Graphical User Interfaces are ever-present in our daily interactions with computer systems, especially on the web. Their implementation is often dependent on convoluted dataflow and operations changing the structure of the interface are often limited in their capability to preserve invariants between the elements. We have begun to address this by proposing an approach based on the abstraction offered by containers, employing their algebraic properties to specify both structures and the operations permitted on them. We outline the approach and suggest possible extensions for what we hope could become a practical theoretical basis of GUIs.