Formal specifications are difficult to read.Executable specifications allow to see the behavior of the specified objects and help the domain specialist to detect errors quickly. We present here a method which allows to write axiomatic specifications which can be executed and discuss the limitations in expressive power imposed by the restriction to constructive axioms and how it can be circumvented. The method results from practical efforts to formalize the meaning of object types for Geographic Information Systems. If such data are shared betweenorganisations, differences in the semantics become apparent and formal methods for their definition become necessary. Most formal methods are based on first order languages. Software engineering often uses algebraic methods, but tools practically used for data exchange standard definitions are restricted to signatures and do not capture the behavior of the operations. We present here an algebraic approach using a functional programming language...

The tool we use influences the product. This paper demonstrates that higher order functions are a necessary tool for research in the GIS area, because higher order functions permit to separate the treatment of attribute data from the organisation of processing in data structures. Higher order functions are functions which have functions as arguments. A function to traverse a data structure can thus have as an argument a function to perform specific operations with the attribute data stored. This is crucial in the GIS arena, where complex spatial data structures are necessary. Higher order functions were tacitly assumed for Tomlin's Map Algebra. The lack of higher order functions in the design stage of GIS and in the implementation is currently most felt for visualization, where the problems of the interaction between the generic computer graphics solutions and the particulars of the application area preclude advanced solutions, which combine the best results from both worlds. Similar ...