Related papers: Polymorphic type inference for the relational alge…
We give an elementary proof of isomorphism of the blob (diagram) algebra and the corresponding extended Temperley-Lieb algebra (defined by presentation).
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Type inference refers to the task of inferring the data type of a given column of data. Current approaches often fail when data contains missing data and anomalies, which are found commonly in real-world data sets. In this paper, we propose…
In this paper we study the problem of quantizing theories defined over a nonclassical configuration space. If one follows the path-integral approach, the first problem one is faced with is the one of definition of the integral over such…
We investigate inductive types in type theory, using the insights provided by homotopy type theory and univalent foundations of mathematics. We do so by introducing the new notion of a homotopy-initial algebra. This notion is defined by a…
Analyzing relational languages by their logical expressiveness is well understood. Something not well understood or even formalized is the vague concept of relational query patterns. What are query patterns? And how can we reason about…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
The fundamentals of formal logic, theory of sets and mathematical structures are narrated in terms of relations language.
The notion of the characteristic Lie algebra of the discrete hyperbolic type equation is introduced. An effective algorithm to compute the algebra for the equation given is suggested. Examples and further applications are discussed.
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of…
The aim of this paper is to derive on the basis of the Euler's formula several analytical relations which hold for certain classes of planar graphs and which can be useful in algorithmic graph theory.
Source identities are fundamental identities between multivariable special functions. We give a geometric derivation of rational and trigonometric source identities. We also give a systematic derivation and extension of various determinant…
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…
We define a Hopf algebra of polylogarithms of an arbitrary field, which is a candidate for a conjectural Hopf algebra of framed mixed Tate motives. Our definition is elementary and mimics Goncharov's construction of higher Bloch groups. We…
We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of…
We define inductively a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the Pi-algebra \pi_* X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology…
We generalise the notion of separable equivalence, originally presented by Linckelmann (2011), to an equivalence relation on additive categories. We use this generalisation to show that from an initial equivalence between two algebras we…
We introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory $T$ is mutually algebraic if and only if it is weakly minimal and trivial if and only if no model $M$ of $T$ has an expansion…
A type assignment system for lambda-calculus enjoys the principal typing property if every typable term M has a special typing, called principal, from which all typings for M can be obtained via suitable operations. The existence of…