40 Years of Computing at Newcastle

Department Technical Report Series No. 559

Correctness of Dataflow and Systolic Algorithms: Case Studies in Higher-Order Algebra.

K. Meinke and L.J. Steggles

University of Newcastle upon Tyne. 1996

Abstract

We present two case studies which illustrate the use of higher-order algebra as a formalism for specification and verification of hardware algorithms. In the first case study we specify a systolic algorithm for convolution and formally verify its correctness using higher-order equational logic. The second case study demonstrates the expressive power of higher-order algebraic specifications by presenting a non-constructive specification of the Hamming stream problem. A dataflow algorithm for computing the Hamming stream is then specified and the correctness of this algorithm is verified by semantical methods. Both case studies illustrate aspects of the metatheory of higher-order equational logic.

Department Technical Report Series - 1996
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Technical Report Abstract No. 559, 30 June 1997