Industrial context 45 2. Two methods for formal verification 52 2. Four formal verification tools 66 2. Examples of industrial use 80 2. Bibliography Chapter 3. Introduction to software quality and verification procedures 3. Static analysis 3. Dynamic tests 3. Abstract interpretation 3. Code verification 3. Robustness verification or contextual verification 3. Carrying out a code verification with Polyspace 3. The creation of critical onboard software 3. Bibliography Chapter 4. Normative context 4. Elaboration of the proof of the robustness method 4. General description of the method 4.
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Static Analysis Of Software The Abstract Interpretation
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Static Analysis by Abstract Interpretation: A Mathematical Programming Approach
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Abstract interpretation
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Two unanimity valuable computers identify blessed for strategies: One crucial requirement is to add enough vagueness so as to make problems manageable while still retaining enough precision for answering the important questions such as "may the program crash? Given a programming or specification language, abstract interpretation consists of giving several semantics linked by relations of abstraction.
A semantics is a mathematical characterization of a possible behavior of the program. The most precise semantics, describing very closely the actual execution of the program, are called the concrete semantics. For instance, the concrete semantics of an imperative programming language may associate to each program the set of execution traces it may produce — an execution trace being a sequence of possible consecutive states of the execution of the program; a state typically consists of the value of the program counter and the memory locations globals, stack and heap.
More abstract semantics are then derived; for instance, one may consider only the set of reachable states in the executions which amounts to considering the last states in finite traces. The goal of static analysis is to derive a computable semantic interpretation at some point. For some elementary operations, such as multiplication , such an abstraction does not lose any precision: For some other operations, the abstraction may lose precision: Sometimes a loss of precision is necessary to make the semantics decidable see Rice's theorem , halting problem.
In general, there is a compromise to be made between the precision of the analysis and its decidability computability , or tractability complexity. In practice the abstractions that are defined are tailored to both the program properties one desires to analyze, and to the set of target programs. The first large scale automated analysis of computer programs with abstract interpretation can be attributed to an accident that resulted in the destruction of the first flight of the Ariane 5 rocket in These two sets are related to each other by defining total functions that map elements from one to the other.
The concrete semantics f is a monotonic function from L 1 to L 2. Program semantics are generally described using fixed points in the presence of loops or recursive procedures. Let us suppose that L is a complete lattice and let f be a monotonic function from L into L. This supposes the existence of best abstractions, which is not necessarily the case. One can assign to each variable x available at a given program point an interval [ L x , H x ].
A state assigning the value v x to variable x will be a concretization of these intervals if for all x , v x is in [ L x , H x ].
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More complex formulas can be derived for multiplication, division, etc. With reasonable arithmetic types, the result for z should be zero. While each of the operations taken individually was exactly abstracted, their composition isn't.