Information Technology Reference
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•
deployment view,
•
state transition view.
All these views have to be captured by carefully chosen syntactic description
methods leading to helpful thought models. The development of systems concentrates
on working out these views leading step by step to an implementation.
We give a mathematical model setting in the following providing abstract views
onto a system. A system is based on an algebra A that describes its basic data types
and elements as well as its characteristic operations. A system has an
interface view
(black box view)
which describes its behavior for the user of a system. Each system
has an implementation in terms of a
state machine
or a
composed system
. A system
always has a
state space
and can be viewed as a
state machine.
System models can be
refined
. They describe systems at particular
levels of abstraction
. A system has a set
of
traces
(processes, system runs) as its histories. Each view defines logical properties
in terms of a mathematical model.
4 System Model: A Meta Model Theory of Software
In this section we introduce a meta model for software systems. We outline its
essential views and how they are related. Later we give a concrete instance of this
meta theory.
4.1 Criteria for a Theory of Modeling
For a scientifically and practically useful approach to modeling in software
engineering we list in the following a number of criteria and essential ingredients.
We need a system model, a mathematical model of a system, powerful enough to
incorporate all envisaged views, supporting the concept of levels of abstraction,
hierarchical decomposition, and modularity. In the following we identify and define
these requirements more precisely.
4.2 A System Meta Model
In a system meta model we incorporate all the concepts needed to describe the
different parts and views of a system. Formally we define a signature of an algebra,
the algebra of system models, and state some algebraic properties.
4.2.1 Data Model
Data occur in systems everywhere. Typically today the data view is defined by a
family of data types (or sorts) describing sets of data. In most cases, in addition,
functions are introduced on the data sets. This leads to heterogeneous algebras. The
theory of data algebras is very well understood by now. A data model is an algebra.
DM denotes the set of all data models. It defines a signature, being a family of names
for types, functions, and operations, together with axioms describing the properties or
with an explicit model.
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