Semilattice

Summary

A join-semilattice is a partially ordered set in which every two elements have a join. A meet-semilattice is one in which every two elements have a meet. Algebraically, a semilattice is a semigroup whose operation is commutative and idempotent. The two views are equivalent, and a lattice is a set that is both a join- and a meet-semilattice for the same order. Semilattices appear in the theory of semigroups, in domain theory and in the analysis of programs.