  Auditing is an increasingly important operation for computer programming, for
example in security (e.g. to enable history-based access control) and to enable
reproducibility and accountability (e.g. provenance in scientific programming).
Most proposed auditing techniques are ad hoc or treat auditing as a
second-class, extralinguistic operation; logical or semantic foundations for
auditing are not yet well-established. Justification Logic (JL) offers one such
foundation; Bavera and Bonelli introduced a computational interpretation of JL
called $\lambda^h$ that supports auditing. However, $\lambda^h$ is technically
complex and strong normalization was only established for special cases. In
addition, we show that the equational theory of $\lambda^h$ is inconsistent. We
introduce a new calculus $\lambda^{hc}$ that is simpler than $\lambda^h$,
consistent, and strongly normalizing. Our proof of strong normalization is
formalized in Nominal Isabelle.
