Computer-assisted simulation proofs

Abstract

This paper presents a scalable approach to reasoning formally about distributed algorithms. It uses results about I/O automata to extract a set of proof obligations for showing that the behaviors of one algorithm are among those of another, and it uses the Larch tools for specification and deduction to discharge these obligations in a natural and easy-to-read fashionl The approach is demonstrated by proving the behavior equivalence of two high-level specifications for a communication protocol.

Owicki/Gries in Isabelle/HOL

“…TLA has been formalized in HOL [28], LP [7] and Isabelle/HOL [15]. Input/Output Automata have been formalized in Isabelle/HOL [17] and in LP [24]. However, it appears that there has been no work on embedding Hoare-logics for shared-variable parallelism in a theorem prover.…”

Verification of a distributed summation algorithm

“…The verification of this paper has not yet been proof-checked by computer, hut I expect that this will be a routine exercise, building on earlier work on mechanical checking ofl/O automata proofs [19,4,15]. Although I have carried out the verification using a simple version of the I/O automaton model, it is probably trivial to translate this story to other state based models, such as Lamport's Temporal Logic of Actions [8].…”

A theory of normed simulations

“…However, there are many examples of situations where these restricted types of simulations cannot be applied. In approaches where the full transfer condition (2) is formalized [Søgaard-Andersen et al 1993a], the user has to supply the simulating execution fragments α to the prover explicitly, which makes the verification process highly interactive. Jonsson [1990] presented a variant of the • D. Griffioen and F. Vaandrager completeness theorem of Abadi and Lamport [1991] in terms of certain forward and backward simulations in which lower-level transitions are matched by at most one higher-level transition.…”