As trusted execution environments (TEE) have become the corner stone for secure cloud computing, it is critical that they are reliable and enforce proper isolation, of which a key ingredient is spatial isolation. Many TEEs are implemented in software such as hypervisors for flexibility, and in a memory-safe language, namely Rust to alleviate potential memory bugs. Still, even if memory bugs are absent from the TEE, it may contain semantic errors such as mis-configurations in its memory subsystem which breaks spatial isolation.

Writing certifiably correct system software is still very labor-intensive, and current programming languages are not well suited for the task. Proof assistants work best on programs written in a high-level functional style, while operating systems need low-level control over the hardware. We present DeepSEA, a language which provides support for layered specification and abstraction refinement, effect encapsulation and composition, and full equational reasoning. A single DeepSEA program is automatically compiled into a certified ``layer'' consisting of a C program (which is then compiled into assembly by CompCert), a low-level functional Coq specification, and a formal (Coq) proof that the C program satisfies the specification. Multiple layers can be composed and interleaved with manual proofs to ascribe a high-level specification to a program by stepwise refinement. We evaluate the language by using it to reimplement two existing verified programs: a SHA-256 hash function and an OS kernel page table manager. This new style of programming language design can directly support the development of correct-by-construction system software.

Concurrent abstraction layers are ubiquitous in modern computer systems because of the pervasiveness of multithreaded programming and multicore hardware. Abstraction layers are used to hide the implementation details (e.g., fine-grained synchronization) and reduce the complex dependencies among components at different levels of abstraction. Despite their obvious importance, concurrent abstraction layers have not been treated formally. This severely limits the applicability of layer-based techniques and makes it difficult to scale verification across multiple concurrent layers.

This paper presents the design of Zombie, a dependently-typed programming language that uses an adaptation of a congruence closure algorithm for proof and type inference. This algorithm allows the type checker to automatically use equality assumptions from the context when reasoning about equality. Most dependently-typed languages automatically use equalities that follow from beta-reduction during type checking; however, such reasoning is incompatible with congruence closure. In contrast, Zombie does not use automatic beta-reduction because types may contain potentially diverging terms. Therefore Zombie provides a unique opportunity to explore an alternative definition of equivalence in dependently-typed language design.

Most dependently-typed programming languages either require that all expressions terminate (e.g. Coq, Agda, and Epigram), or allow infinite loops but are inconsistent when viewed as logics (e.g. Haskell, ATS, Ωmega. Here, we combine these two approaches into a single dependently-typed core language. The language is composed of two fragments that share a common syntax and overlapping semantics: a logic that guarantees total correctness, and a call-by-value programming language that guarantees type safety but not termination. The two fragments may interact: logical expressions may be used as programs; the logic may soundly reason about potentially nonterminating programs; programs can require logical proofs as arguments; and "mobile" program values, including proofs computed at runtime, may be used as evidence by the logic. This language allows programmers to work with total and partial functions uniformly, providing a smooth path from functional programming to dependently-typed programming.

The definition of type equivalence is one of the most important design issues for any typed language. In dependently typed languages, because terms appear in types, this definition must rely on a definition of term equivalence. In that case, decidability of type checking requires decidability for the term equivalence relation.

Many programs operate reactively--patiently waiting for user input, running for a while producing output, and eventually returning to a state where they are ready to accept another input (or occasionally diverging). When a reactive program communicates with multiple parties, we would like to be sure that it can be given secret information by one without leaking it to others.