Specification of Reactive Hardware/Software Systems - Electronic ...

3.5 Combining Compatible Concepts 37
possibilities for using each individual concept. There is a big difference between the
level of understanding needed to practice design, and the level of understanding that is
required to build a new method.
3.5 Combining Compatible Concepts
There are numerous ways to design a method by selecting and combining concepts.
Some concepts can be added to a method independently, others are mutually dependent,
or can even be conflicting. An additional complication is that of context dependent
interpretation and semantics of concepts. This makes the design of a method very
complicated. Starting with a set of requirements, it is hard to determine beforehand
what combinations of concepts can fulfil these requirements. In practice a method or
a language, once designed, cannot be understood in all its properties, features and
drawbacks.
A method must be efficient and easy to learn and use. Therefore it should contain
as few concepts as possible. In practice however there is a need for various different
representations and views which tend to bring in more concepts. A method must be rich
enough to express these various views. To obtain richness while maintaining simplicity,
a method should offer a framework of compatible concepts, that are reused consistently
within the various views.
Concepts that conflict are called incompatible. Wegner [Weg87, Weg90] studied compatibility
of concepts by comparing languages with respect to their concepts and properties.
Some concepts can be combined freely, while others are related and cannot be used
independently. Concepts that can be combined independently are defined to be orthogonal.
To show that a collection of language dimensions is orthogonal, Wegner uses an
existential proof technique. A collection of dimensions is proven to be orthogonal if,
for every subset, there is a language that possesses those dimensions and no dimensions
in the complementary subset. The contribution of Wegner is that he relates the
orthogonal dimensions to the non-orthogonal ones in real programming languages. It
is an attempt to examine design trade-offs and interrelations between languages that
can be identified as interesting points in the design space of object-oriented languages.
[Weg87] is a limited description of six orthogonal dimensions of object-oriented design:
objects, types, delegation, abstraction, concurrency and persistence. [Weg90] is a more
extensive description of object-oriented language concepts and paradigms.
The art of designing a method is to combine concepts and features that can co-exist
in such a way that the resulting method is consistent. In our work we therefore focus
on establishing a consistent unity of compatible concepts, rather than on studying the
orthogonality of concepts. We believe that proving orthogonality of concepts can only
be established by comparing formal methods or formal languages 1 . Most current analysis
and design methods are composed out of informal concepts only. Studying the
1 In fact we think that Wegner’s technique for ’proving’ orthogonality should be strengthened. The
existence of a language without a formal semantics cannot prove orthogonality.