Related papers: FreeCHR: An Algebraic Framework for CHR-Embeddings
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
Constraint Handling Rules (CHR) is a committed-choice declarative language which has been originally designed for writing constraint solvers and which is nowadays a general purpose language. CHR programs consist of multi-headed guarded…
We begin by explaining how any context-free grammar encodes a functor of operads from a freely generated operad into a certain "operad of spliced words". This motivates a more general notion of CFG over any category $C$, defined as a finite…
Concept bottleneck models (CBMs) have emerged as critical tools in domains where interpretability is paramount. These models rely on predefined textual descriptions, referred to as concepts, to inform their decision-making process and offer…
In this paper, we propose a novel hash learning approach that has the following main distinguishing features, when compared to past frameworks. First, the codewords are utilized in the Hamming space as ancillary techniques to accomplish its…
Despite decades of research, there are still a number of concepts commonly found in software programs that are considered challenging for verification: among others, such concepts include concurrency, and the compositional analysis of…
We argue that the implementation and verification of compilers for functional programming languages are greatly simplified by employing a higher-order representation of syntax known as Higher-Order Abstract Syntax or HOAS. The underlying…
Case-based Reasoning (CBR) on high-dimensional and heterogeneous data is a trending yet challenging and computationally expensive task in the real world. A promising approach is to obtain low-dimensional hash codes representing cases and…
This article serves as a preliminary introduction to the design of a new, open-source applied and computational category theory framework, named Categorica, built on top of the Wolfram Language. Categorica allows one to configure and…
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…
Traditional category theory is typically based on set-theoretic principles and ideas, which are often non-constructive. An alternative approach to formalizing category theory is to use E-category theory, where hom sets become setoids. Our…
Classic grammars and regular expressions can be used for a variety of purposes, including parsing, intent detection, and matching. However, the comparisons are performed at a structural level, with constituent elements (words or characters)…
Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures. Ad-hoc notation, diagrams, and pseudocode poorly handle nonlinear broadcasting and the…
This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as…
Deep learning methods are highly accurate, yet their opaque decision process prevents them from earning full human trust. Concept-based models aim to address this issue by learning tasks based on a set of human-understandable concepts.…
We discuss the syntax and semantics of relational Horn logic (RHL) and partial Horn logic (PHL). RHL is an extension of the Datalog programming language that allows introducing and equating variables in conclusions. PHL is a syntactic…
Constrained Horn Clauses (CHCs) are an intermediate program representation that can be generated by several verification tools, and that can be processed and solved by a number of Horn solvers. One of the main challenges when using CHCs in…
Building on the successes of satisfiability modulo theories (SMT), Bj{\o}rner et al. initiated a research programme advocating Horn constraints as a suitable basis for automatic program verification. The notion of first-order constrained…
Word embeddings are rich word representations, which in combination with deep neural networks, lead to large performance gains for many NLP tasks. However, word embeddings are represented by dense, real-valued vectors and they are therefore…
This paper investigates the relationship between the Logical Algorithms language (LA) of Ganzinger and McAllester and Constraint Handling Rules (CHR). We present a translation schema from LA to CHR-rp: CHR with rule priorities, and show…