Equivalence is in the Eye of the Beholder

In a recent provocative paper, Lamport points out “the insubstantiality of processes” by proving the equivalence of two different decompositions of the same intuitive algorithm by means of temporal formulas. We point out that the correct equivalence of algorithms is itself in the eye of the beholder. We discuss a number of related issues and, in particular, whether algorithms can be proved equivalent directly.