lattice package:numhask

Lattices

The combination of two semi lattices makes a lattice if the absorption law holds: see Absorption Law and Lattice

Absorption: a \/ (a /\ b) == a /\ (a \/ b) == a

A join-semilattice with an identity element bottom for \/.

x \/ bottom == bottom

A meet-semilattice with an identity element top for /\.

x /\ top == top

A algebraic structure with element joins: See Semilattice

Associativity: x \/ (y \/ z) == (x \/ y) \/ z
Commutativity: x \/ y == y \/ x
Idempotency:   x \/ x == x

A algebraic structure with element meets: See Semilattice

Associativity: x /\ (y /\ z) == (x /\ y) /\ z
Commutativity: x /\ y == y /\ x
Idempotency:   x /\ x == x

Lattices with both bounds

x /\ bottom == x
x \/ top = x