Related papers: Generic Level Polymorphic N-ary Functions
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
Indexed monoidal algebras are introduced as an equivalent structure for self-dual compact closed categories, and a coherence theorem is proved for the category of such algebras. Turing automata and Turing graph machines are defined by…
For any $n$-ary associative algebra we construct a $\Z_{n-1}$ graded algebra, which is a universal object containing the $n$-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups.
The Agda Universal Algebra Library (UALib) is a library of types and programs (theorems and proofs) we developed to formalize the foundations of universal algebra in dependent type theory using the Agda programming language and proof…
We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of…
In this paper we modify and generalize a construction presented by Novotn\'y: given a groupoid (a set equipped with a binary operation), it is defined a mono-unary algebra corresponding to that specific groupoid. We shall introduce and…
We introduce Voevodsky's univalent foundations and univalent mathematics, and explain how to develop them with the computer system Agda, which is based on Martin-L\"of type theory. Agda allows us to write mathematical definitions,…
Analogous to regular string and tree languages, regular languages of directed acyclic graphs (DAGs) are defined in the literature. Although called regular, those DAG-languages are more powerful and, consequently, standard problems have a…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
In recent years, the interest in using proof assistants to formalise and reason about mathematics and programming languages has grown. Type-logical grammars, being closely related to type theories and systems used in functional programming,…
This paper introduces a simple type system for combinatory logic in which combinators have at most one type, whose polymorphism is revealed by application. The combinatory types exactly describe the structure of their values, which may be…
Array programming languages allow for concise and generic formulations of numerical algorithms, thereby providing a huge potential for program optimisation such as fusion, parallelisation, etc. One of the restrictions that these languages…
Graph-based modeling plays a fundamental role in many areas of computer science. In this paper, we introduce systems of graph formulas with variables for specifying graph properties; this notion generalizes the graph formulas introduced in…
We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…
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…
We study a class of aggregate-join queries with multiple aggregation operators evaluated over annotated relations. We show that straightforward extensions of standard multiway join algorithms and generalized hypertree decompositions (GHDs)…
We introduce the open-ended, modular, self-improving Omega AI unification architecture which is a refinement of Solomonoff's Alpha architecture, as considered from first principles. The architecture embodies several crucial principles of…
We show that morphisms from n A_infinity-algebras to a single one are maps over an operad module with n+1 commuting actions of the operad A_infinity, whose algebras are conventional A_infinity-algebras. Similar statement holds for homotopy…
The aim of this paper is to introduce $n$-ary Hom-algebra structures generalizing the $n$-ary algebras of Lie type enclosing $n$-ary Nambu algebras, $n$-ary Nambu-Lie algebras, $n$-ary Lie algebras, and $n$-ary algebras of associative type…
We consider theories characterized by a set of Ward operators which do not form a closed algebra. We impose the Slavnov--Taylor identity built out of the Ward operators and we derive the acceptable breaking of the algebra and the general…