Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm

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.Comment: See also the ASM web site at http://www.eecs.umich.edu/gasm

Verification of a Prolog compiler - first steps with KIV

This paper describes the first steps of the formal verification of a Prolog compiler with the KIV system. We build upon the mathematical definitions given by Boerger and Rosenzweig in [BR95]. There an operational semantics of Prolog is defined using the formalism of Evolving Algebras, and then transformed in several systematic steps to the Warren Abstract Machine (WAM). To verify these transformation steps formally in KIV, a translation of deterministic Evolving Algebras to Dynamic Logic is defined, which may also be of general interest. With this translation, correctness of transformation steps becomes a problem of program equivalence in Dynamic Logic. We define a proof technique for verifying such problems, which corresponds to the use of proof maps in Evolving Algebras. Although the transfor- mation steps are small enough for a mathematical analysis, this is not sufficient for a successful formal correctness proof. Such a proof requires to explicitly state a lot of facts, which were only impli- citly assumed in the analysis. We will argue that these assumptions cannot be guessed in a first proof attempt, but have to be filled in incrementally. We report on our experience with this `evolutionary\u27 verification process for the first transformation step, and the support KIV offers to do such incremental correctness proofs

ASMs and Operational Algorithmic Completeness of Lambda Calculus

We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family of computable functions (taken as primitive tools, i.e., kind of oracle functions for the algorithm), for every constant K big enough, each computation step of the algorithm can be simulated by exactly K successive reductions in a natural extension of lambda calculus with constants for functions in the above considered family. The proof is based on a fixed point technique in lambda calculus and on Gurevich sequential Thesis which allows to identify sequential deterministic algorithms with Abstract State Machines. This extends to algorithms for partial computable functions in such a way that finite computations ending with exceptions are associated to finite reductions leading to terms with a particular very simple feature.Comment: 37 page