Program analysis using symbolic ranges

1. A computer-implemented method for generating a representation of relationships between variables in a program comprising the steps of:

automatically generating a set of Symbolic Range Constraints (SRCs) for the variables, wherein said SRCs are of the form φ:Λ i=1 n l i ≦x i ≦u i where for each i ε[l,n], the linear expressions l i , u i are made up of variables in the set {x i+1 , . . . , x n }, and wherein said SRCs comprise linear, convex, and triangulated constraints for a given variable order; and

providing said generated set of SRCs to a user.

2. The computer-implemented method of claim 1 employing a JOIN operation on SRC representations.

3. The computer-implemented method of claim 1 employing a MEET operation on SRC representations.

4. The computer-implemented method of claim 1 employing a transfer function of SRC representations with respect to a program statement.

5. The computer-implemented method of claim 1 employing a WIDENING operation on SRC representations.

6. The computer-implemented method of claim 1 employing a NARROWING operation on SRC representations.

7. The computer-implemented method of claim 1 further comprising the step of checking for inclusion of SRC representations.

8. The computer-implemented method of claim 1 which determines the correctness of the program by checking a safety property.

9. The computer-implemented method of claim 1 which determines the correctness of a program by detecting buffer overflow conditions.

10. The computer-implemented method of claim 1 which determines the correctness of a program by detecting null pointer dereferences.

11. The computer-implemented method of claim 1 which, used in an optimizing compiler, optimizes the program for size/performance.

12. The computer-implemented method of claim 1 which, used in a static analyzer, performs a program analysis.

13. The computer-implemented method of claim 1 which, used in a model checker, performs verification of the program.