<s>
In	O
software	B-General_Concept
engineering	I-General_Concept
and	O
computer	B-General_Concept
science	I-General_Concept
,	O
abstraction	B-Application
is	O
:	O
</s>
<s>
The	O
process	O
of	O
removing	O
or	O
generalizing	O
physical	O
,	O
spatial	O
,	O
or	O
temporal	O
details	O
or	O
attributes	B-General_Concept
in	O
the	O
study	O
of	O
objects	O
or	O
systems	O
to	O
focus	O
attention	O
on	O
details	O
of	O
greater	O
importance	O
;	O
it	O
is	O
similar	O
in	O
nature	O
to	O
the	O
process	O
of	O
generalization	B-Algorithm
;	O
</s>
<s>
the	O
creation	O
of	O
abstract	O
concept-objects	O
by	O
mirroring	O
common	O
features	O
or	O
attributes	B-General_Concept
of	O
various	O
non-abstract	O
objects	O
or	O
systems	O
of	O
study	O
–	O
the	O
result	O
of	O
the	O
process	O
of	O
abstraction	B-Application
.	O
</s>
<s>
Abstraction	B-Application
,	I-Application
in	I-Application
general	I-Application
,	O
is	O
a	O
fundamental	O
concept	O
in	O
computer	B-General_Concept
science	I-General_Concept
and	O
software	O
development	O
.	O
</s>
<s>
The	O
process	O
of	O
abstraction	B-Application
can	O
also	O
be	O
referred	O
to	O
as	O
modeling	O
and	O
is	O
closely	O
related	O
to	O
the	O
concepts	O
of	O
theory	O
and	O
design	O
.	O
</s>
<s>
Models	B-Application
can	O
also	O
be	O
considered	O
types	O
of	O
abstractions	B-Application
per	O
their	O
generalization	B-Algorithm
of	O
aspects	O
of	O
reality	O
.	O
</s>
<s>
Abstraction	B-Application
in	O
computer	B-General_Concept
science	I-General_Concept
is	O
closely	O
related	O
to	O
abstraction	B-Application
in	O
mathematics	O
due	O
to	O
their	O
common	O
focus	O
on	O
building	O
abstractions	B-Application
as	O
objects	O
,	O
but	O
is	O
also	O
related	O
to	O
other	O
notions	O
of	O
abstraction	B-Application
used	O
in	O
other	O
fields	O
such	O
as	O
art	O
.	O
</s>
<s>
Abstractions	B-Application
may	O
also	O
refer	O
to	O
real-world	O
objects	O
and	O
systems	O
,	O
rules	O
of	O
computational	O
systems	O
or	O
rules	O
of	O
programming	O
languages	O
that	O
carry	O
or	O
utilize	O
features	O
of	O
abstraction	B-Application
itself	O
,	O
such	O
as	O
:	O
</s>
<s>
the	O
usage	O
of	O
data	O
types	O
to	O
perform	O
data	B-Application
abstraction	I-Application
to	O
separate	O
usage	O
from	O
working	O
representations	O
of	O
data	B-General_Concept
structures	I-General_Concept
within	O
programs	B-Application
;	O
</s>
<s>
the	O
concept	O
of	O
procedures	O
,	O
functions	O
,	O
or	O
subroutines	O
which	O
represent	O
a	O
specific	O
of	O
implementing	O
control	O
flow	O
in	O
programs	B-Application
;	O
</s>
<s>
the	O
rules	O
commonly	O
named	O
"	O
abstraction	B-Application
"	O
that	O
generalize	O
expressions	O
using	O
free	O
and	O
bound	O
variables	O
in	O
the	O
various	O
versions	O
of	O
lambda	B-Language
calculus	I-Language
;	O
</s>
<s>
the	O
usage	O
of	O
S-expressions	B-Protocol
as	O
an	O
abstraction	B-Application
of	O
data	B-General_Concept
structures	I-General_Concept
and	O
programs	B-Application
in	O
the	O
Lisp	B-Language
programming	I-Language
language	I-Language
;	O
</s>
<s>
the	O
process	O
of	O
reorganizing	O
common	O
behavior	O
from	O
non-abstract	O
classes	O
into	O
"	O
abstract	O
classes	O
"	O
using	O
inheritance	B-Language
to	O
abstract	O
over	O
sub-classes	O
as	O
seen	O
in	O
the	O
object-oriented	B-Language
C++	B-Language
and	O
Java	B-Language
programming	I-Language
languages	I-Language
.	O
</s>
<s>
These	O
architectures	O
are	O
made	O
of	O
specific	O
choices	O
of	O
abstractions	B-Application
.	O
</s>
<s>
Greenspun	B-Language
's	I-Language
Tenth	I-Language
Rule	I-Language
is	O
an	O
aphorism	O
on	O
how	O
such	O
an	O
architecture	B-Architecture
is	O
both	O
inevitable	O
and	O
complex	O
.	O
</s>
<s>
A	O
central	O
form	O
of	O
abstraction	B-Application
in	O
computing	O
is	O
language	O
abstraction	B-Application
:	O
new	O
artificial	O
languages	O
are	O
developed	O
to	O
express	O
specific	O
aspects	O
of	O
a	O
system	O
.	O
</s>
<s>
Modeling	B-Language
languages	I-Language
help	O
in	O
planning	O
.	O
</s>
<s>
Computer	B-Language
languages	I-Language
can	O
be	O
processed	O
with	O
a	O
computer	O
.	O
</s>
<s>
An	O
example	O
of	O
this	O
abstraction	B-Application
process	O
is	O
the	O
generational	O
development	O
of	O
programming	O
languages	O
from	O
the	O
machine	O
language	O
to	O
the	O
assembly	O
language	O
and	O
the	O
high-level	O
language	O
.	O
</s>
<s>
The	O
language	O
abstraction	B-Application
continues	O
for	O
example	O
in	O
scripting	B-Language
languages	I-Language
and	O
domain-specific	B-Language
programming	I-Language
languages	I-Language
.	O
</s>
<s>
Within	O
a	O
programming	O
language	O
,	O
some	O
features	O
let	O
the	O
programmer	O
create	O
new	O
abstractions	B-Application
.	O
</s>
<s>
These	O
include	O
subroutines	O
,	O
modules	B-Architecture
,	O
polymorphism	B-Application
,	O
and	O
software	O
components	O
.	O
</s>
<s>
Some	O
other	O
abstractions	B-Application
such	O
as	O
software	O
design	O
patterns	O
and	O
architectural	O
styles	O
remain	O
invisible	O
to	O
a	O
translator	B-Application
and	O
operate	O
only	O
in	O
the	O
design	O
of	O
a	O
system	O
.	O
</s>
<s>
Some	O
abstractions	B-Application
try	O
to	O
limit	O
the	O
range	O
of	O
concepts	O
a	O
programmer	O
needs	O
to	O
be	O
aware	O
of	O
,	O
by	O
completely	O
hiding	O
the	O
abstractions	B-Application
that	O
they	O
in	O
turn	O
are	O
built	O
on	O
.	O
</s>
<s>
The	O
software	B-General_Concept
engineer	I-General_Concept
and	O
writer	O
Joel	O
Spolsky	O
has	O
criticised	O
these	O
efforts	O
by	O
claiming	O
that	O
all	O
abstractions	B-Application
are	O
leaky	O
–	O
that	O
they	O
can	O
never	O
completely	O
hide	O
the	O
details	O
below	O
;	O
however	O
,	O
this	O
does	O
not	O
negate	O
the	O
usefulness	O
of	O
abstraction	B-Application
.	O
</s>
<s>
Some	O
abstractions	B-Application
are	O
designed	O
to	O
inter-operate	O
with	O
other	O
abstractions	B-Application
–	O
for	O
example	O
,	O
a	O
programming	O
language	O
may	O
contain	O
a	O
foreign	B-Application
function	I-Application
interface	I-Application
for	O
making	O
calls	O
to	O
the	O
lower-level	O
language	O
.	O
</s>
<s>
Different	O
programming	O
languages	O
provide	O
different	O
types	O
of	O
abstraction	B-Application
,	O
depending	O
on	O
the	O
intended	O
applications	O
for	O
the	O
language	O
.	O
</s>
<s>
In	O
object-oriented	B-Language
programming	I-Language
languages	I-Language
such	O
as	O
C++	B-Language
,	O
Object	B-Language
Pascal	I-Language
,	O
or	O
Java	B-Language
,	O
the	O
concept	O
of	O
abstraction	B-Application
has	O
itself	O
become	O
a	O
declarative	O
statement	O
–	O
using	O
the	O
syntax	O
function(parameters )	O
=	O
0	O
;	O
(	O
in	O
C++	B-Language
)	O
or	O
the	O
keywords	O
abstract	O
and	O
interface	O
(	O
in	O
Java	B-Language
)	O
.	O
</s>
<s>
Functional	B-Language
programming	I-Language
languages	I-Language
commonly	O
exhibit	O
abstractions	B-Application
related	O
to	O
functions	O
,	O
such	O
as	O
lambda	B-Language
abstractions	I-Language
(	O
making	O
a	O
term	O
into	O
a	O
function	O
of	O
some	O
variable	O
)	O
and	O
higher-order	B-Language
functions	I-Language
(	O
parameters	O
are	O
functions	O
)	O
.	O
</s>
<s>
Modern	O
members	O
of	O
the	O
Lisp	B-Language
programming	I-Language
language	I-Language
family	O
such	O
as	O
Clojure	B-Language
,	O
Scheme	B-Language
and	O
Common	B-Language
Lisp	I-Language
support	O
macro	O
systems	O
to	O
allow	O
syntactic	O
abstraction	B-Application
.	O
</s>
<s>
Other	O
programming	O
languages	O
such	O
as	O
Scala	B-Application
also	O
have	O
macros	O
,	O
or	O
very	O
similar	O
metaprogramming	B-Application
features	O
(	O
for	O
example	O
,	O
Haskell	B-Language
has	O
Template	B-Application
Haskell	I-Application
,	O
and	O
OCaml	B-Language
has	O
MetaOCaml	O
)	O
.	O
</s>
<s>
These	O
can	O
allow	O
a	O
programmer	O
to	O
eliminate	O
boilerplate	O
code	O
,	O
abstract	O
away	O
tedious	O
function	O
call	O
sequences	O
,	O
implement	O
new	O
control	O
flow	O
structures	O
,	O
and	O
implement	O
Domain	B-Language
Specific	I-Language
Languages	I-Language
(	O
DSLs	O
)	O
,	O
which	O
allow	O
domain-specific	O
concepts	O
to	O
be	O
expressed	O
in	O
concise	O
and	O
elegant	O
ways	O
.	O
</s>
<s>
A	O
consequence	O
of	O
syntactic	O
abstraction	B-Application
is	O
also	O
that	O
any	O
Lisp	B-Language
dialect	O
and	O
in	O
fact	O
almost	O
any	O
programming	O
language	O
can	O
,	O
in	O
principle	O
,	O
be	O
implemented	O
in	O
any	O
modern	O
Lisp	B-Language
with	O
significantly	O
reduced	O
(	O
but	O
still	O
non-trivial	O
in	O
most	O
cases	O
)	O
effort	O
when	O
compared	O
to	O
"	O
more	O
traditional	O
"	O
programming	O
languages	O
such	O
as	O
Python	B-Language
,	O
C	B-Language
or	O
Java	B-Language
.	O
</s>
<s>
Specification	O
languages	O
generally	O
rely	O
on	O
abstractions	B-Application
of	O
one	O
kind	O
or	O
another	O
,	O
since	O
specifications	O
are	O
typically	O
defined	O
earlier	O
in	O
a	O
project	O
,	O
(	O
and	O
at	O
a	O
more	O
abstract	O
level	O
)	O
than	O
an	O
eventual	O
implementation	O
.	O
</s>
<s>
The	O
UML	B-Language
specification	O
language	O
,	O
for	O
example	O
,	O
allows	O
the	O
definition	O
of	O
abstract	O
classes	O
,	O
which	O
in	O
a	O
waterfall	O
project	O
,	O
remain	O
abstract	O
during	O
the	O
architecture	B-Architecture
and	O
specification	O
phase	O
of	O
the	O
project	O
.	O
</s>
<s>
Programming	O
languages	O
offer	O
control	B-Application
abstraction	I-Application
as	O
one	O
of	O
the	O
main	O
purposes	O
of	O
their	O
use	O
.	O
</s>
<s>
For	O
example	O
,	O
consider	O
this	O
statement	O
written	O
in	O
a	O
Pascal-like	O
fashion	O
:	O
</s>
<s>
Without	O
control	B-Application
abstraction	I-Application
,	O
a	O
programmer	O
would	O
need	O
to	O
specify	O
all	O
the	O
register/binary	O
-level	O
steps	O
each	O
time	O
they	O
simply	O
wanted	O
to	O
add	O
or	O
multiply	O
a	O
couple	O
of	O
numbers	O
and	O
assign	O
the	O
result	O
to	O
a	O
variable	O
.	O
</s>
<s>
In	O
a	O
larger	O
system	O
,	O
it	O
may	O
involve	O
breaking	O
down	O
complex	O
tasks	O
into	O
many	O
different	O
modules	B-Architecture
.	O
</s>
<s>
Within	O
each	O
of	O
those	O
standalone	O
components	O
there	O
could	O
be	O
many	O
different	O
source	O
files	O
,	O
each	O
containing	O
the	O
program	B-Language
code	I-Language
to	O
handle	O
a	O
part	O
of	O
the	O
problem	O
,	O
with	O
only	O
selected	O
interfaces	O
available	O
to	O
other	O
parts	O
of	O
the	O
program	O
.	O
</s>
<s>
Object-oriented	B-Language
programming	I-Language
embraces	O
and	O
extends	O
this	O
concept	O
.	O
</s>
<s>
Data	B-Application
abstraction	I-Application
enforces	O
a	O
clear	O
separation	O
between	O
the	O
abstract	O
properties	O
of	O
a	O
data	O
type	O
and	O
the	O
concrete	O
details	O
of	O
its	O
implementation	O
.	O
</s>
<s>
Such	O
a	O
lookup	O
table	O
may	O
be	O
implemented	O
in	O
various	O
ways	O
:	O
as	O
a	O
hash	B-Algorithm
table	I-Algorithm
,	O
a	O
binary	B-Language
search	I-Language
tree	I-Language
,	O
or	O
even	O
a	O
simple	O
linear	O
list	O
of	O
(	O
key:value	O
)	O
pairs	O
.	O
</s>
<s>
While	O
much	O
of	O
data	B-Application
abstraction	I-Application
occurs	O
through	O
computer	B-General_Concept
science	I-General_Concept
and	O
automation	O
,	O
there	O
are	O
times	O
when	O
this	O
process	O
is	O
done	O
manually	O
and	O
without	O
programming	O
intervention	O
.	O
</s>
<s>
One	O
way	O
this	O
can	O
be	O
understood	O
is	O
through	O
data	B-Application
abstraction	I-Application
within	O
the	O
process	O
of	O
conducting	O
a	O
systematic	O
review	O
of	O
the	O
literature	O
.	O
</s>
<s>
In	O
this	O
methodology	O
,	O
data	O
is	O
abstracted	O
by	O
one	O
or	O
several	O
abstractors	O
when	O
conducting	O
a	O
meta-analysis	O
,	O
with	O
errors	O
reduced	O
through	O
dual	O
data	B-Application
abstraction	I-Application
followed	O
by	O
independent	O
checking	O
,	O
known	O
as	O
adjudication	O
.	O
</s>
<s>
In	O
object-oriented	B-Language
programming	I-Language
theory	O
,	O
abstraction	B-Application
involves	O
the	O
facility	O
to	O
define	O
objects	O
that	O
represent	O
abstract	O
"	O
actors	O
"	O
that	O
can	O
perform	O
work	O
,	O
report	O
on	O
and	O
change	O
their	O
state	B-Application
,	O
and	O
"	O
communicate	O
"	O
with	O
other	O
objects	O
in	O
the	O
system	O
.	O
</s>
<s>
The	O
term	O
encapsulation	B-Application
refers	O
to	O
the	O
hiding	O
of	O
state	B-Application
details	O
,	O
but	O
extending	O
the	O
concept	O
of	O
data	O
type	O
from	O
earlier	O
programming	O
languages	O
to	O
associate	O
behavior	O
most	O
strongly	O
with	O
the	O
data	O
,	O
and	O
standardizing	O
the	O
way	O
that	O
different	O
data	O
types	O
interact	O
,	O
is	O
the	O
beginning	O
of	O
abstraction	B-Application
.	O
</s>
<s>
When	O
abstraction	B-Application
proceeds	O
into	O
the	O
operations	O
defined	O
,	O
enabling	O
objects	O
of	O
different	O
types	O
to	O
be	O
substituted	O
,	O
it	O
is	O
called	O
polymorphism	B-Application
.	O
</s>
<s>
When	O
it	O
proceeds	O
in	O
the	O
opposite	O
direction	O
,	O
inside	O
the	O
types	O
or	O
classes	O
,	O
structuring	O
them	O
to	O
simplify	O
a	O
complex	O
set	O
of	O
relationships	O
,	O
it	O
is	O
called	O
delegation	B-Application
or	O
inheritance	B-Language
.	O
</s>
<s>
Various	O
object-oriented	B-Language
programming	I-Language
languages	I-Language
offer	O
similar	O
facilities	O
for	O
abstraction	B-Application
,	O
all	O
to	O
support	O
a	O
general	O
strategy	O
of	O
polymorphism	B-Application
in	I-Application
object-oriented	I-Application
programming	I-Application
,	O
which	O
includes	O
the	O
substitution	O
of	O
one	O
type	O
for	O
another	O
in	O
the	O
same	O
or	O
similar	O
role	O
.	O
</s>
<s>
Although	O
not	O
as	O
generally	O
supported	O
,	O
a	O
configuration	O
or	O
image	O
or	O
package	O
may	O
predetermine	O
a	O
great	O
many	O
of	O
these	O
bindings	O
at	O
compile-time	B-Application
,	O
link-time	B-Application
,	O
or	O
loadtime	B-Operating_System
.	O
</s>
<s>
This	O
would	O
leave	O
only	O
a	O
minimum	O
of	O
such	O
bindings	O
to	O
change	O
at	O
run-time	B-Library
.	O
</s>
<s>
Common	B-Application
Lisp	I-Application
Object	I-Application
System	I-Application
or	O
Self	B-Operating_System
,	O
for	O
example	O
,	O
feature	O
less	O
of	O
a	O
class-instance	O
distinction	O
and	O
more	O
use	O
of	O
delegation	B-Application
for	O
polymorphism	B-Application
.	O
</s>
<s>
Individual	O
objects	O
and	O
functions	O
are	O
abstracted	O
more	O
flexibly	O
to	O
better	O
fit	O
with	O
a	O
shared	O
functional	O
heritage	O
from	O
Lisp	B-Language
.	O
</s>
<s>
C++	B-Language
exemplifies	O
another	O
extreme	O
:	O
it	O
relies	O
heavily	O
on	O
templates	B-Language
and	O
overloading	B-Application
and	O
other	O
static	O
bindings	O
at	O
compile-time	B-Application
,	O
which	O
in	O
turn	O
has	O
certain	O
flexibility	O
problems	O
.	O
</s>
<s>
Although	O
these	O
examples	O
offer	O
alternate	O
strategies	O
for	O
achieving	O
the	O
same	O
abstraction	B-Application
,	O
they	O
do	O
not	O
fundamentally	O
alter	O
the	O
need	O
to	O
support	O
abstract	O
nouns	O
in	O
code	O
–	O
all	O
programming	O
relies	O
on	O
an	O
ability	O
to	O
abstract	O
verbs	O
as	O
functions	O
,	O
nouns	O
as	O
data	B-General_Concept
structures	I-General_Concept
,	O
and	O
either	O
as	O
processes	O
.	O
</s>
<s>
Consider	O
for	O
example	O
a	O
sample	O
Java	B-Language
fragment	O
to	O
represent	O
some	O
common	O
farm	O
"	O
animals	O
"	O
to	O
a	O
level	O
of	O
abstraction	B-Application
suitable	O
to	O
model	O
simple	O
aspects	O
of	O
their	O
hunger	O
and	O
feeding	O
.	O
</s>
<s>
It	O
defines	O
an	O
Animal	O
class	O
to	O
represent	O
both	O
the	O
state	B-Application
of	O
the	O
animal	O
and	O
its	O
functions	O
:	O
</s>
<s>
In	O
the	O
above	O
example	O
,	O
the	O
class	O
Animal	O
is	O
an	O
abstraction	B-Application
used	O
in	O
place	O
of	O
an	O
actual	O
animal	O
,	O
LivingThing	O
is	O
a	O
further	O
abstraction	B-Application
(	O
in	O
this	O
case	O
a	O
generalisation	B-Algorithm
)	O
of	O
Animal	O
.	O
</s>
<s>
If	O
one	O
requires	O
a	O
more	O
differentiated	O
hierarchy	O
of	O
animals	O
–	O
to	O
differentiate	O
,	O
say	O
,	O
those	O
who	O
provide	O
milk	O
from	O
those	O
who	O
provide	O
nothing	O
except	O
meat	O
at	O
the	O
end	O
of	O
their	O
lives	O
–	O
that	O
is	O
an	O
intermediary	O
level	O
of	O
abstraction	B-Application
,	O
probably	O
DairyAnimal	O
(	O
cows	O
,	O
goats	O
)	O
who	O
would	O
eat	O
foods	O
suitable	O
to	O
giving	O
good	O
milk	O
,	O
and	O
MeatAnimal	O
(	O
pigs	O
,	O
steers	O
)	O
who	O
would	O
eat	O
foods	O
to	O
give	O
the	O
best	O
meat-quality	O
.	O
</s>
<s>
Such	O
an	O
abstraction	B-Application
could	O
remove	O
the	O
need	O
for	O
the	O
application	O
coder	O
to	O
specify	O
the	O
type	O
of	O
food	O
,	O
so	O
they	O
could	O
concentrate	O
instead	O
on	O
the	O
feeding	O
schedule	O
.	O
</s>
<s>
The	O
two	O
classes	O
could	O
be	O
related	O
using	O
inheritance	B-Language
or	O
stand	O
alone	O
,	O
and	O
the	O
programmer	O
could	O
define	O
varying	O
degrees	O
of	O
polymorphism	B-Application
between	O
the	O
two	O
types	O
.	O
</s>
<s>
A	O
great	O
many	O
operation	O
overloads	B-Language
,	O
data	O
type	O
by	O
data	O
type	O
,	O
can	O
have	O
the	O
same	O
effect	O
at	O
compile-time	B-Application
as	O
any	O
degree	O
of	O
inheritance	B-Language
or	O
other	O
means	O
to	O
achieve	O
polymorphism	B-Application
.	O
</s>
<s>
Decisions	O
regarding	O
what	O
to	O
abstract	O
and	O
what	O
to	O
keep	O
under	O
the	O
control	O
of	O
the	O
coder	O
become	O
the	O
major	O
concern	O
of	O
object-oriented	B-Language
design	O
and	O
domain	B-General_Concept
analysis	I-General_Concept
—	O
actually	O
determining	O
the	O
relevant	O
relationships	O
in	O
the	O
real	O
world	O
is	O
the	O
concern	O
of	O
object-oriented	B-Application
analysis	I-Application
or	O
legacy	O
analysis	O
.	O
</s>
<s>
In	O
general	O
,	O
to	O
determine	O
appropriate	O
abstraction	B-Application
,	O
one	O
must	O
make	O
many	O
small	O
decisions	O
about	O
scope	O
(	O
domain	B-General_Concept
analysis	I-General_Concept
)	O
,	O
determine	O
what	O
other	O
systems	O
one	O
must	O
cooperate	O
with	O
(	O
legacy	O
analysis	O
)	O
,	O
then	O
perform	O
a	O
detailed	O
object-oriented	B-Application
analysis	I-Application
which	O
is	O
expressed	O
within	O
project	O
time	O
and	O
budget	O
constraints	O
as	O
an	O
object-oriented	B-Language
design	O
.	O
</s>
<s>
A	O
decision	O
to	O
differentiate	O
DairyAnimal	O
would	O
change	O
the	O
detailed	O
analysis	O
but	O
the	O
domain	O
and	O
legacy	O
analysis	O
would	O
be	O
unchanged	O
—	O
thus	O
it	O
is	O
entirely	O
under	O
the	O
control	O
of	O
the	O
programmer	O
,	O
and	O
it	O
is	O
called	O
an	O
abstraction	B-Application
in	O
object-oriented	B-Language
programming	I-Language
as	O
distinct	O
from	O
abstraction	B-Application
in	O
domain	O
or	O
legacy	O
analysis	O
.	O
</s>
<s>
When	O
discussing	O
formal	B-Application
semantics	I-Application
of	I-Application
programming	I-Application
languages	I-Application
,	O
formal	B-Architecture
methods	I-Architecture
or	O
abstract	O
interpretation	O
,	O
abstraction	B-Application
refers	O
to	O
the	O
act	O
of	O
considering	O
a	O
less	O
detailed	O
,	O
but	O
safe	O
,	O
definition	O
of	O
the	O
observed	O
program	O
behaviors	O
.	O
</s>
<s>
Abstraction	B-Application
is	O
defined	O
to	O
a	O
concrete	O
(	O
more	O
precise	O
)	O
model	O
of	O
execution	O
.	O
</s>
<s>
Abstraction	B-Application
may	O
be	O
exact	O
or	O
faithful	O
with	O
respect	O
to	O
a	O
property	O
if	O
one	O
can	O
answer	O
a	O
question	O
about	O
the	O
property	O
equally	O
well	O
on	O
the	O
concrete	O
or	O
abstract	O
model	O
.	O
</s>
<s>
For	O
instance	O
,	O
if	O
one	O
wishes	O
to	O
know	O
what	O
the	O
result	O
of	O
the	O
evaluation	O
of	O
a	O
mathematical	O
expression	O
involving	O
only	O
integers	O
+	O
,	O
-	O
,	O
×	O
,	O
is	O
worth	O
modulo	O
n	O
,	O
then	O
one	O
needs	O
only	O
perform	O
all	O
operations	O
modulo	O
n	O
(	O
a	O
familiar	O
form	O
of	O
this	O
abstraction	B-Application
is	O
casting	B-Error_Name
out	I-Error_Name
nines	I-Error_Name
)	O
.	O
</s>
<s>
Abstractions	B-Application
,	O
however	O
,	O
though	O
not	O
necessarily	O
exact	O
,	O
should	O
be	O
sound	O
.	O
</s>
<s>
That	O
is	O
,	O
it	O
should	O
be	O
possible	O
to	O
get	O
sound	O
answers	O
from	O
them	O
—	O
even	O
though	O
the	O
abstraction	B-Application
may	O
simply	O
yield	O
a	O
result	O
of	O
undecidability	O
.	O
</s>
<s>
The	O
level	O
of	O
abstraction	B-Application
included	O
in	O
a	O
programming	O
language	O
can	O
influence	O
its	O
overall	O
usability	B-General_Concept
.	O
</s>
<s>
The	O
Cognitive	O
dimensions	O
framework	O
includes	O
the	O
concept	O
of	O
abstraction	B-Application
gradient	O
in	O
a	O
formalism	O
.	O
</s>
<s>
This	O
framework	O
allows	O
the	O
designer	O
of	O
a	O
programming	O
language	O
to	O
study	O
the	O
trade-offs	O
between	O
abstraction	B-Application
and	O
other	O
characteristics	O
of	O
the	O
design	O
,	O
and	O
how	O
changes	O
in	O
abstraction	B-Application
influence	O
the	O
language	O
usability	B-General_Concept
.	O
</s>
<s>
Abstractions	B-Application
can	O
prove	O
useful	O
when	O
dealing	O
with	O
computer	B-Application
programs	I-Application
,	O
because	O
non-trivial	O
properties	O
of	O
computer	B-Application
programs	I-Application
are	O
essentially	O
undecidable	O
(	O
see	O
Rice	O
's	O
theorem	O
)	O
.	O
</s>
<s>
As	O
a	O
consequence	O
,	O
automatic	O
methods	O
for	O
deriving	O
information	O
on	O
the	O
behavior	O
of	O
computer	B-Application
programs	I-Application
either	O
have	O
to	O
drop	O
termination	O
(	O
on	O
some	O
occasions	O
,	O
they	O
may	O
fail	O
,	O
crash	O
or	O
never	O
yield	O
out	O
a	O
result	O
)	O
,	O
soundness	O
(	O
they	O
may	O
provide	O
false	O
information	O
)	O
,	O
or	O
precision	O
(	O
they	O
may	O
answer	O
"	O
I	O
do	O
n't	O
know	O
"	O
to	O
some	O
questions	O
)	O
.	O
</s>
<s>
Abstraction	B-Application
is	O
the	O
core	O
concept	O
of	O
abstract	O
interpretation	O
.	O
</s>
<s>
Model	B-Application
checking	I-Application
generally	O
takes	O
place	O
on	O
abstract	O
versions	O
of	O
the	O
studied	O
systems	O
.	O
</s>
<s>
Computer	B-General_Concept
science	I-General_Concept
commonly	O
presents	O
levels	O
(	O
or	O
,	O
less	O
commonly	O
,	O
layers	O
)	O
of	O
abstraction	B-Application
,	O
wherein	O
each	O
level	O
represents	O
a	O
different	O
model	O
of	O
the	O
same	O
information	O
and	O
processes	O
,	O
but	O
with	O
varying	O
amounts	O
of	O
detail	O
.	O
</s>
<s>
Each	O
level	O
is	O
embodied	O
,	O
but	O
not	O
determined	O
,	O
by	O
the	O
level	O
beneath	O
it	O
,	O
making	O
it	O
a	O
language	O
of	O
description	O
that	O
is	O
somewhat	O
self-contained	O
.	O
</s>
<s>
Physical	O
level	O
:	O
The	O
lowest	O
level	O
of	O
abstraction	B-Application
describes	O
how	O
a	O
system	O
actually	O
stores	O
data	O
.	O
</s>
<s>
The	O
physical	O
level	O
describes	O
complex	O
low-level	O
data	B-General_Concept
structures	I-General_Concept
in	O
detail	O
.	O
</s>
<s>
Logical	O
level	O
:	O
The	O
next	O
higher	O
level	O
of	O
abstraction	B-Application
describes	O
what	O
data	O
the	O
database	O
stores	O
,	O
and	O
what	O
relationships	O
exist	O
among	O
those	O
data	O
.	O
</s>
<s>
This	O
is	O
referred	O
to	O
as	O
physical	B-General_Concept
data	I-General_Concept
independence	I-General_Concept
.	O
</s>
<s>
Database	B-General_Concept
administrators	I-General_Concept
,	O
who	O
must	O
decide	O
what	O
information	O
to	O
keep	O
in	O
a	O
database	O
,	O
use	O
the	O
logical	O
level	O
of	O
abstraction	B-Application
.	O
</s>
<s>
View	B-Language
level	O
:	O
The	O
highest	O
level	O
of	O
abstraction	B-Application
describes	O
only	O
part	O
of	O
the	O
entire	O
database	O
.	O
</s>
<s>
The	O
view	B-Language
level	O
of	O
abstraction	B-Application
exists	O
to	O
simplify	O
their	O
interaction	O
with	O
the	O
system	O
.	O
</s>
<s>
Some	O
design	B-Language
processes	I-Language
specifically	O
generate	O
designs	O
that	O
contain	O
various	O
levels	O
of	O
abstraction	B-Application
.	O
</s>
<s>
Layered	O
architecture	B-Architecture
partitions	O
the	O
concerns	O
of	O
the	O
application	O
into	O
stacked	O
groups	O
(	O
layers	O
)	O
.	O
</s>
