Design and proof of multipliers by correctness-preserving transformation

Abstract

Transformational development makes it possible to design systems and simultaneously to prove them correct. Transformational developments are presented of multiplier circuits from a common specification. Careful choice of the notation (a functional language with polymorphic and dependent higher-order sub types), and of the foundations for the transformations (some lemmas over the data domains, embeddings of functions into more general ones, and use of the unfold/fold strategy) allows one to highlight the design decisions in a systematic manner. The major design decisions are discussed, and important intermediate versions of the algorithms arising during the derivation are given. One sample development is presented.<>