The design of user interfaces for computer algebra systems and theorem-proving systems is quite a challenge. Everyone who uses our symbolic computation systems wants a nice graphical user interface (GUI), with tools for keeping track of the current session, and also converting a session into a publishable form. The difficulties are in part because of the complexity of the mathematics that we are doing in these systems, the symbolic computation systems themselves, and the manipulations one might want to be able to do with them. For example, in theorem proving we would like to be able to direct the choices that algorithms make. In computer algebra systems, we would like to call other software for purely numerical problems. Consequently, there are many technical problems involved. They include how to display large mathematical formulae, how to display proofs of theorems which have been generated mechanically, how to communicate mathematical formulae between systems and their GUIs, how to input two-dimensional objects such as mathematical formulae, how to interact with an algorithm to guide it to a solution, how to manage a large derivation, and how to manipulate expressions in ways other than using commands. For example, most computer algebra systems provide a command for solving an equation for a given variable x. Some systems allow the user to select x with the mouse, then drag it to the right-hand side of the equations, meaning isolate x and causing an invocation to the system to solve the equation for x. Future systems will surely provide alternatives for user input other than keyboard and mouse-based input. Perhaps we will just say "solve for x".
This special issue, which is dedicated to the problems in the design of GUIs and protocols for symbolic computation systems (and more generally, scientific computation), begins with an extensive survey of computer algebra system GUIs up to and including 1994. It is followed by a paper on the general design of GUIs, and a paper on the design of a GUI for a mathematics system for calculus students. The fourth paper looks at efficient ways to exchange data, both symbolic and numeric, between systems. Finally, we have two papers on GUIs for theorem-proving systems.
Many people have contributed to this special issue. We would especially like to thank the referees.