Specification of the Fast Fourier Transform algorithm as a term rewriting system

Abstract

We specify an algorithm for multiplying polynomials with complex coefficients incorporating, the Fast Fourier Transform algorithm of Cooley and Tukey [CT]. The specification formalism we use is a variant of the formalism ASF described in. [BHK]. The difference with ASF is essentially a matter of semantics: we only use pure equations, and this, with some extra restrictions, allows us to consider the specification as a term rewriting system, and take for its meaning the canonical algebra of normal forms.