相关论文: Rewriting Procedures Generalise to Kan Extensions …
Compositional generalization is the ability to generalize systematically to a new data distribution by combining known components. Although humans seem to have a great ability to generalize compositionally, state-of-the-art neural models…
The main novelty of this paper is to consider an extension of the Calculus of Constructions where predicates can be defined with a general form of rewrite rules. We prove the strong normalization of the reduction relation generated by the…
The Goulden-Jackson cluster method is a powerful tool for obtaining generating functions for counting words in a free monoid by occurrences of a set of subwords. We introduce a generalization of the cluster method for monoid networks, which…
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…
The paper describes development (improvement/extension) approaches for composite (modular) systems (as combinatorial reengineering). The following system improvement/extension actions are considered: (a) improvement of systems component(s)…
Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The…
Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequences and generating functions. We describe how it works 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…
When writing programs, people have the ability to tackle a new complex task by decomposing it into smaller and more familiar subtasks. While it is difficult to measure whether neural program synthesis methods have similar capabilities, what…
A concept of "evolving categories" is suggested to build a simple, scalable, mathematically consistent framework for representing in uniform way both data and algorithms. A state machine for executing algorithms becomes clear, rich and…
Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be…
Cai et al. have recently proposed change structures as a semantic framework for incremental computation. We generalise change structures to arbitrary cartesian categories and propose the notion of change action model as a categorical model…
Context. An extension method is a method declared in a package other than the package of its host class. Thanks to extension methods, developers can adapt to their needs classes they do not own: adding methods to core classes is a typical…
We describe a mathematical framework for equational reasoning about infinite families of string diagrams which is amenable to computer automation. The framework is based on context-free families of string diagrams which we represent using…
Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
We present an online deliberation system using mutual evaluation in order to collaboratively develop solutions. Participants submit their proposals and evaluate each other's proposals; some of them may then be invited by the system to…
We introduce homotopical methods based on rewriting on higher-dimensional categories to prove coherence results in categories with an algebraic structure. We express the coherence problem for (symmetric) monoidal categories as an…
For any group $G$ with subgroup $H$ and a set of representatives $T$ from the set of cosets $G/H$, we develop a rewriting system from $G$ that bequeaths a product into the set decomposition $T\times H$ of $G$, converting it into a group. In…