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Diffstat (limited to 'compiler/rustc_mir_dataflow/src/framework/lattice.rs')
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diff --git a/compiler/rustc_mir_dataflow/src/framework/lattice.rs b/compiler/rustc_mir_dataflow/src/framework/lattice.rs new file mode 100644 index 00000000000..f937b31f4cf --- /dev/null +++ b/compiler/rustc_mir_dataflow/src/framework/lattice.rs @@ -0,0 +1,231 @@ +//! Traits used to represent [lattices] for use as the domain of a dataflow analysis. +//! +//! # Overview +//! +//! The most common lattice is a powerset of some set `S`, ordered by [set inclusion]. The [Hasse +//! diagram] for the powerset of a set with two elements (`X` and `Y`) is shown below. Note that +//! distinct elements at the same height in a Hasse diagram (e.g. `{X}` and `{Y}`) are +//! *incomparable*, not equal. +//! +//! ```text +//! {X, Y} <- top +//! / \ +//! {X} {Y} +//! \ / +//! {} <- bottom +//! +//! ``` +//! +//! The defining characteristic of a lattice—the one that differentiates it from a [partially +//! ordered set][poset]—is the existence of a *unique* least upper and greatest lower bound for +//! every pair of elements. The lattice join operator (`∨`) returns the least upper bound, and the +//! lattice meet operator (`∧`) returns the greatest lower bound. Types that implement one operator +//! but not the other are known as semilattices. Dataflow analysis only uses the join operator and +//! will work with any join-semilattice, but both should be specified when possible. +//! +//! ## `PartialOrd` +//! +//! Given that they represent partially ordered sets, you may be surprised that [`JoinSemiLattice`] +//! and [`MeetSemiLattice`] do not have [`PartialOrd`][std::cmp::PartialOrd] as a supertrait. This +//! is because most standard library types use lexicographic ordering instead of set inclusion for +//! their `PartialOrd` impl. Since we do not actually need to compare lattice elements to run a +//! dataflow analysis, there's no need for a newtype wrapper with a custom `PartialOrd` impl. The +//! only benefit would be the ability to check that the least upper (or greatest lower) bound +//! returned by the lattice join (or meet) operator was in fact greater (or lower) than the inputs. +//! +//! [lattices]: https://en.wikipedia.org/wiki/Lattice_(order) +//! [set inclusion]: https://en.wikipedia.org/wiki/Subset +//! [Hasse diagram]: https://en.wikipedia.org/wiki/Hasse_diagram +//! [poset]: https://en.wikipedia.org/wiki/Partially_ordered_set + +use rustc_index::bit_set::BitSet; +use rustc_index::vec::{Idx, IndexVec}; +use std::iter; + +/// A [partially ordered set][poset] that has a [least upper bound][lub] for any pair of elements +/// in the set. +/// +/// [lub]: https://en.wikipedia.org/wiki/Infimum_and_supremum +/// [poset]: https://en.wikipedia.org/wiki/Partially_ordered_set +pub trait JoinSemiLattice: Eq { + /// Computes the least upper bound of two elements, storing the result in `self` and returning + /// `true` if `self` has changed. + /// + /// The lattice join operator is abbreviated as `∨`. + fn join(&mut self, other: &Self) -> bool; +} + +/// A [partially ordered set][poset] that has a [greatest lower bound][glb] for any pair of +/// elements in the set. +/// +/// Dataflow analyses only require that their domains implement [`JoinSemiLattice`], not +/// `MeetSemiLattice`. However, types that will be used as dataflow domains should implement both +/// so that they can be used with [`Dual`]. +/// +/// [glb]: https://en.wikipedia.org/wiki/Infimum_and_supremum +/// [poset]: https://en.wikipedia.org/wiki/Partially_ordered_set +pub trait MeetSemiLattice: Eq { + /// Computes the greatest lower bound of two elements, storing the result in `self` and + /// returning `true` if `self` has changed. + /// + /// The lattice meet operator is abbreviated as `∧`. + fn meet(&mut self, other: &Self) -> bool; +} + +/// A `bool` is a "two-point" lattice with `true` as the top element and `false` as the bottom: +/// +/// ```text +/// true +/// | +/// false +/// ``` +impl JoinSemiLattice for bool { + fn join(&mut self, other: &Self) -> bool { + if let (false, true) = (*self, *other) { + *self = true; + return true; + } + + false + } +} + +impl MeetSemiLattice for bool { + fn meet(&mut self, other: &Self) -> bool { + if let (true, false) = (*self, *other) { + *self = false; + return true; + } + + false + } +} + +/// A tuple (or list) of lattices is itself a lattice whose least upper bound is the concatenation +/// of the least upper bounds of each element of the tuple (or list). +/// +/// In other words: +/// (A₀, A₁, ..., Aₙ) ∨ (B₀, B₁, ..., Bₙ) = (A₀∨B₀, A₁∨B₁, ..., Aₙ∨Bₙ) +impl<I: Idx, T: JoinSemiLattice> JoinSemiLattice for IndexVec<I, T> { + fn join(&mut self, other: &Self) -> bool { + assert_eq!(self.len(), other.len()); + + let mut changed = false; + for (a, b) in iter::zip(self, other) { + changed |= a.join(b); + } + changed + } +} + +impl<I: Idx, T: MeetSemiLattice> MeetSemiLattice for IndexVec<I, T> { + fn meet(&mut self, other: &Self) -> bool { + assert_eq!(self.len(), other.len()); + + let mut changed = false; + for (a, b) in iter::zip(self, other) { + changed |= a.meet(b); + } + changed + } +} + +/// A `BitSet` represents the lattice formed by the powerset of all possible values of +/// the index type `T` ordered by inclusion. Equivalently, it is a tuple of "two-point" lattices, +/// one for each possible value of `T`. +impl<T: Idx> JoinSemiLattice for BitSet<T> { + fn join(&mut self, other: &Self) -> bool { + self.union(other) + } +} + +impl<T: Idx> MeetSemiLattice for BitSet<T> { + fn meet(&mut self, other: &Self) -> bool { + self.intersect(other) + } +} + +/// The counterpart of a given semilattice `T` using the [inverse order]. +/// +/// The dual of a join-semilattice is a meet-semilattice and vice versa. For example, the dual of a +/// powerset has the empty set as its top element and the full set as its bottom element and uses +/// set *intersection* as its join operator. +/// +/// [inverse order]: https://en.wikipedia.org/wiki/Duality_(order_theory) +#[derive(Clone, Copy, Debug, PartialEq, Eq)] +pub struct Dual<T>(pub T); + +impl<T> std::borrow::Borrow<T> for Dual<T> { + fn borrow(&self) -> &T { + &self.0 + } +} + +impl<T> std::borrow::BorrowMut<T> for Dual<T> { + fn borrow_mut(&mut self) -> &mut T { + &mut self.0 + } +} + +impl<T: MeetSemiLattice> JoinSemiLattice for Dual<T> { + fn join(&mut self, other: &Self) -> bool { + self.0.meet(&other.0) + } +} + +impl<T: JoinSemiLattice> MeetSemiLattice for Dual<T> { + fn meet(&mut self, other: &Self) -> bool { + self.0.join(&other.0) + } +} + +/// Extends a type `T` with top and bottom elements to make it a partially ordered set in which no +/// value of `T` is comparable with any other. A flat set has the following [Hasse diagram]: +/// +/// ```text +/// top +/// / / \ \ +/// all possible values of `T` +/// \ \ / / +/// bottom +/// ``` +/// +/// [Hasse diagram]: https://en.wikipedia.org/wiki/Hasse_diagram +#[derive(Clone, Copy, Debug, PartialEq, Eq)] +pub enum FlatSet<T> { + Bottom, + Elem(T), + Top, +} + +impl<T: Clone + Eq> JoinSemiLattice for FlatSet<T> { + fn join(&mut self, other: &Self) -> bool { + let result = match (&*self, other) { + (Self::Top, _) | (_, Self::Bottom) => return false, + (Self::Elem(a), Self::Elem(b)) if a == b => return false, + + (Self::Bottom, Self::Elem(x)) => Self::Elem(x.clone()), + + _ => Self::Top, + }; + + *self = result; + true + } +} + +impl<T: Clone + Eq> MeetSemiLattice for FlatSet<T> { + fn meet(&mut self, other: &Self) -> bool { + let result = match (&*self, other) { + (Self::Bottom, _) | (_, Self::Top) => return false, + (Self::Elem(ref a), Self::Elem(ref b)) if a == b => return false, + + (Self::Top, Self::Elem(ref x)) => Self::Elem(x.clone()), + + _ => Self::Bottom, + }; + + *self = result; + true + } +} |