<s>
The	O
KeY	O
tool	O
is	O
used	O
in	O
formal	O
verification	O
of	O
Java	B-Language
programs	O
.	O
</s>
<s>
It	O
accepts	O
specifications	O
written	O
in	O
the	O
Java	B-Language
Modeling	I-Language
Language	I-Language
to	O
Java	B-Language
source	O
files	O
.	O
</s>
<s>
There	O
have	O
been	O
several	O
extensions	O
to	O
KeY	O
in	O
order	O
to	O
apply	O
it	O
to	O
the	O
verification	O
of	O
C	B-Language
programs	I-Language
or	O
hybrid	O
systems	O
.	O
</s>
<s>
KeY	O
is	O
jointly	O
developed	O
by	O
Karlsruhe	O
Institute	O
of	O
Technology	O
,	O
Germany	O
;	O
Technische	O
Universität	O
Darmstadt	O
,	O
Germany	O
;	O
and	O
Chalmers	O
University	O
of	O
Technology	O
in	O
Gothenburg	O
,	O
Sweden	O
and	O
is	O
licensed	O
under	O
the	O
GPL	B-License
.	O
</s>
<s>
The	O
usual	O
user	O
input	O
to	O
KeY	O
consists	O
of	O
a	O
Java	B-Language
source	O
file	O
with	O
annotations	O
in	O
JML	B-Language
.	O
</s>
<s>
To	O
this	O
ends	O
,	O
the	O
program	O
is	O
symbolically	B-General_Concept
executed	I-General_Concept
with	O
the	O
resulting	O
changes	O
to	O
program	O
variables	O
stored	O
in	O
so-called	O
updates	O
.	O
</s>
<s>
At	O
the	O
heart	O
of	O
the	O
KeY	B-Application
system	I-Application
lies	O
a	O
first-order	O
theorem	B-Application
prover	I-Application
based	O
on	O
sequent	O
calculus	O
,	O
which	O
is	O
used	O
to	O
close	O
the	O
proof	O
.	O
</s>
<s>
The	O
theoretical	O
foundation	O
of	O
KeY	O
is	O
a	O
formal	O
logic	O
called	O
Java	B-Language
Card	O
DL	O
.	O
</s>
<s>
It	O
is	O
a	O
version	O
of	O
a	O
first-order	O
dynamic	O
logic	O
tailored	O
to	O
Java	B-Language
Card	O
programs	O
.	O
</s>
<s>
As	O
such	O
,	O
it	O
for	O
example	O
allows	O
statements	O
(	O
formulas	O
)	O
like	O
,	O
which	O
intuitively	O
says	O
that	O
the	O
post-condition	O
must	O
hold	O
in	O
all	O
program	O
states	O
reachable	O
by	O
executing	O
the	O
Java	B-Language
Card	O
program	O
in	O
any	O
state	O
that	O
satisfies	O
the	O
pre-condition	O
.	O
</s>
<s>
This	O
dynamic	O
logic	O
can	O
be	O
seen	O
as	O
a	O
special	O
multi-modal	O
logic	O
(	O
with	O
an	O
infinite	O
number	O
of	O
modalities	O
)	O
where	O
for	O
each	O
Java	B-Language
block	O
there	O
are	O
modalities	O
and	O
.	O
</s>
<s>
At	O
the	O
heart	O
of	O
the	O
KeY	B-Application
system	I-Application
lies	O
a	O
first-order	O
theorem	B-Application
prover	I-Application
based	O
on	O
a	O
sequent	O
calculus	O
.	O
</s>
<s>
During	O
that	O
,	O
program	O
modalities	O
are	O
eliminated	O
by	O
symbolic	B-General_Concept
execution	I-General_Concept
.	O
</s>
<s>
As	O
this	O
example	O
shows	O
,	O
symbolic	B-General_Concept
execution	I-General_Concept
in	O
dynamic	O
logic	O
is	O
very	O
similar	O
to	O
calculating	O
weakest	B-Application
preconditions	I-Application
.	O
</s>
<s>
Secondly	O
,	O
symbolic	B-General_Concept
execution	I-General_Concept
runs	O
through	O
the	O
program	O
forward	O
just	O
as	O
an	O
actual	O
execution	O
would	O
.	O
</s>
<s>
An	O
example	O
of	O
symbolic	B-General_Concept
execution	I-General_Concept
with	O
updates	O
:	O
is	O
transformed	O
to	O
in	O
the	O
first	O
step	O
and	O
to	O
in	O
the	O
second	O
step	O
.	O
</s>
<s>
The	O
Symbolic	B-General_Concept
Execution	I-General_Concept
Debugger	O
visualizes	O
the	O
control	O
flow	O
of	O
a	O
program	O
as	O
a	O
symbolic	B-General_Concept
execution	I-General_Concept
tree	O
that	O
contains	O
all	O
feasible	O
execution	O
paths	O
through	O
the	O
program	O
up	O
to	O
a	O
certain	O
point	O
.	O
</s>
<s>
It	O
is	O
provided	O
as	O
a	O
plugin	O
to	O
the	O
Eclipse	B-Application
development	O
platform	O
.	O
</s>
<s>
KeY	O
is	O
usable	O
as	O
a	O
model-based	O
testing	O
tool	O
that	O
can	O
generate	O
unit	O
tests	O
for	O
Java	B-Language
programs	O
.	O
</s>
<s>
The	O
model	O
from	O
which	O
test	O
data	O
and	O
the	O
test	O
case	O
are	O
derived	O
consists	O
of	O
a	O
formal	O
specification	O
(	O
provided	O
in	O
JML	B-Language
)	O
and	O
a	O
symbolic	B-General_Concept
execution	I-General_Concept
tree	O
of	O
the	O
implementation	O
under	O
test	O
which	O
is	O
computed	O
by	O
the	O
KeY	B-Application
system	I-Application
.	O
</s>
<s>
KeY	O
is	O
free	O
software	O
written	O
in	O
Java	B-Language
and	O
licensed	O
under	O
GPL	B-License
.	O
</s>
<s>
As	O
another	O
possibility	O
,	O
KeY	O
can	O
be	O
executed	O
directly	O
via	O
Java	B-Application
web	I-Application
start	I-Application
without	O
the	O
need	O
for	O
compilation	O
and	O
installation	O
.	O
</s>
<s>
State	O
updates	O
are	O
a	O
means	O
of	O
describing	O
state	O
transitions	O
in	O
a	O
Kripke	B-Application
structure	I-Application
.	O
</s>
<s>
It	O
extends	O
the	O
KeY	O
tool	O
with	O
computer	O
algebra	O
systems	O
like	O
Mathematica	B-Language
and	O
corresponding	O
algorithms	O
and	O
proof	O
strategies	O
such	O
that	O
it	O
can	O
be	O
used	O
for	O
practical	O
verification	O
of	O
hybrid	O
systems	O
.	O
</s>
<s>
KeY	O
for	O
C	B-Language
is	O
an	O
adaption	O
of	O
the	O
KeY	B-Application
System	I-Application
to	O
MISRA	B-Language
C	I-Language
,	O
a	O
subset	O
of	O
the	O
C	B-Language
programming	I-Language
language	I-Language
.	O
</s>
<s>
There	O
is	O
also	O
an	O
adaptation	O
to	O
use	O
KeY	O
for	O
the	O
symbolic	B-General_Concept
execution	I-General_Concept
of	O
Abstract	B-Application
State	I-Application
Machines	I-Application
,	O
that	O
was	O
developed	O
at	O
ETH	O
Zürich	O
.	O
</s>
