Related papers: A Calculus for Scoped Effects & Handlers
We construct a new bounded functional calculus for the generators of bounded semigroups on Hilbert spaces and generators of bounded holomorphic semigroups on Banach spaces. The calculus is a natural (and strict) extension of the classical…
The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
In this paper, a new calculus on sequences is defined. Also, the $\lambda$-derivative and the $\lambda$-integration are investigated. The fundamental theorem of $\lambda$-calculus is included. A suitable function basis for the…
A wardian calculus of sequences started almost seventy years ago constitutes the general scheme for extensions of the classical umbral operator calculus considered by many afterwards . At the same time this calculus is an example of the…
The emergence of large-language models (LLMs) has enabled a new class of semantic data processing systems (SDPSs) to support declarative queries against unstructured documents. Existing SDPSs are, however, lacking a unified algebraic…
In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressiveness of a more traditional denotation style. We will formalize a category based type and effect system to…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is…
This paper presents a systematic study of the calculus of interval-valued functions and its application to interval differential equations. To this end, first, we introduce new interval arithmetic operations. Under new operations, the space…
Classical spectral theory provides powerful tools for analyzing linear operators, but does not extend naturally to nonlinear or compositional settings. In particular, there is no general way to transport spectral invariants in a functorial…
The Calculus of Wrapped Compartments (CWC) is a variant of the Calculus of Looping Sequences (CLS). While keeping the same expressiveness, CWC strongly simplifies the development of automatic tools for the analysis of biological systems.…
This paper deals with efficient numerical representation and manipulation of differential and integral operators as symbols in phase-space, i.e., functions of space $x$ and frequency $\xi$. The symbol smoothness conditions obeyed by many…
We introduce the $L_!^S$-calculus, a linear lambda-calculus extended with scalar multiplication and term addition, that acts as a proof language for intuitionistic linear logic (ILL). These algebraic operations enable the direct expression…
The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said…
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest,…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
In this paper we are concerned with understanding the nature of program metrics for calculi with higher-order types, seen as natural generalizations of program equivalences. Some of the metrics we are interested in are well-known, such as…
In this paper we present two flavors of a quantum extension to the lambda calculus. The first one, $\lambda_\rho$, follows the approach of classical control/quantum data, where the quantum data is represented by density matrices. We provide…