Formalisation of Spatial Standards

Abstract

The problem of building and maintaining large and heterogeneous information systems -- not only spatial ones -- is a problem generally acknowledged by the software industry [1]. Software engineering provides different techniques and tools for structuring the software development process into different phases. Thereby, one of the most important phases (and products) is the specification [2, 3]. It structures a task at hand into single actions, describes the restrictions of the actions, and captures which results are expected. However, the specification does not go into detail about how the actions are executed. Specifications are the core of standardization efforts since a specification defines the underlying conceptual model of a standard (i.e. the "world" and its meaning). Standards go one step further, and specify implementation interfaces for tasks (i.e. data structures and operation signatures) to achieve interoperability between information systems. For standards, it is signifi...

Full text

Formalisation of Spatial Standards
Silvia Nittel
Data Mining Lab, Computer Science Dept.
University of California, Los Angeles
silvia@cs.ucla.edu
Stephan Winter
Department of Geoinformation
Technical University Vienna
winter@geoinfo.tuwien.ac.at
Extended Abstract
The problem of building and maintaining large and heterogeneous informa-
tion systems — not only spatial ones — is a problem generally acknowl-
edged by the software industry [1]. Software engineering provides different
1

techniques and tools for structuring the software development process into
different phases. Thereby, one of the most important phases (and products)
is the specification [2, 3]. It structures a task at hand into single actions,
describes the restrictions of the actions, and captures which results are ex-
pected. However, the specification does not go into detail about how the
actions are executed.
Specifications are the core of standardization efforts since a specification
defines the underlying conceptual model of a standard (i.e. the ”world” and
its meaning). Standards go one step further, and specify implementation
interfaces for tasks (i.e. data structures and operation signatures) to achieve
interoperability between information systems. For standards, it is significant
that the semantic aspects of implementation interfaces are unambiguous so
that all people who build products upon the standard have the same under-
standing about the meaning of interfaces. This is complicated by the fact
that:
•specifying experts and implementation experts often cannot communi-
cate directly when standards are published;
•therefore, full understanding of the specification has to be derivable
from the specification documentation directly;
2

•specifications with a status of a standard should be consistent and
error-free to avoid costly changes to products.
Current specification techniques in spatial standard organizations are
based on graphical object oriented modelling in UML [4, 5]; they lack for-
mal modeling of the semantics of interfaces. The requirements in the field
of spatial information systems recently lead to proposals to use algebraic
specifications as an appropriate tool [6, 7, 8, 9, 10]. Algebraic specifications
have mathematical clean form, and allow to capture the semantics of opera-
tions formally [11, 12, 13]. Furthermore, they are constructive, which means
they are executable and their behavior can be checked when implemented
using functional programming languages, and modules can be composed to
more complex systems. Today, languages like Haskell are suitable tools to
implement multi-sorted algebras since they are declarative, operational, and
object-oriented [14]. The work of Kuhn and Frank demonstrates the usability
of Haskell for capturing the semantic of expressions.
In this paper, we go one step further, and investigate the applicability, and
usefulness of multi-sorted algebras and functional programming languages as
a specification tool for spatial interoperability standards. To test our case,
we choose the coverage section of the OpenGIS Consortiums’s (OGC) spatial
3

interoperability standard, and modeled and implemented the specification
of OGC coverages via Haskell. In contrast to the semi-formal UML tool
chosen by OGC we were able to capture operation semantics in a formal,
and less unambiguous way, and test the correctness and consistency of the
specification via executable code. Certainly, a formal specification does not
come without a price. The syntax of functional programming languages
seems to be less intuitive to use and understand in the beginning, and is
a unfamiliar tool for many people involved in the standardization process.
In this paper, we discuss and evaluate the effectiveness of such a tool for
the definition of spatial standards, and discuss its applicability to the real-
world process of standardization. We came to the result that a functional
specification would be a useful and necessary replacement and/or supplement
to the verbal and semi-formal specification methods used today.
References
[1] W. W. Gibbs, “Software’s chronic crisis”, Scientific American, vol. 271,
no. 3, pp. 72–81, 1994.
[2] B. Liskov and S. Zilles, “An introduction to formal specifications of data
4

abstractions”, in Current Trends in Programming Methodology (R. T.
Yeh, ed.), vol. 1, pp. 1–33, Englewood Cliffs, N.J.: Prentice-Hall, 1978.
[3] B. Liskov and J. Guttag, Abstraction and Specification in Program De-
velopment. The MIT Electrical Engineering and Computer Science Se-
ries, Cambridge, MA: MIT Press, 1986.
[4] OMG, “UML resource page”, http://www.omg.org/uml/, 2000.
[5] G. Booch, J. Rumbaugh, and I. Jacobson, The Unified Modeling Lan-
guage Reference Manual. Reading: Addison-Wesley, 1999.
[6] M. J. Egenhofer and A. U. Frank, “Object oriented modeling for GIS”,
Journal of the Urban and Regional Information Systems URISA, vol. 4,
no. 2, pp. 3–19, 1992.
[7] A. U. Frank and W. Kuhn, “Specifying open GIS with functional lan-
guages”, in Advances in Spatial Databases (M. J. Egenhofer and J. R.
Herring, eds.), vol. 951 of Lecture Notes in Computer Science, (Berlin),
pp. 184–195, Springer, 1995.
[8] A. U. Frank and W. Kuhn, “A specification language for interoperable
GIS”, in Interoperating Geographic Information Systems (M. F. Good-
5

child, M. Egenhofer, R. Fegeas, and C. Kottman, eds.), pp. 123–132,
Norwell, MA: Kluwer, 1999.
[9] W. Kuhn, “Approaching the issue of information loss in geographic data
transfers”, Geographical Systems, vol. 4, no. 3, pp. 261–276, 1997.
[10] A. U. Frank, “One step up the abstraction ladder: Combining algebras
— from functional pieces to a whole”, in Spatial Information Theory
(C. Freksa and D. M. Mark eds.), vol. 1661 of Lecture Notes in Computer
Science, Berlin: Springer-Verlag, pp. 95-107, 1999.
[11] J. V. Guttag and J. J. Horning, “The algebraic specification of abstract
data types”, Acta Informatica, vol. 10, pp. 27–52, 1978.
[12] I. V. Horebeek and J. Lewi, Algebraic Specifications in Software Engi-
neering. Berlin: Springer-Verlag, 1989.
[13] J. Loeckx, H.-D. Ehrich, and M. Wolf, Specification of Abstract Data
Types. Chichester: Wiley-Teubner, 1996.
[14] P. Hudak, J. Peterson, and J. H. Fasel, “A gentle introduction to Haskell
98”, http://www.haskell.org/tutorial/, 1999.
6