Automated Formal Static Analysis and Retrieval of Source Code - JKU

Chapter 1
Introduction
From the hand-proof from the 1950’s until the nowadays sophisticated automated tools, the main
goal was the same: proving program (algorithm, software) correctness.
Program testing and debugging lost from the very beginning the war in being the suitable
techniques for proving the program correctness. The only hope remained in the program verification.
But because ,,Everything interesting about the behavior of programs is undecidable.”
[paraphrase of H.G. Rice, 1953] (from A. Mœller slides on An Introduction to Analysis and Verification
of Software), the task that had to be solved by the program verification techniques is a
very challenging one.
We are interested in the imperative program verification using a formal static analysis method
which uses an axiomatic approach in the Hoare triple style; we are given the input (I P ) and the
output (O P ) specification for an imperative program P and we want to show that the program
fulfils its specification. We approach this problem using automated theorem proving, namely we
automatically generate the verification conditions which arise from the program analysis and try
to prove them automatically.
Following the ideas of the axiomatic approach used for the generation of the verification conditions
(symbolic execution and forward reasoning techniques) and for computing the program
function (functional semantics method), we developed, in a logical manner, the syntax, the semantics,
the partial correctness and the termination for the imperative programs which contain
Return statements, assignments (including recursive calls) and conditionals (If with one and
two branches).
For expressing these notions we use, besides the underlying theory of the programs – object
theory, the environment of a meta–theory, in which the notions about reasoning about programs
are expressed. In this way, one could reason also about the system which would automatize these
theoretical notions.
The program termination problem is known to be undecidable, but some gains were achieved
in the last years in [CS02], [B. 06a], were the main goal was to find termination proofs for programs
(liveness property) and in [HJMS], [B. 06b], were the emphasis is to prove that a program
is not error prone (safety property).
We approach the termination property in a purely logical manner, in the underlying theory of
programs, without requiring any model of computations of programs. For example, in the case of
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