[][src]Module rustc_mir::dataflow::lattice

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.

     {X, Y}    <- top
      /  \
   {X}    {Y}
      \  /
       {}      <- bottom

The defining characteristic of a lattice—the one that differentiates it from a partially ordered set—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 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.

Structs

Dual

The counterpart of a given semilattice T using the inverse order.

Enums

FlatSet

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:

Traits

JoinSemiLattice

A partially ordered set that has a least upper bound for any pair of elements in the set.

MeetSemiLattice

A partially ordered set that has a greatest lower bound for any pair of elements in the set.