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.

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Iris from the Ground up: A modular Foundation for Higher-order Concurrent Separation Logic

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.

/pdf/rustbelt-securing-the-foundations-of-the-rust-programming-2vwikjwugy.pdf

RustBelt: securing the foundations of the Rust programming language

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.

/pdf/the-essence-of-higher-order-concurrent-separation-logic-3nq21z92if.pdf

The Essence of Higher-Order Concurrent Separation Logic

A number of tools have been developed for carrying out separation-logic proofs mechanically using an interactive proof assistant. One of the most advanced such tools is the Iris Proof Mode (IPM) for Coq, which offers a rich set of tactics for making separation-logic proofs look and feel like ordinary Coq proofs. However, IPM is tied to a particular separation logic (namely, Iris), thus limiting its applicability. In this paper, we propose MoSeL, a general and extensible Coq framework that brings the benefits of IPM to a much larger class of separation logics. Unlike IPM, MoSeL is applicable to both affine and linear separation logics (and combinations thereof), and provides generic tactics that can be easily extended to account for the bespoke connectives of the logics with which it is instantiated. To demonstrate the effectiveness of MoSeL, we have instantiated it to provide effective tactical support for interactive and semi-automated proofs in six very different separation logics.

https://hal.archives-ouvertes.fr/hal-01898522/document

MoSeL: a general, extensible modal framework for interactive proofs in separation logic

Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for reasoning about a broad range of properties, including equivalence and refinement, and specialized notions such as continuity, information flow security or relative cost. In a higher-order setting, relational program verification can be achieved using relational refinement type systems, a form of refinement types where assertions have a relational interpretation. Relational refinement type systems excel at relating structurally equivalent terms but provide limited support for relating terms with very different structures. We present a logic, called Relational Higher Order Logic (RHOL), for proving relational properties of a simply typed λ-calculus with inductive types and recursive definitions. RHOL retains the type-directed flavour of relational refinement type systems but achieves greater expressivity through rules which simultaneously reason about the two terms as well as rules which only contemplate one of the two terms. We show that RHOL has strong foundations, by proving an equivalence with higher-order logic (HOL), and leverage this equivalence to derive key meta-theoretical properties: subject reduction, admissibility of a transitivity rule and set-theoretical soundness. Moreover, we define sound embeddings for several existing relational type systems such as relational refinement types and type systems for dependency analysis and relative cost, and we verify examples that were out of reach of prior work.

https://dl.acm.org/doi/pdf/10.1145/3110265

A relational logic for higher-order programs

Recently we have seen a renewed interest in programming languages that tame the complexity of state and concurrency through refined type systems with more fine-grained control over effects. In addition to simplifying reasoning and eliminating whole classes of bugs, statically tracking effects opens the door to advanced compiler optimizations. In this paper we present a relational model of a type-and-effect system for a higher-order, concurrent program- ming language. The model precisely captures the semantic invariants expressed by the effect annotations. We demonstrate that these invariants are strong enough to prove advanced program transformations, including automatic parallelization of expressions with suitably disjoint effects. The model also supports refinement proofs between abstract data types implementations with different internal data representations, including proofs that fine-grained concurrent algorithms refine their coarse-grained counterparts. This is the first model for such an expressive language that supports both effect-based optimizations and data abstraction. The logical relation is defined in Iris, a state-of-the-art higher-order concurrent separation logic. This greatly simplifies proving well-definedness of the logical relation and also provides us with a powerful logic for reasoning in the model.

A relational model of types-and-effects in higher-order concurrent separation logic

We present a logical relations model of a higher-order functional programming language with impredicative polymorphism, recursive types, and a Haskell-style ST monad type with runST. We use our logical relations model to show that runST provides proper encapsulation of state, by showing that effectful computations encapsulated by runST are heap independent. Furthermore, we show that contextual refinements and equivalences that are expected to hold for pure computations do indeed hold in the presence of runST. This is the first time such relational results have been proven for a language with monadic encapsulation of state. We have formalized all the technical development and results in Coq.

https://dl.acm.org/doi/pdf/10.1145/3158152

A logical relation for monadic encapsulation of state: proving contextual equivalences in the presence of runST

Building network-connected programs and distributed systems is a powerful way to provide scalability and availability in a digital, always-connected era. However, with great power comes great complexity. Reasoning about distributed systems is well-known to be difficult. In this paper we present Aneris, a novel framework based on separation logic supporting modular, node-local reasoning about concurrent and distributed systems. The logic is higher-order, concurrent, with higher-order store and network sockets, and is fully mechanized in the Coq proof assistant. We use our framework to verify an implementation of a load balancer that uses multi-threading to distribute load amongst multiple servers and an implementation of the two-phase-commit protocol with a replicated logging service as a client. The two examples certify that Aneris is well-suited for both horizontal and vertical modular reasoning.

/pdf/aneris-a-mechanised-logic-for-modular-reasoning-about-4mgcv3ozam.pdf

Aneris: A Mechanised Logic for Modular Reasoning about Distributed Systems

We present a logical relations model of a higher-order functional programming language with impredicative polymorphism, recursive types, and a Haskell-style ST monad type with runST. We use our logical relations model to show that runST provides proper encapsulation of state, by showing that effectful computations encapsulated by runST are heap independent. Furthermore, we show that contextual refinements and equivalences that are expected to hold for pure computations do indeed hold in the presence of runST. This is the first time such relational results have been proven for a langauge with monadic encapsulation of state. We have formalized all the technical development and results in Coq.

Morten Krogh-Jespersen

Papers

A relational model of types-and-effects in higher-order concurrent separation logic

A logical relation for monadic encapsulation of state: proving contextual equivalences in the presence of runST

Aneris: A Mechanised Logic for Modular Reasoning about Distributed Systems

A Logical Relation for Monadic Encapsulation of State: Proving contextual equivalences in the presence of runST