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### Abstract

We mechanise the logic TLA*
[Merz 1999],
an extension of Lamport's Temporal Logic of Actions (TLA)
[Lamport 1994]
for specifying and reasoning
about concurrent and reactive systems. Aiming at a framework for mechanising] the verification of TLA (or TLA*) specifications, this contribution reuses
some elements from a previous axiomatic encoding of TLA in Isabelle/HOL
by the second author [Merz 1998], which has been part of the Isabelle
distribution. In contrast to that previous work, we give here a shallow,
definitional embedding, with the following highlights:

- a theory of infinite sequences, including a formalisation of the concepts of stuttering invariance central to TLA and TLA*;
- a definition of the semantics of TLA*, which extends TLA by a mutually-recursive definition of formulas and pre-formulas, generalising TLA action formulas;
- a substantial set of derived proof rules, including the TLA* axioms and Lamport's proof rules for system verification;
- a set of examples illustrating the usage of Isabelle/TLA* for reasoning about systems.