Abstract. Starting from existing spreadsheet software, like Lotus 1-23R , ExcelR , or Spreadsheet 2000R , we propose a sequence of enhancements to fully integrate constraint-based reasoning, culminating in a system for reactive, graphical, mathematical constructions. This is driven by our view of constraints as the essence of (spreadsheet) computation, rather than as an add-on tool for expert users. We call this extended computational metaphor, spreadspaces. We believe that research towards more general and realistic constraint solving frameworks has to go on in parallel with the effort to make fewer and fewer requests to the user. In other words, users should be asked only for as much as they want to give the system. This amount of information (decided by users but with a minimum set by the system below which most precision is lost) is then used by the system to construct the whole constraint problem. --Ugo Montanari and Francesca Rossi [18] 1 Overview Our ultimate goal in this work i...