A Definitional Encoding of TLA* in Isabelle/HOL

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.

Note that this work is unrelated to the ongoing development of a proof system for the specification language TLA+, which includes an encoding of TLA+ as a new Isabelle object logic [Chaudhuri et al 2010].