<s>
In	O
computer	B-General_Concept
science	I-General_Concept
and	O
software	B-General_Concept
engineering	I-General_Concept
,	O
Alloy	B-Application
is	O
a	O
declarative	O
specification	B-Application
language	I-Application
for	O
expressing	O
complex	O
structural	O
constraints	O
and	O
behavior	O
in	O
a	O
software	O
system	O
.	O
</s>
<s>
Alloy	B-Application
provides	O
a	O
simple	O
structural	O
modeling	O
tool	O
based	O
on	O
first-order	O
logic	O
.	O
</s>
<s>
Alloy	B-Application
is	O
targeted	O
at	O
the	O
creation	O
of	O
micro-models	O
that	O
can	O
then	O
be	O
automatically	O
checked	O
for	O
correctness	O
.	O
</s>
<s>
Alloy	B-Application
specifications	O
can	O
be	O
checked	O
using	O
the	O
Alloy	B-Application
Analyzer	I-Application
.	O
</s>
<s>
Although	O
Alloy	B-Application
is	O
designed	O
with	O
automatic	O
analysis	O
in	O
mind	O
,	O
Alloy	B-Application
differs	O
from	O
many	O
specification	B-Application
languages	I-Application
designed	O
for	O
model-checking	B-Application
in	O
that	O
it	O
permits	O
the	O
definition	O
of	O
infinite	O
models	O
.	O
</s>
<s>
The	O
Alloy	B-Application
Analyzer	I-Application
is	O
designed	O
to	O
perform	O
finite	O
scope	O
checks	O
even	O
on	O
infinite	O
models	O
.	O
</s>
<s>
The	O
Alloy	B-Application
language	I-Application
and	O
analyzer	O
are	O
developed	O
by	O
a	O
team	O
led	O
by	O
Daniel	O
Jackson	O
at	O
the	O
Massachusetts	O
Institute	O
of	O
Technology	O
in	O
the	O
United	O
States	O
.	O
</s>
<s>
The	O
first	O
version	O
of	O
the	O
Alloy	B-Application
language	I-Application
appeared	O
in	O
1997	O
.	O
</s>
<s>
It	O
was	O
a	O
rather	O
limited	O
object	B-Application
modeling	I-Application
language	O
.	O
</s>
<s>
Succeeding	O
iterations	O
of	O
the	O
language	O
"	O
added	O
quantifiers	B-Language
,	O
higher	O
arity	O
relations	O
,	O
polymorphism	B-Application
,	O
subtyping	O
,	O
and	O
signatures	O
"	O
.	O
</s>
<s>
The	O
mathematical	O
underpinnings	O
of	O
the	O
language	O
were	O
heavily	O
influenced	O
by	O
the	O
Z	B-Language
notation	I-Language
,	O
and	O
the	O
syntax	B-Application
of	O
Alloy	B-Application
owes	O
more	O
to	O
languages	O
such	O
as	O
Object	B-Language
Constraint	I-Language
Language	I-Language
.	O
</s>
<s>
The	O
Alloy	B-Application
Analyzer	I-Application
was	O
specifically	O
developed	O
to	O
support	O
so-called	O
"	O
lightweight	O
formal	O
methods	O
"	O
.	O
</s>
<s>
As	O
such	O
,	O
it	O
is	O
intended	O
to	O
provide	O
fully	O
automated	O
analysis	O
,	O
in	O
contrast	O
to	O
the	O
interactive	O
theorem	O
proving	O
techniques	O
commonly	O
used	O
with	O
specification	B-Application
languages	I-Application
similar	O
to	O
Alloy	B-Application
.	O
</s>
<s>
Development	O
of	O
the	O
Analyzer	O
was	O
originally	O
inspired	O
by	O
the	O
automated	O
analysis	O
provided	O
by	O
model	B-Application
checkers	I-Application
.	O
</s>
<s>
However	O
,	O
model-checking	B-Application
is	O
ill-suited	O
to	O
the	O
kind	O
of	O
models	O
that	O
are	O
typically	O
developed	O
in	O
Alloy	B-Application
,	O
and	O
as	O
a	O
result	O
the	O
core	O
of	O
the	O
Analyzer	O
was	O
eventually	O
implemented	O
as	O
a	O
model-finder	O
built	O
atop	O
a	O
boolean	B-Algorithm
SAT	I-Algorithm
solver	I-Algorithm
.	O
</s>
<s>
Through	O
version	O
3.0	O
,	O
the	O
Alloy	B-Application
Analyzer	I-Application
incorporated	O
an	O
integral	O
SAT-based	O
model-finder	O
based	O
on	O
an	O
off-the-shelf	O
SAT-solver	O
.	O
</s>
<s>
Both	O
model-finders	O
essentially	O
translate	O
a	O
model	O
expressed	O
in	O
relational	B-Algorithm
logic	I-Algorithm
into	O
a	O
corresponding	O
boolean	O
logic	O
formula	O
,	O
and	O
then	O
invoke	O
an	O
off-the-shelf	O
SAT-solver	O
on	O
the	O
boolean	O
formula	O
.	O
</s>
<s>
In	O
the	O
event	O
that	O
the	O
solver	O
finds	O
a	O
solution	O
,	O
the	O
result	O
is	O
translated	O
back	O
into	O
a	O
corresponding	O
binding	O
of	O
constants	O
to	O
variables	O
in	O
the	O
relational	B-Algorithm
logic	I-Algorithm
model	O
.	O
</s>
<s>
In	O
order	O
to	O
ensure	O
the	O
model-finding	O
problem	O
is	O
decidable	O
,	O
the	O
Alloy	B-Application
Analyzer	I-Application
performs	O
model-finding	O
over	O
restricted	O
scopes	O
consisting	O
of	O
a	O
user-defined	O
finite	O
number	O
of	O
objects	O
.	O
</s>
<s>
However	O
,	O
the	O
designers	O
of	O
the	O
Alloy	B-Application
Analyzer	I-Application
justify	O
the	O
decision	O
to	O
work	O
within	O
limited	O
scopes	O
through	O
an	O
appeal	O
to	O
the	O
small	O
scope	O
hypothesis	O
:	O
that	O
a	O
high	O
proportion	O
of	O
bugs	O
can	O
be	O
found	O
by	O
testing	O
a	O
program	O
for	O
all	O
test	O
inputs	O
within	O
some	O
small	O
scope	O
.	O
</s>
<s>
Alloy	B-Application
models	O
are	O
relational	O
in	O
nature	O
,	O
and	O
are	O
composed	O
of	O
several	O
different	O
kinds	O
of	O
statements	O
:	O
</s>
<s>
Because	O
Alloy	B-Application
is	O
a	O
declarative	O
language	O
the	O
meaning	O
of	O
a	O
model	O
is	O
unaffected	O
by	O
the	O
order	O
of	O
statements	O
.	O
</s>
