Graphical languages are a convenient shorthand to represent computation, with rewrite rules relating one graph to another. In contrast, proof assistants rely heavily on inductive datatypes, particularly when giving semantics to embedded languages. This creates obstacles to formally reasoning about graphical languages, since imposing an inductive structure obfuscates the diagrammatic nature of graphical languages, along with their corresponding equational theories. To address this gap, we present Vy ZX, a verified library for reasoning about inductively defined graphical languages. These inductive constructs arise naturally from category-theoretic definitions. We developed Vy ZX to V erify the ZX -calculus, a graphical language for reasoning about quantum computation. The ZX-calculus comes with a collection of diagrammatic rewrite rules that preserve the graph’s semantic interpretation. We show how inductive graphs in Vy ZX are used to prove the soundness of the ZX-calculus rewrite rules and apply them in practice using standard proof assistant techniques. We also provide an IDE-integrated visualizer for proof engineers to directly reason about diagrams in graphical form.

We propose a novel framework that provides constructive feedback to an LLM in the “guess-and-check” paradigm by formally verifying its own thinking process and detecting local reasoning errors. We apply this framework to the loop invariant synthesis problem. We prompt the model to produce a step-by-step natural language proof justifying its thinking process for the failed verification condition of its generated loop invariants. Then, we use an LLM to translate the reasoning steps into first-order logic implications, which can be checked automatically. An invalid implication pinpoints the exact logical flaw in the LLM’s thinking process, which we then use to construct targeted feedback for refinement. We have implemented our approach in a tool called LORIS and evaluated it on a main benchmark suite of 460 C programs and an additional benchmark suite of 50 C programs each of which involves non-linear properties. On the main benchmark suite, LORIS solved 445 of the programs, and achieved an overall success rate of 93.1%. LORIS also demonstrates robustness on the challenging non-linear benchmark suite.

Very relaxed concurrency memory models, like those of the Arm-A, RISC-V and IBM Power hardware architectures, underpin much of computing but break a fundamental intuition about programs, namely that syntactic program order and the reads-from relation always both induce order in the execution. Instead, out-of-order execution is allowed except where prevented by certain pairwise dependencies, barriers, or other synchronisation. This means that there is no notion of the ‘current’ state of the program, making it challenging to design (and prove sound) syntax-directed, modular reasoning methods like Hoare logics, as usable resources cannot implicitly flow from one program point to the next. We present AxSL, a family of separation logics for relaxed hardware memory models, and instantiate it on sequential consistency and on the Arm-A memory model. The Arm-A instance captures the fine-grained reasoning underpinning the low-overhead synchronisation idioms used by high-performance systems code. We mechanise AxSL in the Iris separation logic framework, illustrate it on key examples, and prove it sound with respect to the axiomatic memory model of Arm-A. By instantiating AxSL on different memory models, we demonstrate the generality of our approach, and show that it is largely generic in the axiomatic model and in the instruction-set semantics, offering a potential way forward for compositional reasoning for other models, and for the combination of production concurrency models and full-scale ISAs.

In this paper, we focus on Tiny Sol , a minimal calculus for Solidity smart contracts, introduced by Bartoletti, Galletta and Murgia. We start by rephrasing its syntax (to emphasise its object-oriented flavour) and give a new big-step operational semantics for that language. We then use it to define two security properties, namely call integrity and noninterference. These two properties have some similarities in their definition, in that they both require that some part of a program is not influenced by the other part. However, we show that the two properties are actually incomparable. Nevertheless, we provide a type system that statically ensures both noninterference and call integrity; hence, well-typed programs satisfy both properties. We finally discuss the practical usability of the type system and its limitations by means of some simple examples.

Apart from forming the backbone of compiler optimization, static dataflow analysis has been widely applied in a vast variety of applications, such as bug detection, privacy analysis, program comprehension, etc. Despite its importance, performing interprocedural dataflow analysis on large-scale programs is well known to be challenging. In this paper, we propose a novel distributed analysis framework supporting the general interprocedural dataflow analysis. Inspired by large-scale graph processing, we devise dedicated distributed worklist algorithms for both whole-program analysis and incremental analysis. We implement these algorithms and develop a distributed framework called BigDataflow running on a large-scale cluster. The experimental results validate the promising performance of BigDataflow – BigDataflow can finish analyzing the program of millions lines of code in minutes. Compared with the state-of-the-art, BigDataflow achieves much more analysis efficiency.

The component-by-component migration of a program from untyped to typed can trigger unintended performance degradations. When such a degradation occurs, typing well-chosen components can lessen the cost of type enforcement, while typing poorly-chosen components can exacerbate it. This paper examines whether off-the-shelf profiling tools deliver information that is an effective guide for navigating these migration choices in Typed Racket. Using the rational-programmer method, the paper tests this hypothesis with an experiment that involves tens of thousands of performance-debugging scenarios, two different profiler types, and twenty-three strategies that convert profiler output to migration choices. The most effective strategy relies on a boundary profiler to identify the costliest inter-component boundary, then adds deeply-enforced types to both sides. When the output of this profiler fails to identify a boundary, the strategy takes a random migration step—similar to the way many computational approaches resort temporarily to random choices to avoid getting stuck. The strategy completely eliminates the cost of run-time type checks in more than half of the scenarios if at most two performance degradations are tolerable along the way.

We extend intersection types to a computational \(\lambda\) -calculus with algebraic operations à la Plotkin and Power. We achieve this by considering monadic intersections—whereby computational effects appear not only in the operational semantics, but also in the type system . Since in the effectful setting termination is not anymore the only property of interest, we want to analyze the interactive behavior of typed programs with the environment. Indeed, our type system is able to characterize the natural notion of observation, both in the finite and in the infinitary setting. In a second phase, we extend our system with subtyping to incorporate a richer class of effects via monads on preorders instead of sets allowing us to model in particular non-determinism. The main technical tool is a novel combination of syntactic techniques with abstract relational reasoning, which allows us to lift all the required notions, e.g. of typability and logical relation, to the monadic setting.