Undo as concurrent inverse in group editors

Abstract

As an important mechanism for error recovery and exploration of alternatives in interactive and collaborative applications, an undo facility should have the capability of undoing any operation at any time. However, supporting undo in collaborative applications is technically challenging and none of the existing group undo solutions is able to offer such a capability. In this article, we contribute an undo solution with such a capability for group text editors. The basic idea is to interpret an undo command as a concurrent inverse operation by means of operational transformation. To cope with the high complexity of group undo, a generic undo framework has been adopted to separate undo policy from the undo mechanism and to separate transformation control algorithms from transformation functions. The proposed undo solution consists of a generic transformation control algorithm that is capable of generating, transforming, and representing valid inverse operations in any context, and a set of transformation functions that are capable of preserving undo-related transformation conditions and properties. Formal proofs are provided to show the correctness of the undo transformation control algorithm in achieving the required undo effect, undo property, and consistency properties. Solutions to the known undo puzzles are provided to show soundness of the transformation functions. A Web-based group text editor REDUCE (REal-time Distributed Unconstrained Cooperative Editing) has been implemented to demonstrate the feasibility and usability of the proposed undo and other technical solutions. The proposed undo solution is generally applicable to collaborative applications that support concurrent insertion and deletion on shared documents consisting of one or multiple dimensions of linearly ordered data objects with positional references.