  We introduce iposets---posets with interfaces---equipped with a novel gluing
composition along interfaces and the standard parallel composition. We study
their basic algebraic properties as well as the hierarchy of gluing-parallel
posets generated from singletons by finitary applications of the two
compositions. We show that not only series-parallel posets, but also interval
orders, which seem more interesting for modelling concurrent and distributed
systems, can be generated, but not all posets. Generating posets is also
important for constructing free algebras for concurrent semirings and Kleene
algebras that allow compositional reasoning about such systems.
