Structuration of the ALPHA language

This paper presents extensions to ALPHA, a language based upon the formalism of affine recurrence equations (AREs). These extensions address the need for parametric and structured systems of such AREs. Similar to, but more general than the map operator of classical functional languages, the ALPHA structured techniques provide a dense and powerful description of complex systems referencing each other. Such structured systems of AREs may be interpreted as (or translated into) sequential function calls, hierarchical hardware description, or any SIMD flavour of structured programming. With the help of examples, we give an overview of these techniques, and their substitution semantics based on the homomorphic extension of convex polyhedra and affine functions.