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 (1990) 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 (1941) Lambda Calculus and elements of functional computer languages (such as Lisp or Scheme).

The White Rabbit put on his spectacles. "Where shall I begin, please your Majesty? " he asked. "Begin at the beginning, " the King said gravely, "and go on till you come to the end; then stop." Lewis Carroll, Alice's Adventures in Wonderland, XII The Encyclopedia Britannica [16] defines a computer programming language as "...any of various languages for expressing a set of detailed instructions for a digital computer. Such a language consists of characters and rules for combining them into symbols and words. 1