The Naive Execution of Affine Recurrence Equations

: In recognition of the fundamental relation between regular arrays and systems of affine recurrence equations, the Alpha language was developed as the basis of a computer aided design methodology for regular array architectures. Alpha is used to initially specify algorithms at a very high algorithmic level. Regular array architecures can then be derived from the algorithmic specification using a transformational approach supported by the Alpha environment. This design methodology guarantees the final design to be correct by construction, assuming the initial algorithm was correct. In this paper, we address the problem of validating an initial specification. We demonstrate a translation methodolody which compiles Alpha into the imperative sequential language C. The C--code may then be compiled and executed to test the specification. We show how an Alpha program can be naively implemented by viewing it as a set of monolithic arrays and their filling functions, implemented using applicat..