Automated Formal Static Analysis and Retrieval of Source Code - JKU

Chapter 2
Program Verification by Symbolic
Execution in Theorema
2.1 Background
2.1.1 Program Verification
The desire of the software developers was, is and will be to write programs without bugs. For the
achievement of this goal they try to combine the following techniques: programming language
design, debugging, testing.
Programming language design represents the main step in writing a correct software. The
facilities of the nowadays programming languages (type systems, abstract data types, inheritance
and encapsulation for object oriented programming, etc.) provide writing software at high level
of abstraction and implicitly reduce the number of possible errors.
By debugging, one can reduce the number of bugs in a software program in a systematic way
such that it behaves as expected.
Testing is an empirical step towards the software verification. It is performed with the intention
of finding software bugs but it can not provide the certainty of software correctness.
Nighter of these techniques, nor their combination give a software correctness proof.
Program verification is, instead, the technique which insures or disproves the correctness of a
computer program with respect to a specification.
We are interested in verifying programs using theorem proving, more specifically automated
theorem proving.
2.1.1.1 Theorem Proving in Program Verification
We approach the problem of program (algorithm) verification from the formal static point of view,
that is, we analyze the program without executing it. More precisely, we use an approach in the
Hoare ([Hoa69]) like style.
In this formal system, the program correctness problem is formulated as follows: using a
calculus involving the program statements, the verification conditions which arise from program
analysis are generated and proven to be theorems. They are logical formulae and state the fact that
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