Auxiliary Variables in TLA+

Auxiliary variables are often needed for verifying that an implementation is correct with respect to a higher-level specification. They augment the formal description of the implementation without changing its semantics—that is, the set of behaviors that it describes. This paper explains rules for adding history, prophecy, and stuttering variables to TLA specifications, ensuring that the augmented specification is equivalent to the original one. The rules are explained with toy examples, and they are used to verify the correctness of a simplified version of a snapshot algorithm due to Afek et al.