<s>
A	O
term	B-Application
graph	I-Application
is	O
a	O
representation	O
of	O
an	O
expression	O
in	O
a	O
formal	O
language	O
as	O
a	O
generalized	O
graph	O
whose	O
vertices	O
are	O
.	O
</s>
<s>
Term	B-Application
graphs	I-Application
are	O
a	O
more	O
powerful	O
form	O
of	O
representation	O
than	O
expression	O
trees	O
because	O
they	O
can	O
represent	O
not	O
only	O
common	O
subexpressions	O
(	O
i.e.	O
</s>
<s>
For	O
this	O
reason	O
term	B-Application
graphs	I-Application
are	O
often	O
used	O
as	O
an	O
intermediate	O
language	O
at	O
a	O
subsequent	O
compilation	O
stage	O
to	O
abstract	O
syntax	O
tree	O
construction	O
via	O
parsing	O
.	O
</s>
<s>
The	O
phrase	O
"	O
term	B-Application
graph	B-Application
rewriting	I-Application
"	O
is	O
often	O
used	O
when	O
discussing	O
graph	B-Application
rewriting	I-Application
methods	O
for	O
transforming	O
expressions	O
in	O
formal	O
languages	O
.	O
</s>
<s>
Considered	O
from	O
the	O
point	O
of	O
view	O
of	O
graph	B-Application
grammars	I-Application
,	O
term	B-Application
graphs	I-Application
are	O
not	O
regular	O
graphs	O
,	O
but	O
hypergraphs	O
where	O
an	O
n-ary	O
word	O
will	O
have	O
a	O
particular	O
subgraph	O
in	O
first	O
place	O
,	O
another	O
in	O
second	O
place	O
,	O
and	O
so	O
on	O
,	O
a	O
distinction	O
that	O
does	O
not	O
exist	O
in	O
the	O
usual	O
undirected	O
graphs	O
studied	O
in	O
graph	O
theory	O
.	O
</s>
<s>
Term	B-Application
graphs	I-Application
are	O
a	O
prominent	O
topic	O
in	O
programming	O
language	O
research	O
since	O
term	B-Application
graph	I-Application
rewriting	O
rules	O
are	O
capable	O
of	O
formally	O
expressing	O
a	O
compiler	O
's	O
operational	O
semantics	O
.	O
</s>
<s>
Term	B-Application
graphs	I-Application
are	O
also	O
used	O
as	O
abstract	O
machines	O
capable	O
of	O
modelling	O
chemical	O
and	O
biological	O
computations	O
as	O
well	O
as	O
graphical	O
calculi	O
such	O
as	O
concurrency	O
models	O
.	O
</s>
<s>
Term	B-Application
graphs	I-Application
can	O
perform	O
automated	O
verification	O
and	O
logical	O
programming	O
since	O
they	O
are	O
well-suited	O
to	O
representing	O
quantified	O
statements	O
in	O
first	O
order	O
logic	O
.	O
</s>
<s>
Symbolic	O
programming	O
software	O
is	O
another	O
application	O
for	O
term	B-Application
graphs	I-Application
,	O
which	O
are	O
capable	O
of	O
representing	O
and	O
performing	O
computation	O
with	O
abstract	O
algebraic	O
structures	O
such	O
as	O
groups	O
,	O
fields	O
and	O
rings	O
.	O
</s>
<s>
The	O
TERMGRAPH	O
conference	O
focuses	O
entirely	O
on	O
research	O
into	O
term	B-Application
graph	I-Application
rewriting	O
and	O
its	O
applications	O
.	O
</s>
<s>
Term	B-Application
graphs	I-Application
are	O
also	O
used	O
in	O
type	O
inference	O
,	O
where	O
the	O
graph	O
structure	O
aids	O
in	O
implementing	O
type	O
unification	O
.	O
</s>
