REVERSE ENGINEERING THROUGH FORMAL TRANSFORMATION - KNUTHS POLYNOMIALADDITION ALGORITHM

In this paper we will take a detailed look at a larger example of prog ram analysis by transformation. We will be considering Algorithm 2.3.3 .A from Knuths 'Fundamental Algorithms' Knuth (1968) (p. 357) which is an algorithm for the addition of polynomials represented using four-d irectional links. Knuth (1974) describes this as having ''a complicate d structure with excessively unrestrained goto statements'' and goes o n to say ''I hope someday to see the algorithm cleaned up without loss of its efficiency''. Our aim is to manipulate the program, using sema ntics-preserving operations, into an equivalent, high-level specificat ion. The transformations are carried out in the WSL language, a 'wide spectrum language' which includes both low-level program operations an d high level specifications, and which has been specifically designed to be easy to transform.