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\section*{Handout 9 (Static Analysis)}

If we want to improve the safety and security of our programs,
we need a more principled approach to programming. Testing is
good, but as Dijkstra famously said ``Testing can only show
the presence of bugs, not their absence''. While such a more
principled approach has been the subject of intense study for
a long time, only in the past recent years some impressive
results have been achieved. One is the complete formalisation
and (mathematical) verification of a microkernel operating
system called seL4.

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\url{http://sel4.systems}
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\noindent In 2011 this work was included in the MIT Technology
Review in the annual list of the world’s ten most important
emerging
technologies.\footnote{\url{http://www2.technologyreview.com/tr10/?year=2011}}
While this work is impressive, it technical details are too
numerous that they can be explained here. So let us look at
something much simpler, namely finding out properties about
programs in a very simple programming language using
\emph{static analysis}.


\noindent What would be missing in comparison with real
(low-level machine) code? Well, the numbers we assume to be
arbitrary precision, which is not the case in real code. There
basic number formats have a rang and might over-run or
under-run from this range. Our assumption about variables,
does not correspond to actual registers, which are only 
limited on real hardware. Obviously, real code has richer
operations than just addition, multiplication and equality.
But this are not really essential limitations of our simple
examples.

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