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Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
We demonstrate how category theory provides specifications that can efficiently be implemented via imperative algorithms and apply this to the field of graph rewriting. By examples, we show how this paradigm of software development makes it…
In this work, we introduce and study what we believe is an intriguing and, to the best of our knowledge, previously unknown connection between two areas in computational topology, topological data analysis (TDA) and knot theory. Given a…
In dependently typed programming, proofs of basic, structural properties can be embedded implicitly into programs and do not need to be written explicitly. Besides saving the effort of writing separate proofs, a most distinguishing and…
Structured recursion schemes have been widely used in constructing, optimising, and reasoning about programs over inductive and coinductive datatypes. Their plain forms, catamorphisms and anamorphisms, are restricted in expressiveness. Thus…
Structural recursion is a common technique used by programmers in modern languages and is taught to introductory computer science students. But what about its dual, structural corecursion? Structural corecursion is an elegant technique,…
The general purpose of a scientific publication is the exchange and spread of knowledge. A publication usually reports a scientific result and tries to convince the reader that it is valid. With an ever-growing number of papers relying on…
Nested datatypes have been widely studied in the past 25 years, both theoretically using category theory, and practically in programming languages such as Haskell. They consist in recursive polymorphic datatypes where the type parameter…
Generalized linear and additive models are very efficient regression tools but the selection of relevant terms becomes difficult if higher order interactions are needed. In contrast, tree-based methods also known as recursive partitioning…
We consider unicellular maps, or polygon gluings, of fixed genus. A few years ago the first author gave a recursive bijection transforming unicellular maps into trees, explaining the presence of Catalan numbers in counting formulas for…
Eric Brill has recently proposed a simple and powerful corpus-based language modeling approach that can be applied to various tasks including part-of-speech tagging and building phrase structure trees. The method learns a series of symbolic…
Selection functionality is as fundamental to vector graphics as it is for raster data. But vector selection is quite different: instead of pixel-level labeling, we make a binary decision to include or exclude each vector primitive. In the…
Retrieval-augmented language models can better adapt to changes in world state and incorporate long-tail knowledge. However, most existing methods retrieve only short contiguous chunks from a retrieval corpus, limiting holistic…
We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasi-coherent modules on schemes,…
This paper presents a new foundational approach to information theory based on the concept of the information efficiency of a recursive function, which is defined as the difference between the information in the input and the output. The…
We suggest a compositional vector representation of parse trees that relies on a recursive combination of recurrent-neural network encoders. To demonstrate its effectiveness, we use the representation as the backbone of a greedy, bottom-up…
In heap-based languages, knowing that a variable x points to an acyclic data structure is useful for analyzing termination: this information guarantees that the depth of the data structure to which x points is greater than the depth of the…
This article is first in a series of papers where we reprove the statements in constructing the Enhanced Operation Map and the abstract six-functor formalism developed by Liu-Zheng. In this paper, we prove a theorem regarding constructing…
This document is an elementary introduction to string diagrams. It takes a computer science perspective: rather than using category theory as a starting point, we build on intuitions from formal language theory, treating string diagrams as…