<s>
Algebraic	B-Application
specification	I-Application
is	O
a	O
software	B-General_Concept
engineering	I-General_Concept
technique	O
for	O
formally	B-Application
specifying	I-Application
system	O
behavior	O
.	O
</s>
<s>
Algebraic	B-Application
specification	I-Application
seeks	O
to	O
systematically	O
develop	O
more	O
efficient	O
programs	O
by	O
:	O
</s>
<s>
An	O
algebraic	B-Application
specification	I-Application
achieves	O
these	O
goals	O
by	O
defining	O
one	O
or	O
more	O
data	O
types	O
,	O
and	O
specifying	O
a	O
collection	O
of	O
functions	O
that	O
operate	O
on	O
those	O
data	O
types	O
.	O
</s>
<s>
The	O
set	O
of	O
available	O
constructor	O
functions	O
is	O
implied	O
by	O
the	O
specification	B-Application
's	O
signature	O
.	O
</s>
<s>
Additionally	O
,	O
a	O
specification	B-Application
can	O
contain	O
equations	O
defining	O
equivalences	O
between	O
the	O
objects	O
constructed	O
by	O
these	O
functions	O
.	O
</s>
<s>
Additional	B-Language
functions	I-Language
:	O
Functions	O
that	O
operate	O
on	O
the	O
data	O
types	O
,	O
and	O
are	O
defined	O
in	O
terms	O
of	O
the	O
constructor	O
functions	O
.	O
</s>
<s>
Consider	O
a	O
formal	O
algebraic	B-Application
specification	I-Application
for	O
the	O
boolean	O
data	O
type	O
.	O
</s>
<s>
One	O
possible	O
algebraic	B-Application
specification	I-Application
may	O
provide	O
two	O
constructor	O
functions	O
for	O
the	O
data-element	O
:	O
a	O
true	O
constructor	O
and	O
a	O
false	O
constructor	O
.	O
</s>
<s>
In	O
this	O
scenario	O
,	O
all	O
other	O
connective	O
elements	O
,	O
such	O
as	O
XOR	B-Application
and	O
AND	O
,	O
would	O
be	O
additional	B-Language
functions	I-Language
.	O
</s>
<s>
Thus	O
,	O
a	O
data	O
element	O
could	O
be	O
instantiated	O
with	O
either	O
"	O
true	O
"	O
or	O
"	O
false	O
"	O
value	O
,	O
and	O
additional	B-Language
functions	I-Language
could	O
be	O
used	O
to	O
perform	O
any	O
operation	O
on	O
the	O
data	O
element	O
.	O
</s>
<s>
The	O
algebraic	B-Application
specification	I-Application
therefore	O
describes	O
all	B-Architecture
possible	I-Architecture
states	I-Architecture
of	O
the	O
data	O
element	O
,	O
and	O
all	O
possible	O
transitions	O
between	O
states	O
.	O
</s>
<s>
Therefore	O
,	O
any	O
implementation	O
conforming	O
to	O
this	O
specification	B-Application
will	O
behave	O
like	O
the	O
integers	O
,	O
or	O
possibly	O
a	O
restricted	O
range	O
of	O
them	O
,	O
like	O
the	O
usual	O
integer	O
types	O
found	O
in	O
most	O
programming	O
languages	O
.	O
</s>
