Annealing and data decomposition in VDM - A nnealing and...

Annealing and Data Decomposition in VDM ++
S.J. Goldsack, K. Lano
Imperial College, London SW7 2AZ, England
E.H. D/irr
Cap Gemini Sogeti, Netherlands
Abstract
VDM ++ is a formal specification language derived from VDM-
SL and incorporating object-oriented structuring based on lan-
guage extensions which owe much to SmaUTalk (though fea-
tures have been added to cater for specifying reactive real-time
systems). Research on the language has been in progress since
about 1991[1][2], but it is only recently that papers have begun
to be published on the subject[3][4][5].
Several more-detailed papers are in preparation. In particular,
a paper describing the concept of
annealingin
some detail will
be ready shortly 1.
Our attention has recently been drawn to the paper by Jian Lu
[6] which describes a process of data decomposition in VDM
bearing some relationship to our concept of annealing: The
present paper is intended to give an introduction to the an-
nealing concept, and to show how it relates to the work of Jian
Lu.
1 Introduction
Following an initial proposal by Diirr[1][2] VDM ++ was
developed in the ESPRIT project
Afrodite 2,
to form the
specification language for a formal development system.
It has been used in the specification and construction of
a number of significant industrial systems[5].
In the course of the project a toolset, known as the Venus
toolset, was developed by cooperation between the indus-
trial partners Verilog, IFAD and CAP. Information about
Venus, including the syntax for VDM ++ can be accessed
on the World Wide Web at the address:
http://www.ifad.dk/products/venus.
Central to the Afrodite approach is a concept of lay-
1A preliminary version can be obtained by ftp, see [12]. In its
outline form, the concept has already been discussed in [2].
2ESPRIT project no 6500
ered modeling, in which VDM ++ is used to specify a
class (usually referred to as Model0) describing the system
in abstract outline. This is then developed (refined) to
form more detailed specifications, (Model1, Model2 ..etc.)
leading eventually to a form which can be automatically
translated to executable code. The refinement steps may
involve the usual process of reification as understood in
VDM in which data structures are given less abstract rep-
resentations and the operations adapted appropriately.
However, we consider essential to the approach the con-
cept of
annealing 3,
which is a form of refinement in which
the initial class is replaced by a structure of (usually sim-
pler) classes which together haye exactly the behaviour
of the originally-specified system. Data are defined in
the initial class in terms of instance variables of VDM-
SL types together with methods which operate on them.
These are then transformed into
structures
of objects hav-
ing the same overall effect. In the main, the decomposi-
tion will be into objects, containers for data of the original
specification, accessed by object references which replace
the data definitions in the original class. Most often the
motivation for selecting some particular structure will be