<s>
Predicative	B-Application
programming	I-Application
is	O
the	O
original	O
name	O
of	O
a	O
formal	O
method	O
for	O
program	O
specification	B-Application
and	O
refinement	O
,	O
more	O
recently	O
called	O
a	O
Practical	O
Theory	O
of	O
Programming	O
,	O
invented	O
by	O
Eric	O
Hehner	O
.	O
</s>
<s>
The	O
central	O
idea	O
is	O
that	O
each	O
specification	B-Application
is	O
a	O
binary	O
(	O
boolean	O
)	O
expression	O
that	O
is	O
true	O
of	O
acceptable	O
computer	O
behaviors	O
and	O
false	O
of	O
unacceptable	O
behaviors	O
.	O
</s>
<s>
Commands	O
in	O
a	O
programming	O
language	O
are	O
considered	O
to	O
be	O
a	O
special	O
case	O
of	O
specification	B-Application
—	O
those	O
specifications	O
that	O
are	O
compilable	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
the	O
program	O
variables	O
are	O
,	O
,	O
and	O
,	O
the	O
command	O
:=	O
+1	O
is	O
equivalent	O
to	O
the	O
specification	B-Application
(	O
binary	O
expression	O
)	O
=	O
+1	O
∧	O
=	O
∧	O
=	O
in	O
which	O
,	O
,	O
and	O
represent	O
the	O
values	O
of	O
the	O
program	O
variables	O
before	O
the	O
assignment	O
,	O
and	O
,	O
,	O
and	O
represent	O
the	O
values	O
of	O
the	O
program	O
variables	O
after	O
the	O
assignment	O
.	O
</s>
<s>
If	O
the	O
specification	B-Application
is	O
>	O
,	O
we	O
easily	O
prove	O
(	O
:	O
=	O
+1	O
)	O
⇒	O
(	O
>	O
)	O
,	O
which	O
says	O
that	O
:=	O
+1	O
implies	O
,	O
or	O
refines	O
,	O
or	O
implements	O
>	O
.	O
</s>
<s>
There	O
is	O
no	O
need	O
for	O
a	O
loop	B-Application
invariant	I-Application
or	O
least	O
fixed	O
point	O
.	O
</s>
