Crate order_theory 

Traits which describe basic concepts from order theory:

• LeastElement and GreatestElement for unique extremal values.
• Lattice and BoundedLattice, built up from LowerSemilattice, UpperSemilattice and BoundedLowerSemilattice, BoundedUpperSemilattice respectively.
• TrySuccessor, SuccessorExceptForGreatest and Successor for orders with unique successors for some, almost all, or all values respectively.
• TryPredecessor, PredecessorExceptForLeast and Predecessor for orders with unique predecessors for some, almost all, or all values respectively.

Beyond those traits, the ranges module exposes functionality for treating ranges as lattices (where the greatest_lower_bound of two ranges is their intersection, and the least_upper_bound is the smallest range containing all items contained in either of them).

Finally, the [property_checks] module (available when the dev feature is enabled) provides utilities for property testing for all the traits of this crate (and the traits in core::cmp).

Modules

finite_range

Functionality for treating ranges as lattices.

Traits

BoundedLattice

A bounded lattice is a type which is both a BoundedLowerSemilattice and a BoundedUpperSemilattice. Every bounded lattice is also a regular lattice.

BoundedLowerSemilattice

A LowerSemilattice with a least element.

BoundedUpperSemilattice

An UpperSemilattice with a greatest element.

GreatestElement

A partial order with a greatest element (which is necessarily unique).

Lattice

A lattice is a type which is both a LowerSemilattice and an UpperSemilattice.

LeastElement

A partial order with a least element (which is necessarily unique).

LowerSemilattice

A partial order in which for any two elements there exists a unique greatest lower bound.

Predecessor

A partial order where every element has a unique predecessor.

PredecessorExceptForLeast

A partial order where every element but the least element has a unique predecessor.

Successor

A partial order where every element has a unique successor.

SuccessorExceptForGreatest

A partial order where every element but the greatest element has a unique successor.

TryPredecessor

A partial order in which some elements have predecessors, i.e., unique greatest lesser values.

TrySuccessor

A partial order in which some elements have successors, i.e., unique least greater values.

UpperSemilattice

A partial order in which for any two elements there exists a unique least upper bound.