<s>
The	O
Z	B-Language
notation	I-Language
is	O
a	O
formal	B-Application
specification	I-Application
language	I-Application
used	O
for	O
describing	O
and	O
modelling	O
computing	O
systems	O
.	O
</s>
<s>
It	O
is	O
targeted	O
at	O
the	O
clear	O
specification	B-Application
of	O
computer	B-Application
programs	I-Application
and	O
computer-based	O
systems	O
in	O
general	O
.	O
</s>
<s>
While	O
at	O
EDF	O
( Électricité	O
de	O
France	O
)	O
,	O
working	O
with	O
Bertrand	O
Meyer	O
,	O
Abrial	O
also	O
worked	O
on	O
developing	O
Z	B-Language
.	O
</s>
<s>
The	O
Z	B-Language
notation	I-Language
is	O
used	O
in	O
the	O
1980	O
book	O
Méthodes	O
de	O
programmation	O
.	O
</s>
<s>
Z	B-Language
was	O
originally	O
proposed	O
by	O
Abrial	O
in	O
1977	O
with	O
the	O
help	O
of	O
Steve	O
Schuman	O
and	O
Bertrand	O
Meyer	O
.	O
</s>
<s>
Abrial	O
has	O
said	O
that	O
Z	B-Language
is	O
so	O
named	O
"	O
Because	O
it	O
is	O
the	O
ultimate	O
language	O
!	O
"	O
</s>
<s>
although	O
the	O
name	O
"	O
Zermelo	O
"	O
is	O
also	O
associated	O
with	O
the	O
Z	B-Language
notation	I-Language
through	O
its	O
use	O
of	O
Zermelo	O
–	O
Fraenkel	O
set	O
theory	O
.	O
</s>
<s>
In	O
1992	O
,	O
the	O
Z	B-Language
User	O
Group	O
(	O
ZUG	O
)	O
was	O
established	O
to	O
oversee	O
activities	O
concerning	O
the	O
Z	B-Language
notation	I-Language
,	O
especially	O
meetings	O
and	O
conferences	O
.	O
</s>
<s>
Z	B-Language
is	O
based	O
on	O
the	O
standard	O
mathematical	O
notation	O
used	O
in	O
axiomatic	O
set	O
theory	O
,	O
lambda	B-Language
calculus	I-Language
,	O
and	O
first-order	O
predicate	O
logic	O
.	O
</s>
<s>
All	O
expressions	O
in	O
Z	B-Language
notation	I-Language
are	O
typed	O
,	O
thereby	O
avoiding	O
some	O
of	O
the	O
paradoxes	O
of	O
naive	O
set	O
theory	O
.	O
</s>
<s>
Z	B-Language
contains	O
a	O
standardized	O
catalogue	O
(	O
called	O
the	O
mathematical	O
toolkit	O
)	O
of	O
commonly	O
used	O
mathematical	O
functions	O
and	O
predicates	O
,	O
defined	O
using	O
Z	B-Language
itself	O
.	O
</s>
<s>
It	O
is	O
augmented	O
with	O
Z	B-Language
schema	O
boxes	O
,	O
which	O
can	O
be	O
combined	O
using	O
their	O
own	O
operators	O
,	O
based	O
on	O
standard	O
logical	O
operators	O
,	O
and	O
also	O
by	O
including	O
schemas	O
within	O
other	O
schemas	O
.	O
</s>
<s>
This	O
allows	O
Z	B-Language
specifications	B-Application
to	O
be	O
built	O
up	O
into	O
large	O
specifications	B-Application
in	O
a	O
convenient	O
manner	O
.	O
</s>
<s>
Because	O
Z	B-Language
notation	I-Language
(	O
just	O
like	O
the	O
APL	B-Language
language	I-Language
,	O
long	O
before	O
it	O
)	O
uses	O
many	O
non-ASCII	O
symbols	O
,	O
the	O
specification	B-Application
includes	O
suggestions	O
for	O
rendering	O
the	O
Z	B-Language
notation	I-Language
symbols	O
in	O
ASCII	B-Protocol
and	O
in	O
LaTeX	B-Application
.	O
</s>
<s>
There	O
are	O
also	O
Unicode	O
encodings	O
for	O
all	O
standard	O
Z	B-Language
symbols	O
.	O
</s>
<s>
ISO	O
completed	O
a	O
Z	B-Language
standardization	O
effort	O
in	O
2002	O
.	O
</s>
<s>
In	O
1992	O
,	O
Oxford	O
University	O
Computing	O
Laboratory	O
was	O
awarded	O
The	O
Queen	O
's	O
Award	O
for	O
Technological	O
Achievement	O
for	O
their	O
joint	O
development	O
with	O
IBM	O
of	O
Z	B-Language
notation	I-Language
.	O
</s>
