Related papers: Using Rewriting Systems to Compute Kan Extensions …
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…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
In earlier work, we developed a modular approach for automatic complexity analysis of integer programs. However, these integer programs do not allow non-tail recursive calls or subprocedures. In this paper, we consider integer programs with…
The rewriting method for text summarization combines extractive and abstractive approaches, improving the conciseness and readability of extractive summaries using an abstractive model. Exiting rewriting systems take each extractive…
Dependency pairs are a key concept at the core of modern automated termination provers for first-order term rewriting systems. In this paper, we introduce an extension of this technique for a large class of dependently-typed higher-order…
In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…
We generalise classical reconstruction results in algebra, using the language of monads, monoidal categories, module categories, as well as various notions of duality, such as closedness, Grothendieck--Verdier duality (also known as…
Automated writing evaluation systems can improve students' writing insofar as students attend to the feedback provided and revise their essay drafts in ways aligned with such feedback. Existing research on revision of argumentative writing…
Several authors devised type-based termination criteria for ML-like languages allowing non-structural recursive calls. We extend these works to general rewriting and dependent types, hence providing a powerful termination criterion for the…
The classical Eckmann-Hilton argument shows that two monoid structures on a set, such that one is a homomorphism for the other, coincide and, moreover, the resulting monoid is commutative. This argument immediately gives a proof of the…
Dynamic languages such as Python and JavaScript widely use function decorators to extend behavior. In TypeScript, a common way to type such patterns uses Parameters<T> and ReturnType<T>. In practice, this idiom relies on a function-type…
Various models of $(\infty,1)$-categories, including quasi-categories, complete Segal spaces, Segal categories, and naturally marked simplicial sets can be considered as the objects of an $\infty$-cosmos. In a generic $\infty$-cosmos, whose…
We describe a formalism, using groupoids, for the study of rewriting for presentations of inverse monoids, that is based on the Squier complex construction for monoid presentations. We introduce the class of pseudoregular groupoids, an…
String diagrams are pictorial representations for morphisms of symmetric monoidal categories. They constitute an intuitive and expressive graphical syntax, which has found application in a very diverse range of fields including concurrency…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
This paper contains results from two areas -- formal theory of Kan extensions and concrete categories. The contribution to the former topic is based on the extension of the concept of Kan extension to the cones and we prove that limiting…
We study the confluence property of abstract rewriting systems internal to cubical categories. We introduce cubical contractions, a higher-dimensional generalisation of reductions to normal forms, and employ them to construct cubical…
Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to…
We summarize the main known results involving subword reversing, a method of semigroup theory for constructing van Kampen diagrams by referring to a preferred direction. In good cases, the method provides a powerful tool for investigating…
Interviews run on people, programs run on operating systems, voting schemes run on voters, games run on players. Each of these is an example of the abstraction pattern runs on matter. Pattern determines the decision tree that governs how a…