  We propose a new sheaf semantics for secure information flow over a space of
abstract behaviors, based on synthetic domain theory: security classes are
open/closed partitions, types are sheaves, and redaction of sensitive
information corresponds to restricting a sheaf to a closed subspace. Our
security-aware computational model satisfies termination-insensitive
noninterference automatically, and therefore constitutes an intrinsic
alternative to state of the art extrinsic/relational models of noninterference.
Our semantics is the latest application of Sterling and Harper's recent
re-interpretation of phase distinctions and noninterference in programming
languages in terms of Artin gluing and topos-theoretic open/closed modalities.
Prior applications include parametricity for ML modules, the proof of
normalization for cubical type theory by Sterling and Angiuli, and the
cost-aware logical framework of Niu et al. In this paper we employ the phase
distinction perspective twice: first to reconstruct the syntax and semantics of
secure information flow as a lattice of phase distinctions between "higher" and
"lower" security, and second to verify the computational adequacy of our sheaf
semantics vis-\`a-vis an extension of Abadi et al.'s dependency core calculus
with a construct for declassifying termination channels.
