Map Calculus in GIS: a proposal and demonstration

Abstract This paper provides a new representation for fields (continuous surfaces) in Geographical Information Systems (GIS), based on the notion of spatial functions and their combinations. Following Tomlin's (Citation1990) Map Algebra, the term ‘Map Calculus' is used for this new representation. In Map Calculus, GIS layers are stored as functions, and new layers can be created by combinations of other functions. This paper explains the principles of Map Calculus and demonstrates the creation of function-based layers and their supporting management mechanism. The proposal is based on Church's (Citation1941) Lambda Calculus and elements of functional computer languages (such as Lisp or Scheme). Acknowledgements I would like to thank M. Thurstain-Goodwin for providing the motivation for this paper, and his comments on the concept of function-based layers while developing it. Thanks to M. Batty, P. J. Densham, M. F. Goodchild, P. F. Fisher, R. Laurini, P. A. Longley, D. Martin, D. Unwin and two anonymous reviewers for their insights and comments. Special thanks to D. Lloyd. Notes 1ThisFar is taken directly from Tomlin (Citation1990), and while Tomlin discusses the layer as the product of ThisFar operation, here the function itself is stored.