<s>
The	O
Vienna	B-Application
Development	I-Application
Method	I-Application
(	O
VDM	O
)	O
is	O
one	O
of	O
the	O
longest-established	O
formal	B-Architecture
methods	I-Architecture
for	O
the	O
development	O
of	O
computer-based	O
systems	O
.	O
</s>
<s>
Originating	O
in	O
work	O
done	O
at	O
the	O
IBM	O
Laboratory	O
Vienna	O
in	O
the	O
1970s	O
,	O
it	O
has	O
grown	O
to	O
include	O
a	O
group	O
of	O
techniques	O
and	O
tools	O
based	O
on	O
a	O
formal	B-Application
specification	I-Application
language	O
—	O
the	O
VDM	B-Application
Specification	I-Application
Language	I-Application
(	O
VDM-SL	B-Application
)	O
.	O
</s>
<s>
It	O
has	O
an	O
extended	O
form	O
,	O
VDM++	B-Application
,	O
which	O
supports	O
the	O
modeling	O
of	O
object-oriented	B-Language
and	O
concurrent	O
systems	O
.	O
</s>
<s>
There	O
is	O
a	O
history	O
of	O
industrial	O
usage	O
of	O
VDM	O
and	O
its	O
tools	O
and	O
a	O
growing	O
body	O
of	O
research	O
in	O
the	O
formalism	O
has	O
led	O
to	O
notable	O
contributions	O
to	O
the	O
engineering	O
of	O
critical	O
systems	O
,	O
compilers	B-Language
,	O
concurrent	O
systems	O
and	O
in	O
logic	O
for	O
computer	B-General_Concept
science	I-General_Concept
.	O
</s>
<s>
Computing	O
systems	O
may	O
be	O
modeled	O
in	O
VDM-SL	B-Application
at	O
a	O
higher	O
level	O
of	O
abstraction	B-Application
than	O
is	O
achievable	O
using	O
programming	O
languages	O
,	O
allowing	O
the	O
analysis	O
of	O
designs	O
and	O
identification	O
of	O
key	O
features	O
,	O
including	O
defects	O
,	O
at	O
an	O
early	O
stage	O
of	O
system	O
development	O
.	O
</s>
<s>
The	O
origins	O
of	O
VDM-SL	B-Application
lie	O
in	O
the	O
IBM	O
Laboratory	O
in	O
Vienna	O
where	O
the	O
first	O
version	O
of	O
the	O
language	O
was	O
called	O
the	O
Vienna	O
Definition	O
Language	O
(	O
VDL	O
)	O
.	O
</s>
<s>
«	O
Towards	O
the	O
end	O
of	O
1972	O
the	O
Vienna	O
group	O
again	O
turned	O
their	O
attention	O
to	O
the	O
problem	O
of	O
systematically	O
developing	O
a	O
compiler	B-Language
from	O
a	O
language	O
definition	O
.	O
</s>
<s>
The	O
overall	O
approach	O
adopted	O
has	O
been	O
termed	O
the	O
"	O
Vienna	B-Application
Development	I-Application
Method	I-Application
"	O
...	O
</s>
<s>
There	O
is	O
no	O
connection	O
between	O
Meta-IV	B-Language
,	O
and	O
Schorre	O
's	O
META	B-Application
II	I-Application
language	O
,	O
or	O
its	O
successor	O
Tree	B-Application
Meta	I-Application
;	O
these	O
were	O
compiler-compiler	B-Language
systems	O
rather	O
than	O
being	O
suitable	O
for	O
formal	O
problem	O
descriptions	O
.	O
</s>
<s>
So	O
Meta-IV	B-Language
was	O
"	O
used	O
to	O
define	O
major	O
portions	O
of	O
"	O
the	O
PL/I	B-Language
programming	I-Language
language	I-Language
.	O
</s>
<s>
Other	O
programming	O
languages	O
retrospectively	O
described	O
,	O
or	O
partially	O
described	O
,	O
using	O
Meta-IV	B-Language
and	O
VDM-SL	B-Application
include	O
the	O
BASIC	B-Language
programming	I-Language
language	I-Language
,	O
FORTRAN	B-Application
,	O
the	O
APL	B-Language
programming	I-Language
language	I-Language
,	O
ALGOL	B-Language
60	O
,	O
the	O
Ada	B-Language
programming	I-Language
language	I-Language
and	O
the	O
Pascal	B-Application
programming	I-Application
language	I-Application
.	O
</s>
<s>
Meta-IV	B-Language
evolved	O
into	O
several	O
variants	O
,	O
generally	O
described	O
as	O
the	O
Danish	O
,	O
English	O
and	O
Irish	O
Schools	O
.	O
</s>
<s>
The	O
"	O
English	O
School	O
"	O
derived	O
from	O
work	O
by	O
Cliff	O
Jones	O
on	O
the	O
aspects	O
of	O
VDM	O
not	O
specifically	O
related	O
to	O
language	O
definition	O
and	O
compiler	B-Language
design	O
(	O
Jones	O
1980	O
,	O
1990	O
)	O
.	O
</s>
<s>
1982	O
)	O
has	O
tended	O
to	O
stress	O
a	O
constructive	O
approach	O
with	O
explicit	O
operational	O
specification	B-Application
used	O
to	O
a	O
greater	O
extent	O
.	O
</s>
<s>
Work	O
in	O
the	O
Danish	O
school	O
led	O
to	O
the	O
first	O
European	O
validated	O
Ada	B-Language
compiler	B-Language
.	O
</s>
<s>
The	O
VDM-SL	B-Application
and	O
VDM++	B-Application
syntax	O
and	O
semantics	O
are	O
described	O
at	O
length	O
in	O
the	O
VDMTools	O
language	O
manuals	O
and	O
in	O
the	O
available	O
texts	O
.	O
</s>
<s>
A	O
VDM-SL	B-Application
model	O
is	O
a	O
system	O
description	O
given	O
in	O
terms	O
of	O
the	O
functionality	O
performed	O
on	O
data	O
.	O
</s>
<s>
VDM-SL	B-Application
includes	O
basic	O
types	O
modelling	O
numbers	O
and	O
characters	O
as	O
follows	O
:	O
</s>
<s>
Such	O
constraints	O
are	O
defined	O
where	O
they	O
are	O
required	O
in	O
each	O
model	O
by	O
means	O
of	O
data	O
type	O
invariants	B-Application
—	O
Boolean	O
expressions	O
denoting	O
conditions	O
that	O
must	O
be	O
respected	O
by	O
all	O
elements	O
of	O
the	O
defined	O
type	O
.	O
</s>
<s>
Since	O
invariants	B-Application
can	O
be	O
arbitrarily	O
complex	O
logical	O
expressions	O
,	O
and	O
membership	O
of	O
a	O
defined	O
type	O
is	O
limited	O
to	O
only	O
those	O
values	O
satisfying	O
the	O
invariant	B-Application
,	O
type	O
correctness	O
in	O
VDM-SL	B-Application
is	O
not	O
automatically	O
decidable	O
in	O
all	O
situations	O
.	O
</s>
<s>
Enumerated	B-Language
types	I-Language
in	O
VDM-SL	B-Application
are	O
defined	O
as	O
shown	O
above	O
as	O
unions	O
on	O
quote	O
types	O
.	O
</s>
<s>
Cartesian	O
product	O
types	O
may	O
also	O
be	O
defined	O
in	O
VDM-SL	B-Application
.	O
</s>
<s>
Restrictions	O
on	O
days	O
per	O
month	O
and	O
leap	O
years	O
could	O
be	O
incorporated	O
into	O
the	O
invariant	B-Application
if	O
desired	O
.	O
</s>
<s>
The	O
mapping	O
type	O
constructor	O
in	O
VDM-SL	B-Application
(	O
written	O
map	O
T1	O
to	O
T2	O
where	O
T1	O
and	O
T2	O
are	O
predefined	O
types	O
)	O
constructs	O
the	O
type	O
composed	O
of	O
all	O
finite	O
mappings	O
from	O
sets	O
of	O
T1	O
values	O
to	O
sets	O
of	O
T2	O
values	O
.	O
</s>
<s>
The	O
main	O
difference	O
between	O
the	O
VDM-SL	B-Application
and	O
VDM++	B-Application
notations	O
are	O
the	O
way	O
in	O
which	O
structuring	O
is	O
dealt	O
with	O
.	O
</s>
<s>
In	O
VDM-SL	B-Application
there	O
is	O
a	O
conventional	O
modular	O
extension	O
whereas	O
VDM++	B-Application
has	O
a	O
traditional	O
object-oriented	B-Language
structuring	O
mechanism	O
with	O
classes	O
and	O
inheritance	O
.	O
</s>
<s>
In	O
the	O
ISO	O
standard	O
for	O
VDM-SL	B-Application
there	O
is	O
an	O
informative	O
annex	O
that	O
contains	O
different	O
structuring	O
principles	O
.	O
</s>
<s>
More	O
exotic	O
features	O
:	O
In	O
earlier	O
versions	O
of	O
the	O
VDM-SL	B-Application
tools	O
there	O
was	O
also	O
support	O
for	O
parameterized	O
modules	O
and	O
instantiations	O
of	O
such	O
modules	O
.	O
</s>
<s>
In	O
VDM++	B-Application
structuring	O
are	O
done	O
using	O
classes	O
and	O
multiple	O
inheritance	O
.	O
</s>
<s>
Access	O
modifiers	O
:	O
Information	O
hiding	O
in	O
VDM++	B-Application
is	O
done	O
in	O
the	O
same	O
way	O
as	O
in	O
most	O
object	B-Language
oriented	I-Language
languages	I-Language
using	O
access	O
modifiers	O
.	O
</s>
<s>
In	O
VDM++	B-Application
definitions	O
are	O
per	O
default	O
private	O
but	O
in	O
front	O
of	O
all	O
definitions	O
it	O
is	O
possible	O
to	O
use	O
one	O
of	O
the	O
access	O
modifier	O
keywords	O
:	O
private	O
,	O
public	O
and	O
protected	O
.	O
</s>
<s>
In	O
VDM-SL	B-Application
,	O
functions	O
are	O
defined	O
over	O
the	O
data	O
types	O
defined	O
in	O
a	O
model	O
.	O
</s>
<s>
Support	O
for	O
abstraction	B-Application
requires	O
that	O
it	O
should	O
be	O
possible	O
to	O
characterize	O
the	O
result	O
that	O
a	O
function	O
should	O
compute	O
without	O
having	O
to	O
say	O
how	O
it	O
should	O
be	O
computed	O
.	O
</s>
<s>
The	O
specification	B-Application
above	O
would	O
be	O
satisfied	O
,	O
for	O
example	O
,	O
by	O
a	O
function	O
that	O
returned	O
the	O
negative	O
root	O
of	O
4	O
but	O
the	O
positive	O
root	O
of	O
all	O
other	O
valid	O
inputs	O
.	O
</s>
<s>
Note	O
that	O
functions	O
in	O
VDM-SL	B-Application
are	O
required	O
to	O
be	O
deterministic	O
so	O
that	O
a	O
function	O
satisfying	O
the	O
example	O
specification	B-Application
above	O
must	O
always	O
return	O
the	O
same	O
result	O
for	O
the	O
same	O
input	O
.	O
</s>
<s>
A	O
more	O
constrained	O
function	O
specification	B-Application
is	O
arrived	O
at	O
by	O
strengthening	O
the	O
postcondition	O
.	O
</s>
<s>
All	O
function	O
specifications	B-Application
may	O
be	O
restricted	O
by	O
preconditions	O
which	O
are	O
logical	O
predicates	O
over	O
the	O
input	O
variables	O
only	O
and	O
which	O
describe	O
constraints	O
that	O
are	O
assumed	O
to	O
be	O
satisfied	O
when	O
the	O
function	O
is	O
executed	O
.	O
</s>
<s>
VDM-SL	B-Application
also	O
supports	O
the	O
definition	O
of	O
executable	O
functions	O
in	O
the	O
manner	O
of	O
a	O
functional	O
programming	O
language	O
.	O
</s>
<s>
The	O
correctness	O
of	O
an	O
explicit	O
function	O
definition	O
with	O
respect	O
to	O
an	O
implicit	O
specification	B-Application
may	O
be	O
defined	O
as	O
follows	O
.	O
</s>
<s>
Given	O
an	O
implicit	O
specification	B-Application
:	O
</s>
<s>
we	O
say	O
it	O
satisfies	O
the	O
specification	B-Application
iff	O
:	O
</s>
<s>
So	O
,	O
"	O
f	O
is	O
a	O
correct	O
implementation	O
"	O
should	O
be	O
interpreted	O
as	O
"	O
f	O
satisfies	O
the	O
specification	B-Application
"	O
.	O
</s>
<s>
In	O
VDM-SL	B-Application
,	O
functions	O
do	O
not	O
have	O
side-effects	O
such	O
as	O
changing	O
the	O
state	O
of	O
a	O
persistent	O
global	O
variable	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
we	O
have	O
a	O
state	O
consisting	O
of	O
a	O
single	O
variable	O
someStateRegister	O
:	O
nat	O
,	O
we	O
could	O
define	O
this	O
in	O
VDM-SL	B-Application
as	O
:	O
</s>
<s>
In	O
VDM++	B-Application
this	O
would	O
instead	O
be	O
defined	O
as	O
:	O
</s>
<s>
This	O
is	O
a	O
classical	O
example	O
illustrating	O
the	O
use	O
of	O
implicit	O
operation	O
specification	B-Application
in	O
a	O
state-based	O
model	O
of	O
a	O
well-known	O
data	B-General_Concept
structure	I-General_Concept
.	O
</s>
<s>
As	O
a	O
very	O
simple	O
example	O
of	O
a	O
VDM-SL	B-Application
model	O
,	O
consider	O
a	O
system	O
for	O
maintaining	O
details	O
of	O
customer	O
bank	O
account	O
.	O
</s>
<s>
was	O
the	O
leading	O
commercial	O
tools	O
for	O
VDM	O
and	O
VDM++	B-Application
,	O
owned	O
,	O
marketed	O
,	O
maintained	O
and	O
developed	O
by	O
,	O
building	O
on	O
earlier	O
versions	O
developed	O
by	O
the	O
Danish	O
Company	O
IFAD	O
.	O
</s>
<s>
The	O
full	O
version	O
includes	O
automatic	O
code	O
generation	O
for	O
Java	O
and	O
C++	B-Language
,	O
dynamic	O
link	O
library	O
and	O
CORBA	O
support	O
.	O
</s>
<s>
is	O
a	O
community-based	O
open	O
source	O
initiative	O
aimed	O
at	O
providing	O
freely	O
available	O
tool	O
support	O
for	O
all	O
VDM	O
dialects	O
(	O
VDM-SL	B-Application
,	O
VDM++	B-Application
and	O
VDM-RT	O
)	O
originally	O
on	O
top	O
of	O
the	O
Eclipse	O
platform	O
but	O
subsequently	O
on	O
top	O
of	O
the	O
Visual	O
Studio	O
Code	O
platform	O
.	O
</s>
<s>
is	O
a	O
collection	O
of	O
Emacs	O
packages	O
for	O
writing	O
VDM	O
specifications	B-Application
using	O
VDM-SL	B-Application
,	O
VDM++	B-Application
and	O
VDM-RT	O
.	O
</s>
<s>
:	O
from	O
Adelard	O
provides	O
syntax	O
checking	O
,	O
some	O
simple	O
semantic	O
checking	O
,	O
and	O
generation	O
of	O
a	O
LaTeX	B-Application
file	O
enabling	O
specifications	B-Application
to	O
be	O
printed	O
in	O
mathematical	O
notation	O
.	O
</s>
<s>
LaTeX	B-Application
and	O
LaTeX2e	O
macros	O
are	O
available	O
to	O
support	O
the	O
presentation	O
of	O
VDM	O
models	O
in	O
the	O
ISO	O
Standard	O
Language	O
's	O
mathematical	O
syntax	O
.	O
</s>
<s>
Ada	B-Language
and	O
CHILL	B-Language
compilers	B-Language
:	O
The	O
first	O
European	O
validated	O
Ada	B-Language
compiler	B-Language
was	O
developed	O
by	O
Dansk	O
Datamatik	O
Center	O
using	O
VDM	O
.	O
</s>
<s>
Likewise	O
the	O
semantics	O
of	O
CHILL	B-Language
and	O
Modula-2	B-Language
were	O
described	O
in	O
their	O
standards	O
using	O
VDM	O
.	O
</s>
<s>
FeliCa	O
Networks	O
have	O
reported	O
the	O
development	O
of	O
an	O
operating	B-General_Concept
system	I-General_Concept
for	O
an	O
integrated	O
circuit	O
for	O
cellular	O
telephone	O
applications	O
.	O
</s>
<s>
Use	O
of	O
VDM	O
starts	O
with	O
a	O
very	O
abstract	B-Application
model	O
and	O
develops	O
this	O
into	O
an	O
implementation	O
.	O
</s>
<s>
Data	O
reification	O
develops	O
the	O
abstract	B-Application
data	O
types	O
into	O
more	O
concrete	O
data	B-General_Concept
structures	I-General_Concept
,	O
while	O
operation	O
decomposition	O
develops	O
the	O
(	O
abstract	B-Application
)	O
implicit	O
specifications	B-Application
of	O
operations	O
and	O
functions	O
into	O
algorithms	O
that	O
can	O
be	O
directly	O
implemented	O
in	O
a	O
computer	O
language	O
of	O
choice	O
.	O
</s>
<s>
Data	O
reification	O
(	O
stepwise	O
refinement	O
)	O
involves	O
finding	O
a	O
more	O
concrete	O
representation	O
of	O
the	O
abstract	B-Application
data	O
types	O
used	O
in	O
a	O
specification	B-Application
.	O
</s>
<s>
Each	O
reification	O
step	O
for	O
an	O
abstract	B-Application
data	O
representation	O
ABS_REP	O
involves	O
proposing	O
a	O
new	O
representation	O
NEW_REP	O
.	O
</s>
<s>
The	O
new	O
operations	O
and	O
functions	O
should	O
be	O
shown	O
to	O
preserve	O
any	O
data	O
type	O
invariants	B-Application
on	O
the	O
new	O
representation	O
.	O
</s>
<s>
In	O
order	O
to	O
prove	O
that	O
the	O
new	O
operations	O
and	O
functions	O
model	O
those	O
found	O
in	O
the	O
original	O
specification	B-Application
,	O
it	O
is	O
necessary	O
to	O
discharge	O
two	O
proof	O
obligations	O
:	O
</s>
<s>
As	O
most	O
programming	O
languages	O
have	O
a	O
concept	O
comparable	O
to	O
a	O
set	O
(	O
often	O
in	O
the	O
form	O
of	O
an	O
array	O
)	O
,	O
the	O
first	O
step	O
from	O
the	O
specification	B-Application
is	O
to	O
represent	O
the	O
data	O
in	O
terms	O
of	O
a	O
sequence	O
.	O
</s>
<s>
These	O
sequences	O
must	O
not	O
allow	O
repetition	O
,	O
as	O
we	O
do	O
not	O
want	O
the	O
same	O
worker	O
to	O
appear	O
twice	O
,	O
so	O
we	O
must	O
add	O
an	O
invariant	B-Application
to	O
the	O
new	O
data	O
type	O
.	O
</s>
<s>
The	O
Vienna	B-Application
Development	I-Application
Method	I-Application
is	O
valuable	O
for	O
model-based	O
systems	O
.	O
</s>
