Related papers: Arithmetic as a theory modulo
We discuss the role played by logarithmic structures in the theory of moduli.
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC;…
The architecture has its basis in a dialectic search of new choices of representation. We deal with the form on the contemporary architecture under two approaches: expression and content. We examine how mathematical principles based on…
In a previous work, we proved that almost all of the Calculus of Inductive Constructions (CIC), which is the basis of the proof assistant Coq, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of…
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…
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…
We propose a simple approach to formal deformations of associative algebras. It exploits the machinery of multiplicative coresolutions of an associative algebra A in the category of A-bimodules. Specifically, we show that certain…
This note deals with two topics of linear algebra. We give a simple and short proof of the multiplicative property of the determinant and provide a constructive formula for rotations. The derivation of the rotation matrix relies on simple…
We construct affine algebras with an arbitrary amount of simple modules of each dimension.
In this paper we formalize some foundation concepts and theorems of group theory in a variant of type theory called the Calculus of Constructions with Definitions. In this theory we introduce definition of a group, which is both general and…
Resolution modulo is a first-order theorem proving method that can be applied both to first-order presentations of simple type theory (also called higher-order logic) and to set theory. When it is applied to some first-order presentations…
We use recurrence equations (alias difference equations) to enumerate the number of formula-representations of positive integers using only addition and multiplication, and using addition, multiplication, and exponentiation, where all the…
This survey provides a practical and algorithmic perspective on Drinfeld modules over $\mathbb F_q[T]$. Starting with the construction of the Carlitz module, we present Drinfeld modules in any rank and some of their arithmetic properties.…
In this paper, we study rewriting modulo a set of algebraic axioms in categories enriched in linear categories, called linear~$(2,2)$-categories. We introduce the structure of linear~$(3,2)$-polygraph modulo as a presentation of a…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
The purpose of the present work is to provide short and supple teaching notes for a $30$ hours introductory course on elementary \textit{Enumerative Algebraic Combinatorics}. We fully adopt the \textit{Rota way}. The themes are organized…
This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial,…
Factorization -- a simple form of standardization -- is concerned with reduction strategies, i.e. how a result is computed. We present a new technique for proving factorization theorems for compound rewriting systems in a modular way, which…
Narrowing is a procedure that was first studied in the context of equational E-unification and that has been used in a wide range of applications. The classic completeness result due to Hullot states that any term rewriting derivation…