1. A data-processing system, comprising: a main processor for executing multiple interactive user application programs; at least one workstation controller, including means for coupling said workstation controller to said main processor for transferring data streams between said workstation controller and respective ones of said application programs, certain of said data streams being mouse data streams responsive to mouse-button actuations by a user and actions defined by said application programs in response to said mouse-button actuations, memory means for storing workstation-controller data and program code, a communications adapter for sending and receiving data frames, certain of said data frames being mouse-button-event data frames, a microprocessor executing said workstation-controller program code for converting selected ones of said data streams into said data frames, and for converting selected ones of said mouse-button-event data frames into further ones of said data streams and transmitting them to said main processor; a plurality of dependent workstation terminals all coupled to said one workstation controller, each of said terminals comprising a display having specified rows and columns each capable of displaying one of a set of characters, a keyboard for receiving individual keystrokes from a user, a mouse having body means for producing data representing movement events and button means for producing button events when actuated by said user, a communications adapter for sending and receiving said data frames, a terminal microprocessor executing terminal program code for (a) processing received data frames so as to (b) display specified ones of said characters at specified rows and columns of said display, for (c) transmitting data frames representing said keystrokes, for (d) storing a current mouse position in response to said mouse-movement events, for (e) displaying on said display a mouse cursor at said mouse position directly in response to said current mouse position stored in said terminal memory means, and for (f) transmitting said mouse-button-event data frames to said workstation controller in response exclusively to said mouse-button events and not in response to said mouse-movement events, said mouse-event data frames containing both said current mouse position and an indication specifying said mouse-button event, memory means for storing said terminal program code, said terminal program code stored for at least functions (d) through (f) remaining the same with respect to all of said multiple application programs executing in said main processor wherein each of said mouse-button-event data frames contains a type of mouse-button event, and a specification of said current mouse position in terms of one of said rows and one of said columns in said display, said mouse-button-event data frames remaining the same with respect to all of said multiple application programs.