Step-Indexed Normalization for a Language with General Recursion

The Trellys project has produced several designs for practical dependently typed languages. These languages are broken into two fragments-a_logical_fragment where every term normalizes and which is consistent when interpreted as a logic, and a_programmatic_fragment with general recursion and other convenient but unsound features. In this paper, we present a small example language in this style. Our design allows the programmer to explicitly mention and pass information between the two fragments. We show that this feature substantially complicates the metatheory and present a new technique, combining the traditional Girard-Tait method with step-indexed logical relations, which we use to show normalization for the logical fragment.Comment: In Proceedings MSFP 2012, arXiv:1202.240

Existential Types for Relaxed Noninterference

Information-flow security type systems ensure confidentiality by enforcing noninterference: a program cannot leak private data to public channels. However, in practice, programs need to selectively declassify information about private data. Several approaches have provided a notion of relaxed noninterference supporting selective and expressive declassification while retaining a formal security property. The labels-as-functions approach provides relaxed noninterference by means of declassification policies expressed as functions. The labels-as-types approach expresses declassification policies using type abstraction and faceted types, a pair of types representing the secret and public facets of values. The original proposal of labels-as-types is formulated in an object-oriented setting where type abstraction is realized by subtyping. The object-oriented approach however suffers from limitations due to its receiver-centric paradigm. In this work, we consider an alternative approach to labels-as-types, applicable in non-object-oriented languages, which allows us to express advanced declassification policies, such as extrinsic policies, based on a different form of type abstraction: existential types. An existential type exposes abstract types and operations on these; we leverage this abstraction mechanism to express secrets that can be declassified using the provided operations. We formalize the approach in a core functional calculus with existential types, define existential relaxed noninterference, and prove that well-typed programs satisfy this form of type-based relaxed noninterference

Logical relations for coherence of effect subtyping

A coercion semantics of a programming language with subtyping is typically defined on typing derivations rather than on typing judgments. To avoid semantic ambiguity, such a semantics is expected to be coherent, i.e., independent of the typing derivation for a given typing judgment. In this article we present heterogeneous, biorthogonal, step-indexed logical relations for establishing the coherence of coercion semantics of programming languages with subtyping. To illustrate the effectiveness of the proof method, we develop a proof of coherence of a type-directed, selective CPS translation from a typed call-by-value lambda calculus with delimited continuations and control-effect subtyping. The article is accompanied by a Coq formalization that relies on a novel shallow embedding of a logic for reasoning about step-indexing

Step-Indexed Logical Relations for Probability (long version)

It is well-known that constructing models of higher-order probabilistic programming languages is challenging. We show how to construct step-indexed logical relations for a probabilistic extension of a higher-order programming language with impredicative polymorphism and recursive types. We show that the resulting logical relation is sound and complete with respect to the contextual preorder and, moreover, that it is convenient for reasoning about concrete program equivalences. Finally, we extend the language with dynamically allocated first-order references and show how to extend the logical relation to this language. We show that the resulting relation remains useful for reasoning about examples involving both state and probabilistic choice.Comment: Extended version with appendix of a FoSSaCS'15 pape

Types for Information Flow Control: Labeling Granularity and Semantic Models

Language-based information flow control (IFC) tracks dependencies within a program using sensitivity labels and prohibits public outputs from depending on secret inputs. In particular, literature has proposed several type systems for tracking these dependencies. On one extreme, there are fine-grained type systems (like Flow Caml) that label all values individually and track dependence at the level of individual values. On the other extreme are coarse-grained type systems (like HLIO) that track dependence coarsely, by associating a single label with an entire computation context and not labeling all values individually. In this paper, we show that, despite their glaring differences, both these styles are, in fact, equally expressive. To do this, we show a semantics- and type-preserving translation from a coarse-grained type system to a fine-grained one and vice-versa. The forward translation isn't surprising, but the backward translation is: It requires a construct to arbitrarily limit the scope of a context label in the coarse-grained type system (e.g., HLIO's "toLabeled" construct). As a separate contribution, we show how to extend work on logical relation models of IFC types to higher-order state. We build such logical relations for both the fine-grained type system and the coarse-grained type system. We use these relations to prove the two type systems and our translations between them sound.Comment: 31st IEEE Symposium on Computer Security Foundations (CSF 2018

Type Abstraction for Relaxed Noninterference

Information-flow security typing statically prevents confidential information to leak to public channels. The fundamental information flow property, known as noninterference, states that a public observer cannot learn anything from private data. As attractive as it is from a theoretical viewpoint, noninterference is impractical: real systems need to intentionally declassify some information, selectively. Among the different information flow approaches to declassification, a particularly expressive approach was proposed by Li and Zdancewic, enforcing a notion of relaxed noninterference by allowing programmers to specify declassification policies that capture the intended manner in which public information can be computed from private data. This paper shows how we can exploit the familiar notion of type abstraction to support expressive declassification policies in a simpler, yet more expressive manner. In particular, the type-based approach to declassification---which we develop in an object-oriented setting---addresses several issues and challenges with respect to prior work, including a simple notion of label ordering based on subtyping, support for recursive declassification policies, and a local, modular reasoning principle for relaxed noninterference. This work paves the way for integrating declassification policies in practical security-typed languages

Dependent Object Types

We propose a new type-theoretic foundation of Scala and languages like it: the Dependent Object Types (DOT) calculus. DOT models Scala’s path-dependent types, abstract type members and its mixture of nominal and structural typing through the use of refinement types. The core formalism makes no attempt to model inheritance and mixin composition. DOT normalizes Scala’s type system by unifying the constructs for type members and by providing classical intersection and union types which simplify greatest lower bound and least upper bound computations. In this paper, we present the DOT calculus, both formally and informally. We also discuss our work-in-progress to prove typesafety of the calculus

Step-Indexed Syntactic Logical Relations for Recursive and Quantified Types

We present a sound and complete proof technique, based on syntactic logical relations, for showing contextual equivalence of expressions in a #-calculus with recursive types and impredicative universal and existential types. Our development builds on the step-indexed PER model of recursive types presented by Appel and McAllester. We have discovered that a direct proof of transitivity of that model does not go through, leaving the "PER" status of the model in question. We show how to extend the Appel-McAllester model to obtain a logical relation that we can prove is transitive, as well as sound and complete with respect to contextual equivalence. We then augment this model to support relational reasoning in the presence of quantified types