An Abstract Domain to Infer Types over Zones

Abstract. Spreadsheet languages are very commonly used, by large user bases, yet they are error prone. However, many semantic issues and errors could be avoided by enforcing a stricter type discipline. As declaring and specifying type information would represent a prohibitive amount of work for users, we propose an abstract interpretation based static analysis for spreadsheet programs that infers type constraints over zones of spread-sheets, viewed as two-dimensional arrays. Our abstract domain consists in a cardinal power from a numerical abstraction describing zones in a spreadsheet to an abstraction of cell values, including type properties. We formalize this abstract domain and its operators (transfer functions, join, widening and reduction) as well as a static analysis for a simpli-values and present an implementation of our analysis.