Static Analysis and Deductive Verification of Programs
This thesis is concerned with analysis of programs. Analysis of programs can be divided into two camps: static analysis and formal verification.
Static program analyses compute a result and terminate for all programs. Since virtually all interesting semantic properties are undecidable, a static program analysis needs to be approximative to ensure termination. When designing such an analysis it can be hard to know which features that have the largest impact on the precision and should be added. This is the subject of the first paper in this thesis in which we investigate the impact a number of features have on the precision of usage analysis.
Formal verification often refers to deductive verification based on logic and theorem proving. When verifying a property, the program and the property are both translated into logical formulas and a theorem prover is used to show that the property holds for the program. Formal verification is a much more precise and general purpose technique than static analysis. This does, however, not come for free. It is extremely hard to find good heuristics for guiding the automatic construction of proofs. Therefore, user interaction is often required which makes the verification very time consuming and expensive.
Static program analysis is limited by its approximative nature and program verification by its high cost. It is, therefore, interesting to try to combine the strengths of the two techniques. This can be done in both directions: by letting a static program analysis use a theorem prover designed for program verification or letting a program verifier use a static program analysis. The latter combination is the subject of the second and third paper in this thesis.
We make the following contributions:
* We investigate the impact of a number of features on the precision of usage analysis.
* We show how a static program analysis can be embedded into a theorem prover.
* We show how interactive techniques for handling loops can sometimes be made automatic by using a dependence analysis.