(o_sub_set);
+                    // We drop full entries.
+                    !s_sub_set.is_full()
+                });
+                // Everything left in `o_set` is missing from `s_set`, i.e. counts as full. Since
+                // unioning with full returns full, we can drop those entries.
+            }
+            (Alt { subpats: s_set, .. }, Alt { subpats: mut o_set, .. }) => {
+                s_set.retain(|i, s_sub_set| {
+                    // Missing entries count as empty.
+                    let o_sub_set = o_set.remove(&i).unwrap_or(Empty);
+                    s_sub_set.union(o_sub_set);
+                    // We drop empty entries.
+                    !s_sub_set.is_empty()
+                });
+                // Everything left in `o_set` is missing from `s_set`, i.e. counts as empty. Since
+                // unioning with empty changes nothing, we can take those entries as is.
+                s_set.extend(o_set);
+            }
+            _ => panic!("bug"),
+        }
+
+        if self.is_full() {
+            *self = Full;
+        }
+    }
+
+    /// Returns a list of the unreachable subpatterns. If `self` is empty (i.e. the
+    /// whole pattern is unreachable) we return `None`.
+    fn list_unreachable_subpatterns(&self, cx: &MatchCheckCtx<'_>) -> Option<Vec<PatId>> {
+        /// Panics if `set.is_empty()`.
+        fn fill_subpats(
+            set: &SubPatSet,
+            unreachable_pats: &mut Vec<PatId>,
+            cx: &MatchCheckCtx<'_>,
+        ) {
+            match set {
+                SubPatSet::Empty => panic!("bug"),
+                SubPatSet::Full => {}
+                SubPatSet::Seq { subpats } => {
+                    for (_, sub_set) in subpats {
+                        fill_subpats(sub_set, unreachable_pats, cx);
+                    }
+                }
+                SubPatSet::Alt { subpats, pat, alt_count, .. } => {
+                    let expanded = pat.expand_or_pat(cx);
+                    for i in 0..*alt_count {
+                        let sub_set = subpats.get(&i).unwrap_or(&SubPatSet::Empty);
+                        if sub_set.is_empty() {
+                            // Found a unreachable subpattern.
+                            unreachable_pats.push(expanded[i]);
+                        } else {
+                            fill_subpats(sub_set, unreachable_pats, cx);
+                        }
+                    }
+                }
+            }
+        }
+
+        if self.is_empty() {
+            return None;
+        }
+        if self.is_full() {
+            // No subpatterns are unreachable.
+            return Some(Vec::new());
+        }
+        let mut unreachable_pats = Vec::new();
+        fill_subpats(self, &mut unreachable_pats, cx);
+        Some(unreachable_pats)
+    }
+
+    /// When `self` refers to a patstack that was obtained from specialization, after running
+    /// `unspecialize` it will refer to the original patstack before specialization.
+    fn unspecialize(self, arity: usize) -> Self {
+        use SubPatSet::*;
+        match self {
+            Full => Full,
+            Empty => Empty,
+            Seq { subpats } => {
+                // We gather the first `arity` subpatterns together and shift the remaining ones.
+                let mut new_subpats = FxHashMap::default();
+                let mut new_subpats_first_col = FxHashMap::default();
+                for (i, sub_set) in subpats {
+                    if i < arity {
+                        // The first `arity` indices are now part of the pattern in the first
+                        // column.
+                        new_subpats_first_col.insert(i, sub_set);
+                    } else {
+                        // Indices after `arity` are simply shifted
+                        new_subpats.insert(i - arity + 1, sub_set);
+                    }
+                }
+                // If `new_subpats_first_col` has no entries it counts as full, so we can omit it.
+                if !new_subpats_first_col.is_empty() {
+                    new_subpats.insert(0, Seq { subpats: new_subpats_first_col });
+                }
+                Seq { subpats: new_subpats }
+            }
+            Alt { .. } => panic!("bug"),
+        }
+    }
+
+    /// When `self` refers to a patstack that was obtained from splitting an or-pattern, after
+    /// running `unspecialize` it will refer to the original patstack before splitting.
+    ///
+    /// For example:
+    /// ```
+    /// match Some(true) {
+    ///     Some(true) => {}
+    ///     None | Some(true | false) => {}
+    /// }
+    /// ```
+    /// Here `None` would return the full set and `Some(true | false)` would return the set
+    /// containing `false`. After `unsplit_or_pat`, we want the set to contain `None` and `false`.
+    /// This is what this function does.
+    fn unsplit_or_pat(mut self, alt_id: usize, alt_count: usize, pat: PatId) -> Self {
+        use SubPatSet::*;
+        if self.is_empty() {
+            return Empty;
+        }
+
+        // Subpatterns coming from inside the or-pattern alternative itself, e.g. in `None | Some(0
+        // | 1)`.
+        let set_first_col = match &mut self {
+            Full => Full,
+            Seq { subpats } => subpats.remove(&0).unwrap_or(Full),
+            Empty => unreachable!(),
+            Alt { .. } => panic!("bug"), // `self` is a patstack
+        };
+        let mut subpats_first_col = FxHashMap::default();
+        subpats_first_col.insert(alt_id, set_first_col);
+        let set_first_col = Alt { subpats: subpats_first_col, pat, alt_count };
+
+        let mut subpats = match self {
+            Full => FxHashMap::default(),
+            Seq { subpats } => subpats,
+            Empty => unreachable!(),
+            Alt { .. } => panic!("bug"), // `self` is a patstack
+        };
+        subpats.insert(0, set_first_col);
+        Seq { subpats }
+    }
+}
+
+/// This carries the results of computing usefulness, as described at the top of the file. When
+/// checking usefulness of a match branch, we use the `NoWitnesses` variant, which also keeps track
+/// of potential unreachable sub-patterns (in the presence of or-patterns). When checking
+/// exhaustiveness of a whole match, we use the `WithWitnesses` variant, which carries a list of
+/// witnesses of non-exhaustiveness when there are any.
+/// Which variant to use is dictated by `WitnessPreference`.
+#[derive(Clone, Debug)]
+enum Usefulness {
+    /// Carries a set of subpatterns that have been found to be reachable. If empty, this indicates
+    /// the whole pattern is unreachable. If not, this indicates that the pattern is reachable but
+    /// that some sub-patterns may be unreachable (due to or-patterns). In the absence of
+    /// or-patterns this will always be either `Empty` (the whole pattern is unreachable) or `Full`
+    /// (the whole pattern is reachable).
+    NoWitnesses(SubPatSet),
+    /// Carries a list of witnesses of non-exhaustiveness. If empty, indicates that the whole
+    /// pattern is unreachable.
+    WithWitnesses(Vec<Witness>),
+}
+
+impl Usefulness {
+    fn new_useful(preference: WitnessPreference) -> Self {
+        match preference {
+            ConstructWitness => WithWitnesses(vec![Witness(vec![])]),
+            LeaveOutWitness => NoWitnesses(SubPatSet::full()),
+        }
+    }
+    fn new_not_useful(preference: WitnessPreference) -> Self {
+        match preference {
+            ConstructWitness => WithWitnesses(vec![]),
+            LeaveOutWitness => NoWitnesses(SubPatSet::empty()),
+        }
+    }
+
+    /// Combine usefulnesses from two branches. This is an associative operation.
+    fn extend(&mut self, other: Self) {
+        match (&mut *self, other) {
+            (WithWitnesses(_), WithWitnesses(o)) if o.is_empty() => {}
+            (WithWitnesses(s), WithWitnesses(o)) if s.is_empty() => *self = WithWitnesses(o),
+            (WithWitnesses(s), WithWitnesses(o)) => s.extend(o),
+            (NoWitnesses(s), NoWitnesses(o)) => s.union(o),
+            _ => unreachable!(),
+        }
+    }
+
+    /// When trying several branches and each returns a `Usefulness`, we need to combine the
+    /// results together.
+    fn merge(pref: WitnessPreference, usefulnesses: impl Iterator<Item = Self>) -> Self {
+        let mut ret = Self::new_not_useful(pref);
+        for u in usefulnesses {
+            ret.extend(u);
+            if let NoWitnesses(subpats) = &ret {
+                if subpats.is_full() {
+                    // Once we reach the full set, more unions won't change the result.
+                    return ret;
+                }
+            }
+        }
+        ret
+    }
+
+    /// After calculating the usefulness for a branch of an or-pattern, call this to make this
+    /// usefulness mergeable with those from the other branches.
+    fn unsplit_or_pat(self, alt_id: usize, alt_count: usize, pat: PatId) -> Self {
+        match self {
+            NoWitnesses(subpats) => NoWitnesses(subpats.unsplit_or_pat(alt_id, alt_count, pat)),
+            WithWitnesses(_) => panic!("bug"),
+        }
+    }
+
+    /// After calculating usefulness after a specialization, call this to recontruct a usefulness
+    /// that makes sense for the matrix pre-specialization. This new usefulness can then be merged
+    /// with the results of specializing with the other constructors.
+    fn apply_constructor(
+        self,
+        pcx: PatCtxt<'_>,
+        matrix: &Matrix,
+        ctor: &Constructor,
+        ctor_wild_subpatterns: &Fields,
+    ) -> Self {
+        match self {
+            WithWitnesses(witnesses) if witnesses.is_empty() => WithWitnesses(witnesses),
+            WithWitnesses(witnesses) => {
+                let new_witnesses = if matches!(ctor, Constructor::Missing) {
+                    let mut split_wildcard = SplitWildcard::new(pcx);
+                    split_wildcard.split(pcx, matrix.head_ctors(pcx.cx));
+                    // Construct for each missing constructor a "wild" version of this
+                    // constructor, that matches everything that can be built with
+                    // it. For example, if `ctor` is a `Constructor::Variant` for
+                    // `Option::Some`, we get the pattern `Some(_)`.
+                    let new_patterns: Vec<_> = split_wildcard
+                        .iter_missing(pcx)
+                        .map(|missing_ctor| {
+                            Fields::wildcards(pcx, missing_ctor).apply(pcx, missing_ctor)
+                        })
+                        .collect();
+                    witnesses
+                        .into_iter()
+                        .flat_map(|witness| {
+                            new_patterns.iter().map(move |pat| {
+                                let mut witness = witness.clone();
+                                witness.0.push(pat.clone());
+                                witness
+                            })
+                        })
+                        .collect()
+                } else {
+                    witnesses
+                        .into_iter()
+                        .map(|witness| witness.apply_constructor(pcx, &ctor, ctor_wild_subpatterns))
+                        .collect()
+                };
+                WithWitnesses(new_witnesses)
+            }
+            NoWitnesses(subpats) => NoWitnesses(subpats.unspecialize(ctor_wild_subpatterns.len())),
+        }
+    }
+}
+
+#[derive(Copy, Clone, Debug)]
+enum WitnessPreference {
+    ConstructWitness,
+    LeaveOutWitness,
+}
+
+/// A witness of non-exhaustiveness for error reporting, represented
+/// as a list of patterns (in reverse order of construction) with
+/// wildcards inside to represent elements that can take any inhabitant
+/// of the type as a value.
+///
+/// A witness against a list of patterns should have the same types
+/// and length as the pattern matched against. Because Rust `match`
+/// is always against a single pattern, at the end the witness will
+/// have length 1, but in the middle of the algorithm, it can contain
+/// multiple patterns.
+///
+/// For example, if we are constructing a witness for the match against
+///
+/// ```
+/// struct Pair(Option<(u32, u32)>, bool);
+///
+/// match (p: Pair) {
+///    Pair(None, _) => {}
+///    Pair(_, false) => {}
+/// }
+/// ```
+///
+/// We'll perform the following steps:
+/// 1. Start with an empty witness
+///     `Witness(vec![])`
+/// 2. Push a witness `true` against the `false`
+///     `Witness(vec![true])`
+/// 3. Push a witness `Some(_)` against the `None`
+///     `Witness(vec![true, Some(_)])`
+/// 4. Apply the `Pair` constructor to the witnesses
+///     `Witness(vec![Pair(Some(_), true)])`
+///
+/// The final `Pair(Some(_), true)` is then the resulting witness.
+#[derive(Clone, Debug)]
+pub(crate) struct Witness(Vec<Pat>);
+
+impl Witness {
+    /// Asserts that the witness contains a single pattern, and returns it.
+    fn single_pattern(self) -> Pat {
+        assert_eq!(self.0.len(), 1);
+        self.0.into_iter().next().unwrap()
+    }
+
+    /// Constructs a partial witness for a pattern given a list of
+    /// patterns expanded by the specialization step.
+    ///
+    /// When a pattern P is discovered to be useful, this function is used bottom-up
+    /// to reconstruct a complete witness, e.g., a pattern P' that covers a subset
+    /// of values, V, where each value in that set is not covered by any previously
+    /// used patterns and is covered by the pattern P'. Examples:
+    ///
+    /// left_ty: tuple of 3 elements
+    /// pats: [10, 20, _]           => (10, 20, _)
+    ///
+    /// left_ty: struct X { a: (bool, &'static str), b: usize}
+    /// pats: [(false, "foo"), 42]  => X { a: (false, "foo"), b: 42 }
+    fn apply_constructor(
+        mut self,
+        pcx: PatCtxt<'_>,
+        ctor: &Constructor,
+        ctor_wild_subpatterns: &Fields,
+    ) -> Self {
+        let pat = {
+            let len = self.0.len();
+            let arity = ctor_wild_subpatterns.len();
+            let pats = self.0.drain((len - arity)..).rev();
+            ctor_wild_subpatterns.replace_fields(pcx.cx, pats).apply(pcx, ctor)
+        };
+
+        self.0.push(pat);
+
+        self
+    }
+}
+
+/// Algorithm from <http://moscova.inria.fr/~maranget/papers/warn/index.html>.
+/// The algorithm from the paper has been modified to correctly handle empty
+/// types. The changes are:
+///   (0) We don't exit early if the pattern matrix has zero rows. We just
+///       continue to recurse over columns.
+///   (1) all_constructors will only return constructors that are statically
+///       possible. E.g., it will only return `Ok` for `Result<T, !>`.
+///
+/// This finds whether a (row) vector `v` of patterns is 'useful' in relation
+/// to a set of such vectors `m` - this is defined as there being a set of
+/// inputs that will match `v` but not any of the sets in `m`.
+///
+/// All the patterns at each column of the `matrix ++ v` matrix must have the same type.
+///
+/// This is used both for reachability checking (if a pattern isn't useful in
+/// relation to preceding patterns, it is not reachable) and exhaustiveness
+/// checking (if a wildcard pattern is useful in relation to a matrix, the
+/// matrix isn't exhaustive).
+///
+/// `is_under_guard` is used to inform if the pattern has a guard. If it
+/// has one it must not be inserted into the matrix. This shouldn't be
+/// relied on for soundness.
+fn is_useful(
+    cx: &MatchCheckCtx<'_>,
+    matrix: &Matrix,
+    v: &PatStack,
+    witness_preference: WitnessPreference,
+    is_under_guard: bool,
+    is_top_level: bool,
+) -> Usefulness {
+    let Matrix { patterns: rows, .. } = matrix;
+
+    // The base case. We are pattern-matching on () and the return value is
+    // based on whether our matrix has a row or not.
+    // NOTE: This could potentially be optimized by checking rows.is_empty()
+    // first and then, if v is non-empty, the return value is based on whether
+    // the type of the tuple we're checking is inhabited or not.
+    if v.is_empty() {
+        let ret = if rows.is_empty() {
+            Usefulness::new_useful(witness_preference)
+        } else {
+            Usefulness::new_not_useful(witness_preference)
+        };
+        return ret;
+    }
+
+    assert!(rows.iter().all(|r| r.len() == v.len()));
+
+    // FIXME(Nadrieril): Hack to work around type normalization issues (see rust-lang/rust#72476).
+    let ty = matrix.heads().next().map_or(cx.type_of(v.head()), |r| cx.type_of(r));
+    let pcx = PatCtxt { cx, ty: &ty, is_top_level };
+
+    // If the first pattern is an or-pattern, expand it.
+    let ret = if v.head().is_or_pat(cx) {
+        //expanding or-pattern
+        let v_head = v.head();
+        let vs: Vec<_> = v.expand_or_pat(cx).collect();
+        let alt_count = vs.len();
+        // We try each or-pattern branch in turn.
+        let mut matrix = matrix.clone();
+        let usefulnesses = vs.into_iter().enumerate().map(|(i, v)| {
+            let usefulness = is_useful(cx, &matrix, &v, witness_preference, is_under_guard, false);
+            // If pattern has a guard don't add it to the matrix.
+            if !is_under_guard {
+                // We push the already-seen patterns into the matrix in order to detect redundant
+                // branches like `Some(_) | Some(0)`.
+                matrix.push(v, cx);
+            }
+            usefulness.unsplit_or_pat(i, alt_count, v_head)
+        });
+        Usefulness::merge(witness_preference, usefulnesses)
+    } else {
+        let v_ctor = v.head_ctor(cx);
+        // if let Constructor::IntRange(ctor_range) = v_ctor {
+        //     // Lint on likely incorrect range patterns (#63987)
+        //     ctor_range.lint_overlapping_range_endpoints(
+        //         pcx,
+        //         matrix.head_ctors_and_spans(cx),
+        //         matrix.column_count().unwrap_or(0),
+        //         hir_id,
+        //     )
+        // }
+
+        // We split the head constructor of `v`.
+        let split_ctors = v_ctor.split(pcx, matrix.head_ctors(cx));
+        // For each constructor, we compute whether there's a value that starts with it that would
+        // witness the usefulness of `v`.
+        let start_matrix = matrix;
+        let usefulnesses = split_ctors.into_iter().map(|ctor| {
+            // debug!("specialize({:?})", ctor);
+            // We cache the result of `Fields::wildcards` because it is used a lot.
+            let ctor_wild_subpatterns = Fields::wildcards(pcx, &ctor);
+            let spec_matrix =
+                start_matrix.specialize_constructor(pcx, &ctor, &ctor_wild_subpatterns);
+            let v = v.pop_head_constructor(&ctor_wild_subpatterns, cx);
+            let usefulness =
+                is_useful(cx, &spec_matrix, &v, witness_preference, is_under_guard, false);
+            usefulness.apply_constructor(pcx, start_matrix, &ctor, &ctor_wild_subpatterns)
+        });
+        Usefulness::merge(witness_preference, usefulnesses)
+    };
+
+    ret
+}
+
+/// The arm of a match expression.
+#[derive(Clone, Copy)]
+pub(crate) struct MatchArm {
+    pub(crate) pat: PatId,
+    pub(crate) has_guard: bool,
+}
+
+/// Indicates whether or not a given arm is reachable.
+#[derive(Clone, Debug)]
+pub(crate) enum Reachability {
+    /// The arm is reachable. This additionally carries a set of or-pattern branches that have been
+    /// found to be unreachable despite the overall arm being reachable. Used only in the presence
+    /// of or-patterns, otherwise it stays empty.
+    Reachable(Vec<PatId>),
+    /// The arm is unreachable.
+    Unreachable,
+}
+
+/// The output of checking a match for exhaustiveness and arm reachability.
+pub(crate) struct UsefulnessReport {
+    /// For each arm of the input, whether that arm is reachable after the arms above it.
+    pub(crate) _arm_usefulness: Vec<(MatchArm, Reachability)>,
+    /// If the match is exhaustive, this is empty. If not, this contains witnesses for the lack of
+    /// exhaustiveness.
+    pub(crate) non_exhaustiveness_witnesses: Vec<Pat>,
+}
+
+/// The entrypoint for the usefulness algorithm. Computes whether a match is exhaustive and which
+/// of its arms are reachable.
+///
+/// Note: the input patterns must have been lowered through
+/// `check_match::MatchVisitor::lower_pattern`.
+pub(crate) fn compute_match_usefulness(
+    cx: &MatchCheckCtx<'_>,
+    arms: &[MatchArm],
+) -> UsefulnessReport {
+    let mut matrix = Matrix::empty();
+    let arm_usefulness: Vec<_> = arms
+        .iter()
+        .copied()
+        .map(|arm| {
+            let v = PatStack::from_pattern(arm.pat);
+            let usefulness = is_useful(cx, &matrix, &v, LeaveOutWitness, arm.has_guard, true);
+            if !arm.has_guard {
+                matrix.push(v, cx);
+            }
+            let reachability = match usefulness {
+                NoWitnesses(subpats) if subpats.is_empty() => Reachability::Unreachable,
+                NoWitnesses(subpats) => {
+                    Reachability::Reachable(subpats.list_unreachable_subpatterns(cx).unwrap())
+                }
+                WithWitnesses(..) => panic!("bug"),
+            };
+            (arm, reachability)
+        })
+        .collect();
+
+    let wild_pattern =
+        cx.pattern_arena.borrow_mut().alloc(Pat::wildcard_from_ty(&cx.infer[cx.match_expr]));
+    let v = PatStack::from_pattern(wild_pattern);
+    let usefulness = is_useful(cx, &matrix, &v, ConstructWitness, false, true);
+    let non_exhaustiveness_witnesses = match usefulness {
+        WithWitnesses(pats) => pats.into_iter().map(Witness::single_pattern).collect(),
+        NoWitnesses(_) => panic!("bug"),
+    };
+    UsefulnessReport { _arm_usefulness: arm_usefulness, non_exhaustiveness_witnesses }
+}
+
+pub(crate) type PatternArena = Arena<Pat>;
+
+mod helper {
+    use super::MatchCheckCtx;
+
+    pub(super) trait PatIdExt: Sized {
+        // fn is_wildcard(self, cx: &MatchCheckCtx<'_>) -> bool;
+        fn is_or_pat(self, cx: &MatchCheckCtx<'_>) -> bool;
+        fn expand_or_pat(self, cx: &MatchCheckCtx<'_>) -> Vec<Self>;
+    }
+
+    // Copy-pasted from rust/compiler/rustc_data_structures/src/captures.rs
+    /// "Signaling" trait used in impl trait to tag lifetimes that you may
+    /// need to capture but don't really need for other reasons.
+    /// Basically a workaround; see [this comment] for details.
+    ///
+    /// [this comment]: https://github.com/rust-lang/rust/issues/34511#issuecomment-373423999
+    // FIXME(eddyb) false positive, the lifetime parameter is "phantom" but needed.
+    #[allow(unused_lifetimes)]
+    pub(crate) trait Captures<'a> {}
+
+    impl<'a, T: ?Sized> Captures<'a> for T {}
+}