Concrete and Abstract Cost Semantics for Spreadsheets

We give a simple but precise operational semantics for the evaluation of extended spreadsheet formulas, with array formulas, sheet-defined functions and closures, as found in the Funcalc spreadsheet platform. We build on this to give a simple cost semantics for evaluation of a spread- sheet formula and for full and minimal recalculation of a spreadsheet. Following the ideas presented by Schmidt we provide a big step trace-based abstract interpretation for the cost semantics. We then present a set of functions which can be used to calculate the cost of executing an evaluation of a spreadsheet expression following Gomez et al., inspired by Rosendahl. These functions are related to the above operational semantics, cost semantics and abstract interpretation.
The above semantic presentations all form the formal foundations for various cost calculations implemented in the Funcalc spreadsheet platform.