Hierarchical static analysis of structured systems of affine recurrence equations

The ALPHA language, based on systems of affine recurrence equations over polyhedral domains, allows the expression of complex algorithms as hierarchical, parameterized structures of such systems. This paper discusses the static analysis of ALPHA programs, an extended type-checking process based on the single assignment rule. We present techniques ensuring, on one hand, that a system is valid (with respect to this rule) within a certain range of its parameters, and on the other, that no system is used with invalid values of its parameters. These techniques have been implemented in a versatile tool for ALPHA which is demonstrated on the example of the Gaussian elimination.