<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
and	O
more	O
precisely	O
regarding	O
data	B-General_Concept
structures	I-General_Concept
,	O
a	O
persistent	B-Data_Structure
array	I-Data_Structure
is	O
a	O
persistent	B-Application
data	I-Application
structure	I-Application
with	O
properties	O
similar	O
to	O
a	O
(	O
non-persistent	O
)	O
array	B-Data_Structure
.	O
</s>
<s>
That	O
is	O
then	O
,	O
after	O
a	O
value	O
's	O
update	O
in	O
a	O
persistent	B-Data_Structure
array	I-Data_Structure
,	O
there	O
exists	O
two	O
persistent	B-Data_Structure
arrays	I-Data_Structure
.	O
</s>
<s>
One	O
persistent	B-Data_Structure
array	I-Data_Structure
in	O
which	O
the	O
update	O
is	O
taken	O
into	O
account	O
,	O
and	O
one	O
which	O
is	O
equal	O
to	O
the	O
array	B-Data_Structure
before	O
the	O
update	O
.	O
</s>
<s>
is	O
a	O
data	B-General_Concept
structure	I-General_Concept
,	O
</s>
<s>
There	O
exists	O
two	O
kinds	O
of	O
persistent	B-Data_Structure
arrays	I-Data_Structure
.	O
</s>
<s>
persistent	B-Data_Structure
array	I-Data_Structure
may	O
be	O
updated	O
at	O
most	O
once	O
.	O
</s>
<s>
Many	O
implementations	O
of	O
persistent	B-Data_Structure
arrays	I-Data_Structure
exists	O
.	O
</s>
<s>
persistent	B-Data_Structure
array	I-Data_Structure
.	O
</s>
<s>
example	O
,	O
a	O
balanced	B-Data_Structure
tree	I-Data_Structure
.	O
</s>
<s>
data	B-General_Concept
structure	I-General_Concept
would	O
take	O
logarithmic	O
time	O
.	O
</s>
<s>
This	O
implementation	O
is	O
used	O
in	O
the	O
OCaml	B-Language
module	O
parray.ml	O
by	O
Jean-Christophe	O
Filliâtre	O
.	O
</s>
<s>
an	O
update	O
on	O
another	O
array	B-Data_Structure
.	O
</s>
<s>
A	O
descendant	O
of	O
an	O
array	B-Data_Structure
ar	O
is	O
eitherar	O
or	O
the	O
descendant	O
of	O
a	O
child	O
of	O
ar	O
.	O
</s>
<s>
initial	O
array	B-Data_Structure
of	O
the	O
parent	O
of	O
ar	O
.	O
</s>
<s>
array	B-Data_Structure
and	O
all	O
of	O
its	O
descendants	O
.	O
</s>
<s>
an	O
actual	O
array	B-Data_Structure
called	O
array	B-Data_Structure
and	O
the	O
tree	B-Application
of	O
arrays	O
.	O
</s>
<s>
admits	O
an	O
arbitrary	O
root	O
-	O
not	O
necessarily	O
the	O
initial	O
array	B-Data_Structure
.	O
</s>
<s>
root	O
may	O
be	O
moved	O
to	O
an	O
arbitrary	O
node	O
of	O
the	O
tree	B-Application
.	O
</s>
<s>
distance	O
between	O
the	O
array	B-Data_Structure
and	O
the	O
root	O
of	O
its	O
family	O
.	O
</s>
<s>
an	O
array	B-Data_Structure
only	O
takes	O
constant	O
time	O
.	O
</s>
<s>
Accessing	O
an	O
element	O
i	O
of	O
an	O
array	B-Data_Structure
ar	O
is	O
done	O
as	O
follows	O
.	O
</s>
<s>
done	O
by	O
first	O
moving	O
the	O
root	O
to	O
ar2	O
,	O
changing	O
the	O
label	O
of	O
eto	O
(	O
i	O
,	O
ar2[i]	O
)	O
,	O
and	O
changing	O
array[i]	O
to	O
v	O
.	O
</s>
<s>
number	O
of	O
element	O
in	O
an	O
array	B-Data_Structure
.	O
</s>
