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.

[1]  Patrice Quinton,et al.  Derivation of Data Parallel Code from a Functional Program , 1994 .

[2]  Doran Wilde,et al.  The ALPHA language , 1994 .

[3]  Eric Gautrin,et al.  Synthesis of systolic arrays by equation transformations , 1991, Proceedings of the International Conference on Application Specific Array Processors.

[4]  Sanjay V. Rajopadhye,et al.  The naive execution of affine recurrence equations , 1995, Proceedings The International Conference on Application Specific Array Processors.

[5]  Christophe Mauras.  Alpha : un langage equationnel pour la conception et la programmation d'architectures paralleles synchrones , 1989 .

[6]  Patrice Quinton,et al.  The ALPHA language and its use for the design of systolic arrays , 1991, J. VLSI Signal Process..

[7]  Richard M. Karp,et al.  The Organization of Computations for Uniform Recurrence Equations , 1967, JACM.