On the semantics for spreadsheets with sheet-defined functions

We give an operational semantics for the evaluation of spreadsheets, including sheet-defined and built-in numeric functions in the Funcalc spreadsheet platform. The semantics allows for different implementations and we discuss sheet-defined functions implemented using both interpretation and run-time code generation. The semantics specifies the expected result of a computation, also considering non-deterministic functions, independently of an evaluation mechanism. It can be extended to include the cost of formula evaluation for a cost analysis e.g. for use in parallelization of computations. An interesting future direction is to investigate experimentally how close our semantics is to that of major spreadsheet implementations.