Abstract With the explosion in popularity of the Rust programming language, a wealth of tools have recently been developed to analyze, verify, and test Rust programs. Alas, the Rust ecosystem remains relatively young, meaning that every one of these tools has had to re-implement difficult, time-consuming machinery to interface with the Rust compiler and its cargo build system, to hook into the Rust compiler’s internal representation, and to expose an abstract syntax tree (AST) that is suitable for analysis rather than optimized for efficiency. We address this missing building block of the Rust ecosystem, and propose Charon, an analysis framework for Rust. Charon acts as a swiss-army knife for analyzing Rust programs, and deals with all of the tedium above, providing clients with an AST that can serve as the foundation of many analyses. We demonstrate the usefulness of Charon through a series of case studies, ranging from a Rust verification framework (Aeneas), a compiler from Rust to C (Eurydice), and a novel taint-checker for cryptographic code. To drive the point home, we also re-implement a popular existing analysis (Rudra), and show that it can be replicated by leveraging the Charon framework.

Abstract Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model various application domains, from signal-flow graphs to Petri nets and electrical circuits. In this paper, we introduce to the family its most expressive member to date: Graphical Piecewise-Linear Algebra, a new language to specify piecewise-linear subsets of vector spaces. Like the previous members of the family, it comes with a complete axiomatisation, which means it can be used to reason about the corresponding semantic domain purely equationally, forgetting the set-theoretic interpretation. We show completeness using a single axiom on top of Graphical Polyhedral Algebra, and show that this extension is the smallest that can capture a variety of relevant constructs. Finally, we showcase its use by modelling the behaviour of stateless electronic circuits of ideal elements, a domain that had remained outside the remit of previous diagrammatic languages.

Optics are a data representation for compositional data access, with lenses as a popular special case. Hedges has presented a diagrammatic calculus for lenses, but in a way that does not generalize to other classes of optic. We present a calculus that works for all optics, not just lenses; this is done by embedding optics into their presheaf category, which naturally features string diagrams. We apply our calculus to the common case of lenses, extend it to effectful lenses, and explore how the laws of optics manifest in this setting.

Profunctor optics are a neat and composable representation of bidirectional data accessors, including lenses, and their dual, prisms. The profunctor representation exploits higher-order functions and higher-kinded type constructor classes, but the relationship between this and the familiar representation in terms of "getter" and "setter" functions is not at all obvious. We derive the profunctor representation from the concrete representation, making the relationship clear. It turns out to be a fairly direct application of the Yoneda Lemma, arguably the most important result in category theory. We hope this derivation aids understanding of the profunctor representation. Conversely, it might also serve to provide some insight into the Yoneda Lemma.