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In type systems with dependency tracking, programmers can assign an ordered set of levels to computations and prevent information flow from high-level computations to the low-level ones. The key notion in such systems isindistinguishability: a definition of program equivalence that takes into account the parts of the program that an observer may depend on. In this paper, we investigate the use of dependency tracking in the context of dependently-typed languages. We present the Dependent Calculus of Indistinguishability (DCOI), a system that adopts indistinguishability as the definition of equality used by the type checker. DCOI also internalizes that relation as an observer-indexed propositional equality type, so that programmers may reason about indistinguishability within the language. Our design generalizes and extends prior systems that combine dependency tracking with dependent types and is the first to support conversion and propositional equality at arbitrary observer levels. We have proven type soundness and noninterference theorems for DCOI and have developed a prototype implementation of its type checker. 

In dependently-typed functional programming languages that allow general recursion, programs used as proofs must be evaluated to retain type soundness. As a result, programmers must make a trade-off between performance and safety. To address this problem, we propose System DE, an explicitly-typed, moded core calculus that supports termination tracking and equality reflection. Programmers can write inductive proofs about potentially diverging programs in a logical sublanguage and reflect those proofs to the type checker, while knowing that such proofs will be erased by the compiler before execution. A key feature of System DE is its use of modes for both termination and relevance tracking, which not only simplifies the design but also leaves it open for future extension. System DE is suitable for use in the Glasgow Haskell Compiler, but could serve as the basis for any general purpose dependently-typed language. 

We present a formal model of Checked C, a dialect of C that aims to enforce spatial memory safety. Our model pays particular attention to the semantics of dynamically sized, potentially null-terminated arrays. We formalize this model in Coq, and prove that any spatial memory safety errors can be blamed on portions of the program labeled unchecked; this is a Checked C feature that supports incremental porting and backward compatibility. While our model's operational semantics uses annotated (“fat”) pointers to enforce spatial safety, we show that such annotations can be safely erased. Using PLT Redex we formalize an executable version of our model and a compilation procedure to an untyped C-like language, as well as use randomized testing to validate that generated code faithfully simulates the original. Finally, we develop a custom random generator for well-typed and almost-well-typed terms in our Redex model, and use it to search for inconsistencies between our model and the Clang Checked C implementation. We find these steps to be a useful way to co-develop a language (Checked C is still in development) and a core model of it.