Map algebra extended with functors for temporal data

This paper shows how to extend and generalize Ton-din's Map Algebra to apply uniformly for spatial, temporal, and spatio-temporal data. A specific data layer can be seen as a function from location to a value (Goodchild's geographic reality). Map layer but also time series and other similar constructions are functors, mapping local operations to layers, time series, etc. Ton-din's Focal Operations are mostly convolutions and the zonal operations are summaries for zones. The mathematical framework explained justifies polymorphic overloading of operation names like + are made to work for layers, time series, etc. There is also a uniform method to apply user-defined local functions to them. The result is a consistent extension of Map Algebra with a simplified user interface. The implementation covers raster operations and demonstrates the generality of the concept.