Evolving Algebras: an Attempt to Discover Semantics

This tutorial is based on lecture notes from the Fall 1990 course on Principles of Programming Languages at the University of Michigan. (My young friend Quisani did not attend the lectures.) The present version incorporates some changes provoked by the necessity to update the bibliography. The main part of the paper is still the same, however, and the examples are unchanged even though many things happened in the meantime. In particular, we (the collective we) have learned how to build evolving algebras by the method of successive re nements, and the current evolving algebra description of the C programming language in [GH] doesn't look much like the strcpy example anymore. Now, we understand better how to compose evolving algebras and how to prove things with evolving algebras. A typical misconception is that the operational approach is necessarily too detailed. Some people think that an approach suited for complexity analysis does not give a good high-level speci cation language. I believe in a high-level speci cation language based on evolving algebras; the successive re nement method is then one tool to prove implementation correctness. But this and various other issues (how to incorporate real time into evolving algebras for example) will have to be addressed elsewhere.