BPMN and Beyond Business process modelling notation, workflow ...

ASM Foundations of Database Management 13
4 Conclusion
The ASM approach allows the development of a theory of database system operating.
It has the following advantages:
– The signature of object-relational databases can be specified based on hierarchical
predicate logic. Therefore, the theory of static integrity constraints can
be entirely embedded into the theory of sequential abstract-state machines
[4].
– The run of a database system is parallel. As an example that is not covered
in this paper we elaborated transaction semantics that handles conflicts in
concurrency. Parallel runs of transactions must behave in the same manner
as a sequential run of the transactions. This concept is entirely covered by
partially ordered runs.
– Interaction of database systems with user or information systems can be
handled by ASM as discussed above.
– Database systems are considered on a variety of abstractions layers. Users
consider a database system as an input-output engine with a powerful memory.
At the conceptual layer, a database system is far more complex. The implementation
is even more complex. Therefore, the consideration of database
systems semantics requires also a powerful theory of refinement as provided
by ASM.
Our main aim in this paper is to develop a theory of database systems at the user
layer. The other abstraction layers may be seen as refinements of the business
user layer. We omitted all examples to the space limitations.
The next abstraction level must consider specifical approaches of database
engines at the implementation layer. In this case, we need a general notion
of database semantics. Database dynamics has not yet been well understood.
Transactions may serve as an example. So far we have only used sequential ASM.
We might however use power ASM that allow to abstract from intermediate
computational steps.
Acknowledgement
The authors would like to thank Egon Börger and to Andreas Prinz for their
helpful comments and discussions. Egon Börger proposed to use power ASM
instead of sequential ASM for the treatment of transactions. We than P. Schmidt
for proofreading.
References
1. A. Bienemann, K.-D. Schewe, and B. Thalheim. Towards a theory of genericity
based on government and binding. In Proc. ER’06, LNCS 4215, pages 311–324.
Springer, 2006.