Iris is a framework for higher-order concurrent separation logic, which has been implemented in the Coq proof assistant and deployed very effectively in a wide variety of verification projects. Iris was designed with the express goal of simplifying and consolidating the foundations of modern separation logics, but it has evolved over time, and the design and semantic foundations of Iris itself have yet to be fully written down and explained together properly in one place. Here, we attempt to fill this gap, presenting a reasonably complete picture of the latest version of Iris (version 3.1), from first principles and in one coherent narrative.

Rust is a new systems programming language that promises to overcome the seemingly fundamental tradeoff between high-level safety guarantees and low-level control over resource management. Unfortunately, none of Rust's safety claims have been formally proven, and there is good reason to question whether they actually hold. Specifically, Rust employs a strong, ownership-based type system, but then extends the expressive power of this core type system through libraries that internally use unsafe features. In this paper, we give the first formal (and machine-checked) safety proof for a language representing a realistic subset of Rust. Our proof is extensible in the sense that, for each new Rust library that uses unsafe features, we can say what verification condition it must satisfy in order for it to be deemed a safe extension to the language. We have carried out this verification for some of the most important libraries that are used throughout the Rust ecosystem.

Abstract. Concurrent separation logics (CSLs) have come of age, and with age they have accumulated a great deal of complexity. Previous work on the Iris logic attempted to reduce the complex logical mechanisms of modern CSLs to two orthogonal concepts: partial commutative monoids (PCMs) and invariants. However, the realization of these concepts in Iris still bakes in several complex mechanisms-such as weakest preconditions and mask-changing view shifts-as primitive notions.In this paper, we take the Iris story to its (so to speak) logical conclusion, applying the reductionist methodology of Iris to Iris itself. Specifically, we define a small, resourceful base logic, which distills the essence of Iris: it comprises only the assertion layer of vanilla separation logic, plus a handful of simple modalities. We then show how the much fancier logical mechanisms of Iris-in particular, its entire program specification layer-can be understood as merely derived forms in our base logic. This approach helps to explain the meaning of Iris's program specifications at a much higher level of abstraction than was previously possible. We also show that the step-indexed "later" modality of Iris is an essential source of complexity, in that removing it leads to a logical inconsistency. All our results are fully formalized in the Coq proof assistant. IntroductionIn his paper The Next 700 Separation Logics, Parkinson [26] observed that "separation logic has brought great advances in the world of verification. However, there is a disturbing trend for each new library or concurrency primitive to require a new separation logic." He argued that what is needed is a general logic for concurrent reasoning, into which a variety of useful specifications can be encoded via the abstraction facilities of the logic. "By finding the right core logic," he wrote, "we can concentrate on the difficult problems."The logic he suggested as a potential candidate for such a core concurrency logic was deny-guarantee [12]. Deny-guarantee was indeed groundbreaking in its support for "fictional separation"-the idea that even if threads are concurrently manipulating the same shared piece of physical state, one can view them as operating on logically disjoint pieces of it and use separation logic to reason modularly about those pieces. It was, however, far from the last word on the subject. Rather, 2 Krebbers, Jung, Bizjak, Jourdan, Dreyer, Birkedal it spawned a new breed of logics with ever more powerful fictional-separation mechanisms for reasoning modularly about interference [11,16,29,9,30,27]. Several of these also incorporated support for impredicative invariants [28,18,17,4], which are needed if one aims to verify code in languages with semantically cyclic features (such as ML or Rust, which support higher-order state).Although exciting, the progress in this area has come at a cost: as these new separation logics become ever more expressive, each one accumulates increasingly baroque and bespoke proof rules, which are primitive in the sense that their sou...

Conventionally, phase I dose-finding trials aim to determine the maximum tolerated dose of a new drug under the assumption that both toxicity and efficacy monotonically increase with the dose. This paradigm, however, is not suitable for some molecularly targeted agents, such as monoclonal antibodies, for which efficacy often increases initially with the dose and then plateaus. For molecularly targeted agents, the goal is to find the optimal dose, defined as the lowest safe dose that achieves the highest efficacy. We develop a Bayesian phase I/II dose-finding design to find the optimal dose. We employ a logistic model with a plateau parameter to capture the increasing-then-plateau feature of the dose-efficacy relationship. We take the weighted likelihood approach to accommodate for the case where efficacy is possibly late-onset. Based on observed data, we continuously update the posterior estimates of toxicity and efficacy probabilities and adaptively assign patients to the optimal dose. The simulation studies show that the proposed design has good operating characteristics. This method is going to be applied in more than two phase I clinical trials as no other method is available for this specific setting. We also provide an R package dfmta that can be downloaded from CRAN website.