compiler/io.github.aplcornell.viaduct.algebra

Package-level declarations

Types

BoundedJoinSemiLattice

interface BoundedJoinSemiLattice<T : JoinSemiLattice<T>>

Provides the identity element in a JoinSemiLattice.

BoundedLattice

interface BoundedLattice<T : Lattice<T>> : BoundedJoinSemiLattice<T> , BoundedMeetSemiLattice<T>

Provides the least and greatest elements in a Lattice.

BoundedMeetSemiLattice

interface BoundedMeetSemiLattice<T : MeetSemiLattice<T>>

Provides the identity element in a MeetSemiLattice.

FreeDistributiveLattice

class FreeDistributiveLattice<A> : HeytingAlgebra<FreeDistributiveLattice<A>>

The free distributive lattice over an arbitrary set A of elements. In addition to lattice identities, the following hold:

FreeDistributiveLatticeCongruence

class FreeDistributiveLatticeCongruence<A>(congruence: List<FreeDistributiveLattice.LessThanOrEqualTo<A>>) : LatticeCongruence<FreeDistributiveLattice<A>>

HeytingAlgebra

interface HeytingAlgebra<T : HeytingAlgebra<T>> : Lattice<T>

A Heyting algebra is a bounded lattice that supports an implication operation → where A → B is the greatest element x that satisfies A ∧ x ≤ B.

JoinSemiLattice

interface JoinSemiLattice<T : JoinSemiLattice<T>>

A set that supports binary least upper bounds.

Lattice

interface Lattice<T : Lattice<T>> : JoinSemiLattice<T> , MeetSemiLattice<T>

A set with unique least upper bounds and greatest lower bounds.

LatticeCongruence

interface LatticeCongruence<A : Lattice<A>>

MeetSemiLattice

interface MeetSemiLattice<T : MeetSemiLattice<T>>

A set that supports binary greatest lower bounds.

PartialOrder

interface PartialOrder<T>

Like Comparable, but not all pairs of elements have to be ordered.