<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
a	O
computation	O
is	O
said	O
to	O
diverge	O
if	O
it	O
does	O
not	O
terminate	O
or	O
terminates	O
in	O
an	O
exceptional	O
state	B-Application
.	O
</s>
<s>
Various	O
subfields	O
of	O
computer	B-General_Concept
science	I-General_Concept
use	O
varying	O
,	O
but	O
mathematically	O
precise	O
,	O
definitions	O
of	O
what	O
it	O
means	O
for	O
a	O
computation	O
to	O
converge	O
or	O
diverge	O
.	O
</s>
<s>
In	O
abstract	O
rewriting	O
,	O
an	O
abstract	O
rewriting	O
system	O
is	O
called	O
convergent	B-Application
if	O
it	O
is	O
both	O
confluent	O
and	O
terminating	B-Application
.	O
</s>
<s>
The	O
notation	O
t	O
↓	O
n	O
means	O
that	O
t	O
reduces	O
to	O
normal	O
form	O
n	O
in	O
zero	O
or	O
more	O
reductions	O
,	O
t	O
↓	O
means	O
t	O
reduces	O
to	O
some	O
normal	O
form	O
in	O
zero	O
or	O
more	O
reductions	O
,	O
and	O
t	O
↑	O
means	O
t	O
does	O
not	O
reduce	O
to	O
a	O
normal	O
form	O
;	O
the	O
latter	O
is	O
impossible	O
in	O
a	O
terminating	B-Application
rewriting	O
system	O
.	O
</s>
<s>
In	O
the	O
lambda	B-Language
calculus	I-Language
an	O
expression	O
is	O
divergent	O
if	O
it	O
has	O
no	O
normal	O
form	O
.	O
</s>
<s>
In	O
denotational	B-Application
semantics	I-Application
an	O
object	O
function	O
f	O
:	O
A	O
→	O
B	O
can	O
be	O
modelled	O
as	O
a	O
mathematical	O
function	O
where	O
⊥	O
(	O
bottom	O
)	O
indicates	O
that	O
the	O
object	O
function	O
or	O
its	O
argument	O
diverges	O
.	O
</s>
<s>
In	O
the	O
calculus	O
of	O
communicating	O
sequential	O
processes	O
,	O
divergence	B-Application
is	O
a	O
drastic	O
situation	O
where	O
a	O
process	O
performs	O
an	O
endless	O
series	O
of	O
hidden	O
actions	O
.	O
</s>
