Related papers: A Purely Functional Computer Algebra System Embedd…
In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean…
In functional logic programs, rules are applicable independently of textual order, i.e., any rule can potentially be used to evaluate an expression. This is similar to logic languages and contrary to functional languages, e.g., Haskell…
We consider in C^n the class of symmetric homogeneous quadratic dynamical systems. We introduce the notion of algebraic integrability for this class. We present a class of symmetric quadratic dynamical systems that are algebraically…
Weyl algebra is a simple noncommutative system used in quantum mechanics. Here I introduce the weyl package, written in the R computing language, which furnishes functionality for working with univariate and multivariate Weyl algebras. The…
Every $\mathrm{C}^*$-algebra, regardless of its density character, can be embedded into the Calkin algebra in a forcing extension of the universe obtained without collapsing any cardinal.
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
This paper introduces semi-ring dictionaries, a powerful class of compositional and purely functional collections that subsume other collection types such as sets, multisets, arrays, vectors, and matrices. We developed SDQL, a statically…
Computability logic (CoL) is a formal theory of interactive computation. It understands computational problems as games played by two players: a machine and its environment, uses logical formalism to describe valid principles of…
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…
One of the key concepts in testing is that of adequate test sets. A test selection criterion decides which test sets are adequate. In this paper, a language schema for specifying a large class of test selection criteria is developed; the…
Datatype-generic programming increases program abstraction and reuse by making functions operate uniformly across different types. Many approaches to generic programming have been proposed over the years, most of them for Haskell, but…
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…
General program synthesis has become an important application area for genetic programming (GP), and for artificial intelligence more generally. Code Building Genetic Programming (CBGP) is a recently introduced GP method for general program…
This document is intended as a stand-alone textbook chapter to be used for introducing some functional programming concepts into a course in which the primary teaching language is Java. For details of the approach, please see the paper…
We present probabilistic neural programs, a framework for program induction that permits flexible specification of both a computational model and inference algorithm while simultaneously enabling the use of deep neural networks.…
We present IQu, namely a quantum programming language that extends Reynold's Idealized Algol, the paradigmatic core of Algol-like languages. IQu combines imperative programming with high-order features, mediated by a simple type theory. IQu…
We present a methodology for integrating functional data into deep densely connected feed-forward neural networks. The model is defined for scalar responses with multiple functional and scalar covariates. A by-product of the method is a set…
We propose the vision of a functional data model (FDM) and an associated functional query language (FQL). Our proposal has far-reaching consequences: we show a path to come up with a modern QL that solves (almost if not) all problems of SQL…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…