Related papers: ViCAR: Visualizing Categories with Automated Rewri…
In deductive verification and software model checking, dealing with certain specification language constructs can be problematic when the back-end solver is not sufficiently powerful or lacks the required theories. One way to deal with this…
We develop further the theory of monoidal bicategories by introducing and studying bicategorical counterparts of the notions of a linear exponential comonad, as considered in the study of linear logic, and of a codereliction transformation,…
Context: Container orchestration tools supporting infrastructure-as-code allow new forms of collaboration between developers and operatives. Still, their text-based nature permits naive mistakes and is more difficult to read as complexity…
In a previous work, we proved that almost all of the Calculus of Inductive Constructions (CIC), which is the basis of the proof assistant Coq, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of…
In a previous work, we proved that an important part of the Calculus of Inductive Constructions (CIC), the basis of the Coq proof assistant, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of…
This is a draft of the textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later…
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
interpreters are tools to compute approximations for behaviors of a program. These approximations can then be used for optimisation or for error detection. In this paper, we show how to describe an abstract interpreter using the type-theory…
Image classification, which classifies images by pre-defined categories, has been the dominant approach to visual representation learning over the last decade. Visual learning through image-text alignment, however, has emerged to show…
In this paper, we study the category $C(Rep(\mathcal{Q}, \mathcal{A}))$ of complexes of representations of quiver $\mathcal{Q}$ with values in an abelian category $\mathcal{A}$. We develop a method for constructing some model structures on…
The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…
Equality saturation, a technique for program optimisation and reasoning, has gained attention due to the resurgence of equality graphs (e-graphs). E-graphs represent equivalence classes of terms under rewrite rules, enabling simultaneous…
Software visualization seeks to represent software artifacts graphical-ly in two or three dimensions, with the goal of enhancing comprehension, anal-ysis, maintenance, and evolution of the source code. In this context, visualiza-tions…
In this work, we explore a double categorical framework for categories of enriched graphs, categories and the newly introduced notion of cocategories. A fundamental goal is to establish an enrichment of V-categories in V-cocategories, which…
Computational content encoded into constructive type theory proofs can be used to make computing experiments over concrete data structures. In this paper, we explore this possibility when working in Coq with chain complexes of infinite type…
While interest in models that generalize at test time to new compositions has risen in recent years, benchmarks in the visually-grounded domain have thus far been restricted to synthetic images. In this work, we propose COVR, a new test-bed…
We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…
Visualizations play a critical role in validating and improving statistical models. However, the design space of model check visualizations is not well understood, making it difficult for authors to explore and specify effective graphical…
We define a traced pseudomonoid as a pseudomonoid in a monoidal bicategory equipped with extra structure, giving a new characterisation of Cauchy complete traced monoidal categories as algebraic structures in $\mathbf{Prof}$, the monoidal…