Related papers: Introducing the vfunc R package
In this article, we present a new R package fc that provides a streamlined, standard evaluation-based approach to function composition. Using fc, a sequence of functions can be composed together such that returned objects from composed…
The main purpose of this paper is to give characterization theorems on derivations as well as on linear functions. Among others the following problem will be investigated: Let $n\in\mathbb{Z}$, $f, g\colon\mathbb{R}\to\mathbb{R}$ be…
The Additive Transform of an arithmetic function represents a novel approach to examining the interplay between multiplicative arithmetic function and additive functions. This transform concept introduces a method to systematically generate…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…
We introduce a two-parameter family of discrepancy measures, termed \emph{$(G,f)$-divergences}, obtained by applying a non-decreasing function $G$ to an $f$-divergence $D_f$. Building on Csisz\'ar's formulation of mutual $f$-information, we…
The free algebra is an interesting and useful algebraic object. Here I introduce "freealg", an R package which furnishes computational support for free algebras. The package uses the standard template library's "map" class for efficiency,…
This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be…
Graph Interpolation Grammars are a declarative formalism with an operational semantics. Their goal is to emulate salient features of the human parser, and notably incrementality. The parsing process defined by GIGs incrementally builds a…
Generic programming is an effective methodology for developing reusable software libraries. Many programming languages provide generics and have features for describing interfaces, but none completely support the idioms used in generic…
Set functions are a feature of functional logic programming to encapsulate all results of a non-deterministic computation in a single data structure. Given a function $f$ of a functional logic program written in Curry, we describe a…
For each $a \in \mathbb{R}$, we define a Borel function $f_a : \mathbb{R} \to \mathbb{R}$ which encodes $a$ in a certain sense. We show that for each Borel $g : \mathbb{R} \to \mathbb{R}$, $f_a \cap g = \emptyset$ implies $a \in…
A range of methodologies and techniques are available to guide the design and implementation of language extensions and domain-specific languages. A simple yet powerful technique is based on source-to-source transformations interleaved…
For two arithmetical functions $f$ and $g$, we study the convolution sum of the form $\sum_{n \le N} f(n) g(n+h)$ in the context of its asymptotic formula with explicit error terms. Here we introduce the concept of finite Ramanujan…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
Incremental computations attempt to exploit input similarities over time, reusing work that is unaffected by input changes. To maximize this reuse in a general-purpose programming setting, programmers need a mechanism to identify dynamic…
Many Prolog programs are unnecessarily impure because of inadequate means to express syntactic inequality. While the frequently provided built-in `dif/2` is able to correctly describe expected answers, its direct use in programs often leads…
Polynomial functions $f : \mathbb{N}_+ \longrightarrow \mathbb{N}_+$ are studied for which sums of arbitrary length $f (1) + f (2) + f (3) + >... + f (n)$, with $n \in \mathbb{N}_+$, can be expressed by polynomial functions $g :…
In this paper, we extend the classical arithmetic defined over the set of natural numbers N, to the set of all finite directed connected multigraphs having a pair of distinct distinguished vertices. Specifically, we introduce a model F on…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
The technique of guessing can be very fruitful when dealing with sequences which arise in practice. This holds true especially when guessing is performed algorithmically and efficiently. One highly useful tool for this purpose is the…