A Computational Interpretation of Parametricity

Bernardy, Jean-Philippe; Moulin, Guilhem

doi:10.1109/lics.2012.25

Cited by 18 publications

(12 citation statements)

References 28 publications

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“…These include a type theory with a computational interpretation of parametricity [4], and new cubical type theories [1,7,11,25] inspired by the cubical sets model of homotopy type theory [5]. We have begun to translate the examples discussed here to cubical type theory, to compare these new type theories against working axiomatically.…”

Section: Related and Future Workmentioning

confidence: 99%

A Cubical Approach to Synthetic Homotopy Theory

Licata¹,

Brunerie²

2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

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Abstract-Homotopy theory can be developed synthetically in homotopy type theory, using types to describe spaces, the identity type to describe paths in a space, and iterated identity types to describe higher-dimensional paths. While some aspects of homotopy theory have been developed synthetically and formalized in proof assistants, some seemingly easy examples have proved difficult because the required manipulations of paths becomes complicated. In this paper, we describe a cubical approach to developing homotopy theory within type theory. The identity type is complemented with higher-dimensional cube types, such as a type of squares, dependent on four points and four lines, and a type of three-dimensional cubes, dependent on the boundary of a cube. Path-over-a-path types and higher generalizations are used to describe cubes in a fibration over a cube in the base. These higher-dimensional cube and path-over types can be defined from the usual identity type, but isolating them as independent conceptual abstractions has allowed for the formalization of some previously difficult examples.

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Section: Related and Future Workmentioning

confidence: 99%

A Cubical Approach to Synthetic Homotopy Theory

Licata¹,

Brunerie²

2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

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“…Since we do not model absence of side-channels in RHTT, we also cannot prove this inability within RHTT. We are currently working on supporting this kind of reasoning, by extending RHTT with internalized reasoning about parametricity, as in the work of and Bernardy and Moulin [2012] (see also Section 8).…”

Section: Local Contextsmentioning

confidence: 99%

“…The closest related proofs in the imperative world of which we are aware, are the recent ones for ML with references [Ahmed et al 2009] and for separation logic [Birkedal and Yang 2008;Thamsborg et al 2012]. The parametricity property can even be internalized into a pure type system [Bernardy and Moulin 2012], enabling a form of reasoning similar to the logic of Plotkin and Abadi [1993]. We intend to investigate in the future if and how this proof can be extended to mutable state and our STsec types.…”

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confidence: 99%

Dependent Type Theory for Verification of Information Flow and Access Control Policies

Nanevski

Banerjee

Garg

2013

ACM Trans. Program. Lang. Syst.

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We present Relational Hoare Type Theory (RHTT), a novel language and verification system capable of expressing and verifying rich information flow and access control policies via dependent types. We show that a number of security policies which have been formalized separately in the literature can all be expressed in RHTT using only standard type-theoretic constructions such as monads, higher-order functions, abstract types, abstract predicates, and modules. Example security policies include conditional declassification, information erasure, and state-dependent information flow and access control. RHTT can reason about such policies in the presence of dynamic memory allocation, deallocation, pointer aliasing and arithmetic.

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“…We also plan to study the interplay between UR and parametricity, and consider how internalized reasoning about type abstraction [6] may be used to formally prove that a module interface tightly encapsulates the internal state of the module.…”

Section: Discussion and Future Workmentioning

confidence: 99%

“…Thus, B must prove that it only uses data structures which are well-encapsulated by type abstraction. While recently there has been a flurry of work on developing logics for parametricity [5,6], the goals of which include reasoning about encapsulation via type abstraction, we are unaware of a system in which parametricity has been reconciled with information flow (i.e., absence of leaks) and mutable state.…”

Section: Introductionmentioning

confidence: 99%

Dependent types for enforcement of information flow and erasure policies in heterogeneous data structures

Stewart

Banerjee

Nanevski

2013

Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming

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We consider verification of information flow and erasure properties in programs with heterogeneous heap-based data structures, in the presence of procedures with local state. A heterogeneous data structure, such as a hash table implementing a medical record database, may store both secret and public data simultaneously. In contrast, extant work primarily focuses on homogeneous data structures which store data of a uniform security level. Heterogeneity, however, does not come for free. For example, standard implementations of hash tables do not support heterogeneity, and may leak sensitive information easily owing to hash collisions. In this paper we identify unique representation as a sufficient condition for a heterogeneous data structure to be leak-free, while simultaneously supporting abstraction and modularity in verification. As a case study, we implement and verify a novel uniquely-represented variant of heterogeneous hash tables. Furthermore, we demonstrate modular reasoning by showing how specifications of the hash table methods can be used in a client application; we thereby obtain abstract and concise formal proofs of erasure. We formalize our work in Relational Hoare Type Theory (RHTT), an expressive, higherorder imperative language and program logic embedded in the Coq proof assistant.

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A Computational Interpretation of Parametricity

Cited by 18 publications

References 28 publications

A Cubical Approach to Synthetic Homotopy Theory

A Cubical Approach to Synthetic Homotopy Theory

Dependent Type Theory for Verification of Information Flow and Access Control Policies

Dependent types for enforcement of information flow and erasure policies in heterogeneous data structures

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