  Guarded Kleene Algebra with Tests (GKAT) is a fragment of Kleene Algebra with
Tests (KAT) that was recently introduced to reason efficiently about imperative
programs. In contrast to KAT, GKAT does not have an algebraic axiomatization,
but relies on an analogue of Salomaa's axiomatization of Kleene Algebra. In
this paper, we present an algebraic axiomatization and prove two completeness
results for a large fragment of GKAT consisting of skip-free programs.
