The paper studies the systematic design and implementation of interactive components whose input interface is enriched by undo commands. An undo command inverts the interaction history returning to a previously visited state. We formalize different policies for undo commands cancelling the most recent input, the most recent occurrence of a specified input, and the final history segment after a user defined checkpoint. For each undo policy, we specify the component?s modified input/output behaviour in terms of the original behaviour as a function from input streams to output streams. Then we systematically transform the modified input/output behaviour into an implementation by a state transition machine. The resulting formal method extends the state transition table of an interactive component in a systematic way when its input interface is enriched by undo commands under different policies.