This dissertation proposes an information processing model based on sets that can be seen as a generalization of the classic model of graphs for hypertexts. This model estimates a semantic model of an application domain, and the sets of objects are defined from this. Information processing tasks that the users should execute, with support of the application, are described as functional compositions of operations applied over the information items and over the defined sets. This model type allows the application construction with interfaces of direct manipulation on items and sets, and includes, among others, the faceted navigation interfaces that are currently found in the Web. In this type of interface, the user builds the functional composition that represents the desired computation in the incremental form, through the direct manipulation of elements in the interface.This dissertation specifies this model, and presents an implementation in the .Net environment. Beyond the definition of items and sets, it generates a Domain Specific Language (DSL) that allows the direct expression of operations on items and sets. The proposed model, and its implementation, is integrated with a framework for generating direct manipulation interfaces on sets, that is the focus of another dissertation. A study case is presented, using the model, its implementation and the integration with the interface, illustrating how the approach facilitates different types of tasks that are frequently executed by Web application users.