A definition of types in an information system is given from ld abstractions through data constructs, schema and definitions to physical data values. Category theory suggests that four levels are sufficient to provide ultimate closure for computational types to construct information systems. The Godement calculus provides rules governing the composition of the mappings at different levels. Examples of information systems are reviewed in terms of the four-level architecture including IRDS, the Grid, the semantic web and MOF/MDA. 1 The four fundamental levels and their formalisation Interoperability is still a major problem in information systems. Most achievements have been with systems using a similar model or paradigm. Where heterogeneous systems are involved, progress has required much manual adjustment to mappings. Recently the development of the Grid has exposed the great difficulty of employing data held in formal database systems as opposed to operating system files [Watson, ...
B. Nick Rossiter, Michael A. Heather