88 research outputs found
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
Relational Parametricity for Computational Effects
According to Strachey, a polymorphic program is parametric if it applies a
uniform algorithm independently of the type instantiations at which it is
applied. The notion of relational parametricity, introduced by Reynolds, is one
possible mathematical formulation of this idea. Relational parametricity
provides a powerful tool for establishing data abstraction properties, proving
equivalences of datatypes, and establishing equalities of programs. Such
properties have been well studied in a pure functional setting. Many programs,
however, exhibit computational effects, and are not accounted for by the
standard theory of relational parametricity. In this paper, we develop a
foundational framework for extending the notion of relational parametricity to
programming languages with effects.Comment: 31 pages, appears in Logical Methods in Computer Scienc
Relational Parametricity and Control
We study the equational theory of Parigot's second-order
λμ-calculus in connection with a call-by-name continuation-passing
style (CPS) translation into a fragment of the second-order λ-calculus.
It is observed that the relational parametricity on the target calculus induces
a natural notion of equivalence on the λμ-terms. On the other hand,
the unconstrained relational parametricity on the λμ-calculus turns
out to be inconsistent with this CPS semantics. Following these facts, we
propose to formulate the relational parametricity on the λμ-calculus
in a constrained way, which might be called ``focal parametricity''.Comment: 22 pages, for Logical Methods in Computer Scienc
Bibliography on Realizability
AbstractThis document is a bibliography on realizability and related matters. It has been collected by Lars Birkedal based on submissions from the participants in âA Workshop on Realizability Semantics and Its Applicationsâ, Trento, Italy, June 30âJuly 1, 1999. It is available in BibTEX format at the following URL: http://www.cs.cmu.edu./~birkedal/realizability-bib.html
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