Related papers: Rewriting Structured Cospans: A Syntax For Open Sy…
One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce "structured cospans" as a way to study networks with inputs and outputs. Given a functor $L \colon…
We introduce an intuitive algorithmic methodology for enacting automated rewriting of string diagrams within a general double-pushout (DPO) framework, in which the sequence of rewrites is chosen in accordance with the causal structure of…
String diagrams are a powerful and intuitive graphical syntax, originated in the study of symmetric monoidal categories. In the last few years, they have found application in the modelling of various computational structures, in fields as…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
Non-confluent and non-terminating constructor-based term rewrite systems are useful for the purpose of specification and programming. In particular, existing functional logic languages use such kind of rewrite systems to define possibly…
The paper presents a language model that develops syntactic structure and uses it to extract meaningful information from the word history, thus enabling the use of long distance dependencies. The model assigns probability to every joint…
Decorated cospans provide a categorical framework for composing open systems along shared interfaces. This paper is a computational proof of concept: we show that the framework produces a working coupled dynamical system when the…
Several types of term rewriting systems can be distinguished by the way their rules overlap. In particular, we define the classes of prefix, suffix, bottom-up and top-down systems, which generalize similar classes on words. Our aim is to…
There is a growing need for abstractions in logic specification languages such as FO(.) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always…
A coherent presentation of an n-category is a presentation by generators, relations and relations among relations. Confluent and terminating rewriting systems generate coherent presentations, whose relations among relations are defined by…
The analysis of cyber-physical systems (CPS) is challenging due to the large state space and the continuous changes occurring in their constituent parts. Design practices favor modularity to help reducing this complexity. In a previous…
We study the termination of rewriting modulo a set of equations in the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. In a previous…
The intricate hierarchical structure of syntax is fundamental to the intricate and systematic nature of human language. This study investigates the premise that language models, specifically their attention distributions, can encapsulate…
As speakers turn their thoughts into sentences, they maintain a balance between the complexity of words and syntax. However, it is unclear whether this syntax-lexicon tradeoff is unique to the spoken language production that is under the…
Natural language is characterized by compositionality: the meaning of a complex expression is constructed from the meanings of its constituent parts. To facilitate the evaluation of the compositional abilities of language processing…
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…
A generally intelligent learner should generalize to more complex tasks than it has previously encountered, but the two common paradigms in machine learning -- either training a separate learner per task or training a single learner for all…
Modelling musical structure is vital yet challenging for artificial intelligence systems that generate symbolic music compositions. This literature review dissects the evolution of techniques for incorporating coherent structure, from…
Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language…
Some personal recollections on the introduction of `abstract proof systems' as a framework for formulating syntax-independent, general results about rule derivability and admissibility. With a particular eye on the inspiration I owe to Roel…