Related papers: Breaking a monad-comonad symmetry between computat…
Delta lenses are a kind of morphism between categories which are used to model bidirectional transformations between systems. Classical state-based lenses, also known as very well-behaved lenses, are both algebras for a monad and coalgebras…
Industrial visual inspection aims at detecting surface defects in products during the manufacturing process. Although existing anomaly detection models have shown great performance on many public benchmarks, their limited adjustability and…
The design of scientific experiments deserves its own variation of formal verification to catch cases where scientists made important mistakes, such as forgetting to take confounding variables into account. One of the most fundamental…
With a view on applications in computing, in particular concurrency theory and higher-dimensional rewriting, we develop notions of $n$-fold monoid and comonoid objects in $n$-fold monoidal categories and bicategories. We present a series of…
Anomaly detection usually assumes that abnormality is an intrinsic property of an observation. A defect is a defect, and a rare object is rare, regardless of where it appears. Many real-world anomalies do not work this way. A runner on a…
We present a framework for compositional program verification based on polynomial functors in dependent type theory. In this framework, polynomial functors serve as program interfaces, Kleisli morphisms for the free monad monad serve as…
We establish a duality between monads and monadic morphisms in any $(\infty,2)$-category and characterize monadic morphisms in a wide class of examples. This duality unifies several dualities between algebraic structures and their…
Unsupervised Time series anomaly detection plays a crucial role in applications across industries. However, existing methods face significant challenges due to data distributional shifts across different domains, which are exacerbated by…
In type-and-coeffect systems, contexts are enriched by coeffects modeling how they are actually used, typically through annotations on single variables. Coeffects are computed bottom-up, combining, for each term, the coeffects of its…
The stochastic interpretation of Parikh's game logic should not follow the usual pattern of Kripke models, which in turn are based on the Kleisli morphisms for the Giry monad, rather, a specific and more general approach to probabilistic…
Time series anomaly detection plays a crucial role in a wide range of real-world applications. Given that time series data can exhibit different patterns at different sampling granularities, multi-scale modeling has proven beneficial for…
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…
Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…
In previous work, Abramsky, Dawar and Wang (LiCS 2017) and Abramsky and Shah (CSL 2018) have shown how a range of model comparison games which play a central role in finite model theory, including Ehrenfeucht-Fraisse, pebbling, and…
We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…
We study a family of distributors-induced bicategorical models of lambda-calculus, proving that they can be syntactically presented via intersection type systems. We first introduce a class of 2-monads whose algebras are monoidal categories…
A well-known challenge in the semantics of programming languages is how to combine non-determinism and probability. At a technical level, the problem arises from the fact that there is a no distributive law between the powerset monad and…
An $n$-sesquicategory is an $n$-globular set with strictly associative and unital composition and whiskering operations, which are however not required to satisfy the Godement interchange laws which hold in $n$-categories. In…
Output controllability and functional observability are properties that enable, respectively, the control and estimation of part of the state vector. These notions are of utmost importance in applications to high-dimensional systems, such…