models; metaphors; visual formalisms; user interface design The user interface has both syntactic functions· supplying commands and arguments to programs and semantic functions . visually presenting application semantics and supporting problem solving cognition. In this paper we argue that though both functions are important, it is time to devote more resources to the problems of the semantic interface. Complex problem solving activities, e.g, for design and analysis tasks, benefit from clear visualizations of application semantics in the user interface. Designing the semantic interface requires computational building blocks capable of representing and visually presenting application semantics in a clear, precise way. We argue that neither mental models nor metaphors provide a basis for designing and implementing such building blocks, but that visual formalisms do. We compare the benefits of mental models, metaphors and visual formalisms as the basis for designing the user interface, with particular attention to the practical solutions each provides to application developers. We describe our implementation of a visual formalism to show the potential for visual formalisms to serve as reusable computational structures that support the development of semantically rich applications.