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The Lapidary user interface tool allows all pictorial aspects of programs to be specified graphically. In addition, the behavior of these objects at run-time can be specified using dialogue boxes and by demonstration. In particular, Lapidary allows the designer to draw pictures of application-specific graphical objects which will be created and maintained at run-time by the application. This includes the graphical entities that the end user will manipulate (such as the components of the picture), the feedback that shows which objects are selected (such as small boxes on the sides and comers of an object), and the dynamic feedback objects (such as hair-line boxes to show where an object is being dragged). In addition, Lapidary supports the construction and use of "widgets" (sometimes called interaction techniques or gadgets) such as menus, scroll bars, buttons and icons. Lapidary therefore supports using a predefined library of widgets, and dejining a new library with a unique "look and feel."The run-time behavior of all these objects can be specified in a straightforward way using constraints and abstract descriptions of the interactive response to the input devices. Lapidary generalizes from the specific example pictures to allow the graphics and behaviors to be specified by demonstration.

Pointer variables have long been considered useful for constructing and manipulating data structures in traditional programming languages. This article discusses how pointer variables can be integrated into one-way constraint models and indicates how these constraints can be usefully employed in user interfaces. Pointer variables allow constraints to model a wide array of dynamic application behavior, simplify the implementation of structured objects and demonstrational systems, and improve the storage and efficiency of constraint-based applications. This article presents two incremental algorithms—one lazy and one eager— for solving constraints with pointer variables. Both algorithms are capable of handling (1) arbitrary systems of one-way constraints, including constraints that involve cycles, and (2) editing models that allow multiple changes between calls to the constraint solver. These algorithms are fault tolerant in that they can handle and recover gracefully from formulas that crash due to programmer error. Constraints that use pointer variables have been implemented in a comprehensive user interface toolkit, Garnet, and our experience with applications written in Garnet have proven the usefulness of pointer variable constraints. Many large-scale applications have been implemented using these constraints.

One-way dataflow constraints have gained popularity in many types of interactive systems because of their simplicity, efficiency, and manageability. Although it is widely acknowledged that multiway dataflow constraints could make it easier to specify certain relationships in these applications, concerns about their predictability and efficiency have impeded their acceptance. Constraint hierarchies have been developed to address the predictability problem, and incremental algorithms have been developed to address the efficiency problem. However, existing incremental algorithms for satisfying constraint hierarchies encounter two difficulties: (1) they are incapable of guaranteeing an acyclic solution if a constraint hierarchy has one or more cyclic solutions and (2) they require worst-case exponential time to satisfy systems of multioutput constraints. This article surmounts these difficulties by presenting an incremental algorithm called QuickPlan that satisfies in worst-case O(N') time any hierarchy of multiway, multioutput dataflow constraints that has at least one acyclic solution, where N is the number of constraints. With benchmarks and real problems that can be solved efficiently using existing algorithms, its performance is competitive or superior. With benchmarks and real problems that cannot be solved using existing algorithms or that cannot be solved efficiently, QuickPlan finds solutions and does so efficiently, typically in O(N) time or less. QuickPlan is based on the strategy of propagation of degrees of freedom. The only restriction it imposes is that every constraint method must use all of the variables in the constraint as either an input or an output variable. This requirement is met in every constraint-based, interactive application that we have developed or seen.. 31 'Henceforth, the term "constraint" will mean dataflow constraint, and the term "constraint solver" will mean dataflow constraint solver.