The most prominent formal criterion for secure compilation is full
abstraction, the preservation and reflection of contextual equivalence. Recent
work introduced robust compilation, defined as the preservation of robust
satisfaction of hyperproperties, i.e., their satisfaction against arbitrary
attackers. In this paper, we initially set out to compare these two approaches
to secure compilation. To that end, we provide an exact description of the
hyperproperties that are robustly satisfied by programs compiled with a fully
abstract compiler, and show that they can be meaningless or trivial. We then
propose a novel criterion for secure compilation formulated in the framework of
Mathematical Operational Semantics (MOS), guaranteeing both full abstraction
and the preservation of robust satisfaction of hyperproperties in a more
sensible manner.

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