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.

Nothing too fancy going on in this crate, just providing a couple traits which are really handy to be able to use as trait bounds every once in a while.

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.