The work of Fuzz has pioneered the use of functional programming languages where types allow reasoning about the sensitivity of programs. Fuzz and subsequent work (e.g., DFuzz and Duet) use advanced technical devices like linear types, modal types, and partial evaluation. These features usually require the design of a new programming language from scratch—a significant task on its own! While these features are part of the classical toolbox of programming languages, they are often unfamiliar to non-experts in this field. Fortunately, recent studies (e.g., Solo ) have shown that linear and complex types in general, are not strictly needed for the task of determining programs’ sensitivity since this can be achieved by annotating base types with static sensitivity information. In this work, we take a different approach. We propose to enrich base types with information about the metric relation between values, and we present the novel idea of applying parametricity to derive direct proofs for the sensitivity of functions. A direct consequence of our result is that calculating and proving the sensitivity of functions is reduced to simply type-checking in a programming language with support for polymorphism and type-level naturals. We formalize our main result in a calculus, prove its soundness, and implement a software library in the programming language Haskell-where we reason about the sensitivity of canonical examples. We show that the simplicity of our approach allows us to exploit the type inference of the host language to support a limited form of sensitivity inference. Furthermore, we extend the language with a privacy monad to showcase how our library can be used in practical scenarios such as the implementation of differentially private programs, where the privacy guarantees depend on the sensitivity of user-defined functions. Our library, called Spar , is implemented in less than 500 lines of code.

Fitch-style modal lambda calculi enable programming with necessity modalities in a typed lambda calculus by extending the typing context with a delimiting operator that is denoted by a lock. The addition of locks simplifies the formulation of typing rules for calculi that incorporate different modal axioms, but each variant demands different, tedious and seemingly ad hoc syntactic lemmas to prove normalization. In this work, we take a semantic approach to normalization, called normalization by evaluation (NbE), by leveraging the possible-world semantics of Fitch-style calculi to yield a more modular approach to normalization. We show that NbE models can be constructed for calculi that incorporate the K, T and 4 axioms of modal logic, as suitable instantiations of the possible-world semantics. In addition to existing results that handle 𝛽-equivalence, our normalization result also considers 𝜂-equivalence for these calculi. Our key results have been mechanized in the proof assistant Agda. Finally, we showcase several consequences of normalization for proving meta-theoretic properties of Fitch-style calculi as well as programming-language applications based on different interpretations of the necessity modality.

Language-based information-flow control (IFC) techniques often rely on special purpose, ad-hoc primitives to address different covert channels that originate in the runtime system, beyond the scope of language constructs. Since these piecemeal solutions may not compose securely, there is a need for a unified mechanism to control covert channels. As a first step towards this goal, we argue for the design of a general interface that allows programs to safely interact with the runtime system and the available computing resources. To coordinate the communication between programs and the runtime system, we propose the use of asynchronous exceptions (interrupts), which, to the best of our knowledge, have not been considered before in the context of IFC languages. Since asynchronous exceptions can be raised at any point during execution-often due to the occurrence of an external event-threads must temporarily mask them out when manipulating locks and shared data structures to avoid deadlocks and, therefore, breaking program invariants. Crucially, the naive combination of asynchronous exceptions with existing features of IFC languages (e.g., concurrency and synchronization variables) may open up new possibilities of information leakage. In this paper, we present MACasync, a concurrent, statically enforced IFC language that, as a novelty, features asynchronous exceptions. We show how asynchronous exceptions easily enable (out of the box) useful programming patterns like speculative execution and some degree of resource management. We prove that programs in MACasync satisfy progress-sensitive non-interference and mechanize our formal claims in the Agda proof assistant.