Related papers: Extensional equality preservation and verified gen…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
This article aims to provide a novel formalization of the concept of computational irreducibility in terms of the exactness of functorial correspondence between a category of data structures and elementary computations and a corresponding…
It was shown recently that the f-diagonal tensor in the T-SVD factorization must satisfy some special properties. Such f-diagonal tensors are called s-diagonal tensors. In this paper, we show that such a discussion can be extended to any…
The repeated execution of reasoning tasks is desirable in many applicative scenarios, such as stream reasoning and event processing. When using answer set programming in such contexts, one can avoid the iterative generation of ground…
A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
A number of constructions in function field arithmetic involve extensions from linear objects using digit expansions. This technique is described here as a method of constructing orthonormal bases in spaces of continuous functions. We…
In this paper, we focus attention on extending the topological conjugacy of adding machine maps and minimal systems to iterated function systems. We provide necessary and sufficient conditions for an iterated function system to be…
Interest in anti-unification, the dual problem of unification, is on the rise due to applications within the field of software analysis and related areas. For example, anti-unification-based techniques have found uses within clone detection…
This paper introduces an efficient approach to solve quadratic and nonlinear programming problems subject to linear equality constraints via the Theory of Functional Connections. This is done without using the traditional Lagrange…
The execution of sequential programs allows them to be represented using mathematical functions formed by the composition of statements following one after the other. Each such statement is in itself a partial function, which allows only…
Erasure enriches type theory with a distinction between runtime relevant and irrelevant data, allowing the compilation step to safely erase the latter. Versions of this feature are implemented by many systems, including Agda, Idris, and…
We investigate the behavior of extension monads, introduced in the 1990s by the second author, in terms of structure results for infinitely many finitary operations and common constructions in varieties or categories of algebras.…
We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…
The existence of a positive linear functional acting on the space of (differences between) conformal blocks has been shown to rule out regions in the parameter space of conformal field theories (CFTs). We argue that at the boundary of the…
Strong monads are important for several applications, in particular, in the denotational semantics of effectful languages, where strength is needed to sequence computations that have free variables. Strength is non-trivial: it can be…
In semantics and in programming practice, algebraic concepts such as monads or, essentially equivalently, (large) Lawvere theories are a well-established tool for modelling generic side-effects. An important issue in this context are…
This paper proves a homomorphism between extensional formal semantics and distributional vector space semantics, demonstrating structural compatibility. Formal semantics models meaning as reference, using logical structures to map…
Recursive algebraic data types (term algebras, ADTs) are one of the most well-studied theories in logic, and find application in contexts including functional programming, modelling languages, proof assistants, and verification. At this…
This thesis proposes a combinatorial generalization of a nilpotent operator on a vector space. The resulting object is highly natural, with basic connections to a variety of fields in pure mathematics, engineering, and the sciences. For the…