In many places, inserted text is highlighted in red. Preface p. xx " all of which are useful in structuring concurrent applications. " Chapter 1 p. 4 In Fig. 1.1, line 4 should say for (int j = (i * block) + 1; j <= (i + 1)* block; j++) { p. 11 p. 18 Second paragraph of Mutual Exclusion bullet: " Initially the can is either up or down. Let us say it was down. Then only the pets can go in, and mutual exclusion holds. " Replace question 6 bullet 2 with:  Suppose the method M accounts for 30% of the program's computation time. Let sn be the program's speedup on n processes, assuming the rest of the program is perfectly parallelizable. Your boss tells you to double this speedup: the revised program should have speedup s'n ≥ sn/2. You advertize for a programmer to replace M with an improved version, k times faster. What value of k should you require? Chapter 2 p. 23 Figure 2.3 should be amended as shown: public long getAndIncrement() { lock.lock(); try { long temp = value; value = temp + 1; return temp; } finally { lock.unlock(); } } p. 25 Pragma 2.3.1: " We explain the reasons in Chapter 3 and Appendix B. " p. 26 In Fig. 2.5, remove all declarations of variables as volatile. Indeed as stated in Pragma 2.3.1 on page 25, one should use memory barriers when implementing these algorithms. However, in this chapter (in all code) we avoid such issues to keep the algorithms simple. Adding volatile to these variables would require more complex coding that would distract readers from the core issues at hand.

The Art of Multiprocessor Programming

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

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.

/pdf/iris-from-the-ground-up-a-modular-foundation-for-higher-3648wnpcux.pdf

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

We present Iris, a concurrent separation logic with a simple premise: monoids and invariants are all you need. Partial commutative monoids enable us to express---and invariants enable us to enforce---user-defined *protocols* on shared state, which are at the conceptual core of most recent program logics for concurrency. Furthermore, through a novel extension of the concept of a *view shift*, Iris supports the encoding of *logically atomic specifications*, i.e., Hoare-style specs that permit the client of an operation to treat the operation essentially as if it were atomic, even if it is not.

/pdf/iris-monoids-and-invariants-as-an-orthogonal-basis-for-fpeli900g9.pdf

Iris: Monoids and Invariants as an Orthogonal Basis for Concurrent Reasoning

Geographically distributed systems often rely on replicated eventually consistent data stores to achieve availability and performance. To resolve conflicting updates at different replicas, researchers and practitioners have proposed specialized consistency protocols, called replicated data types, that implement objects such as registers, counters, sets or lists. Reasoning about replicated data types has however not been on par with comparable work on abstract data types and concurrent data types, lacking specifications, correctness proofs, and optimality results.To fill in this gap, we propose a framework for specifying replicated data types using relations over events and verifying their implementations using replication-aware simulations. We apply it to 7 existing implementations of 4 data types with nontrivial conflict-resolution strategies and optimizations (last-writer-wins register, counter, multi-value register and observed-remove set). We also present a novel technique for obtaining lower bounds on the worst-case space overhead of data type implementations and use it to prove optimality of 4 implementations. Finally, we show how to specify consistency of replicated stores with multiple objects axiomatically, in analogy to prior work on weak memory models. Overall, our work provides foundational reasoning tools to support research on replicated eventually consistent stores.

/pdf/replicated-data-types-specification-verification-optimality-59b5ugvpxc.pdf

Replicated data types: specification, verification, optimality

Concurrent data-structures, such as stacks, queues, and deques, often implicitly enforce a total order over elements in their underlying memory layout. However, much of this order is unnecessary: linearizability only requires that elements are ordered if the insert methods ran in sequence. We propose a new approach which uses timestamping to avoid unnecessary ordering. Pairs of elements can be left unordered if their associated insert operations ran concurrently, and order imposed as necessary at the eventual removal. We realise our approach in a new non-blocking data-structure, the TS (timestamped) stack. Using the same approach, we can define corresponding queue and deque data-structures. In experiments on x86, the TS stack outperforms and outscales all its competitors -- for example, it outperforms the elimination-backoff stack by factor of two. In our approach, more concurrency translates into less ordering, giving less-contended removal and thus higher performance and scalability. Despite this, the TS stack is linearizable with respect to stack semantics. The weak internal ordering in the TS stack presents a challenge when establishing linearizability: standard techniques such as linearization points work well when there exists a total internal order. We present a new stack theorem, mechanised in Isabelle, which characterises the orderings sufficient to establish stack semantics. By applying our stack theorem, we show that the TS stack is indeed linearizable. Our theorem constitutes a new, generic proof technique for concurrent stacks, and it paves the way for future weakly ordered data-structure designs.

https://dl.acm.org/doi/pdf/10.1145/2775051.2676963

A Scalable, Correct Time-Stamped Stack

Weaving a concurrency control protocol into a program is difficult and error-prone. One way to alleviate this burden is deterministic parallelism. In this well-studied approach to parallelisation, a sequential program is annotated with sections that can execute concurrently, with automatically injected control constructs used to ensure observable behaviour consistent with the original program.This paper examines the formal specification and verification of these constructs. Our high-level specification defines the conditions necessary for correct execution; these conditions reflect program dependencies necessary to ensure deterministic behaviour. We connect the high-level specification used by clients of the library with the low-level library implementation, to prove that a client's requirements for determinism are enforced. Significantly, we can reason about program and library correctness without breaking abstraction boundaries.To achieve this, we use concurrent abstract predicates, based on separation logic, to encapsulate racy behaviour in the library's implementation. To allow generic specifications of libraries that can be instantiated by client programs, we extend the logic with higher-order parameters and quantification. We show that our high-level specification abstracts the details of deterministic parallelism by verifying two different low-level implementations of the library.

/pdf/modular-reasoning-for-deterministic-parallelism-4fkr6h7081.pdf

Modular reasoning for deterministic parallelism

Synchronization constructs lie at the heart of any reliable concurrent program. Many such constructs are standard (e.g., locks, queues, stacks, and hash-tables). However, many concurrent applications require custom synchronization constructs with special-purpose behavior. These constructs present a significant challenge for verification. Like standard constructs, they rely on subtle racy behavior, but unlike standard constructs, they may not have well-understood abstract interfaces. As they are custom built, such constructs are also far more likely to be unreliable.This article examines the formal specification and verification of custom synchronization constructs. Our target is a library of channels used in automated parallelization to enforce sequential behavior between program statements. Our high-level specification captures the conditions necessary for correct execution; these conditions reflect program dependencies necessary to ensure sequential behavior. We connect the high-level specification with the low-level library implementation to prove that a client’s requirements are satisfied. Significantly, we can reason about program and library correctness without breaking abstraction boundaries.To achieve this, we use a program logic called iCAP (impredicative Concurrent Abstract Predicates) based on separation logic. iCAP supports both high-level abstraction and low-level reasoning about races. We use this to show that our high-level channel specification abstracts three different, increasingly complex low-level implementations of the library. iCAP’s support for higher-order reasoning lets us prove that sequential dependencies are respected, while iCAP’s next-generation semantic model lets us avoid ugly problems with cyclic dependencies.

/pdf/verifying-custom-synchronization-constructs-using-higher-50uyj5ds3d.pdf

Verifying Custom Synchronization Constructs Using Higher-Order Separation Logic

Bidirectional model transformations (bx) are mechanisms for auto-matically restoring consistency between multiple concurrently modified models. They are, however, challenging to implement; many model transformation languages not supporting them at all. In this paper, we propose an approach for automatically obtaining the consistency guarantees of bx without the complexities of a bx language. First, we show how to “fake” true bidirectionality using pairs of unidirectional transformations and inter-model consistency constraints in Epsilon. Then, we propose to automatically verify that these transformations are consistency preserving — thus indistinguishable from true bx — by defining translations to graph rewrite rules and nested conditions, and leveraging recent proof calculi for graph transformation verification.

Towards rigorously faking bidirectional model transformations

Modern program logics have made it feasible to verify the most complex concurrent algorithms. However, many such logics are complex, and most lack automated tool support. We propose Starling, a new lightweight logic and automated tool for concurrency verification. Starling takes a proof outline written in an abstracted Hoare-logic style, and converts it into proof terms that can be discharged by a sequential solver. Starling’s approach is generic in its structure, making it easy to target different solvers. In this paper we verify shared-variable algorithms using the Z3 SMT solver, and heap-based algorithms using the GRASShopper solver. We have applied our approach to a range of concurrent algorithms, including Rust’s atomic reference counter, the Linux ticketed lock, the CLH queue-lock, and a fine-grained list algorithm.

/pdf/starling-lightweight-concurrency-verification-with-views-4tdnj4s4xc.pdf

Starling: Lightweight Concurrency Verification with Views

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