305 research outputs found
What should a generic object be?
Jacobs has proposed definitions for (weak, strong, split) generic objects for
a fibered category; building on his definition of generic object and split
generic object, Jacobs develops a menagerie of important fibrational structures
with applications to categorical logic and computer science, including higher
order fibrations, polymorphic fibrations, -fibrations, triposes, and
others. We observe that a split generic object need not in particular be a
generic object under the given definitions, and that the definitions of
polymorphic fibrations, triposes, etc. are strict enough to rule out many
fundamental examples: for instance, the fibered preorder induced by a partial
combinatory algebra in realizability is not a tripos in the sense of Jacobs. We
argue for a new alignment of terminology that emphasizes the forms of generic
object that appear most commonly in nature, i.e. in the study of internal
categories, triposes, and the denotational semantics of polymorphic types. In
addition, we propose a new class of acyclic generic objects inspired by recent
developments in the semantics of homotopy type theory, generalizing the
realignment property of universes to the setting of an arbitrary fibration
Sheaf semantics of termination-insensitive noninterference
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.Comment: Extended version of FSCD '22 paper with full technical appendice
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