A new programming language construct, called DOupon, subsumes Dijkstra's selective (IF) and iterative (DO) constructs. DOupon has a predicate transformer approximately equivalent in complexity to that for DO. In addition, it simplifies a wide variety of algorithms, in form as well as in discovery and proof. Several theorems are demonstrated that are useful for correctness proofs and for optimization and that are not applicable to DO or IF. The general usefulness of DOupon derives from a separation of the concerns of invariance, through iteration, from those of termination.

Any interactive system can be described in terms of the devices it involves, and their interconnections. Similarly, each device can be described in terms of simpler devices and their interconnections. Such descriptions are strictly modular, and well structured.

Any graphical input device may be represented by a data structure, modified from time to time by actions in response to certain events, and the ability to cause certain events as part of its repertoire of actions. Portions of a device's state may be made visible to other devices in a controlled way, and the remainder hidden. Conversely, a device may make use of the visible portions of another device's state. Typically, the pattern of device interaction forms a hierarchy, but no device is part of any other. This provides for the interchangeability of a single device with a group of devices, and allows a single device to support the function of several others. Device independence is thus enhanced without the usual sacrifice of human factors considerations.