Objects of Alternative Set Theory in Set@l Programming Language

  • Ilya I. Levin
  • Alexey I. DordopuloEmail author
  • Ivan V. Pisarenko
  • Andrey K. Melnikov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11657)


Software porting between high-performance computer systems with different architectures requires a major code revision due to the architectural limitation of available programming languages. To solve the problem, we have proposed an architecture-independent Set@l programming language based on the principles of set-theoretic codeview and aspect-oriented programming. In Set@l, a program consists of a source code, which describes an information graph of a computational problem, and aspects, which adapt an algorithm to the architecture and configuration of a computer system. If an algorithm remains unchanged during its architectural adaptation, calculations and their parallelizing are described within the Cantor-Bolzano set theory. In the case of algorithm modification, some collections are indefinite, and we can not treat them as traditional sets with sharply defined elements. To describe indefinite objects, Set@l applies the alternative set theory developed by P. Vopenka. If collection has indefinite type and structure at some level of abstraction, it belongs to a “class” type. In contrast to a class, the indefiniteness of a semiset is an essential and inalienable attribute. The application of classes, sets and semisets allows to describe various methods of the algorithm implementation and parallelizing as an entire Set@l program. In this paper the Jacobi algorithm for the solution of linear equation systems is considered as an example of the utilization of classes and semisets.


Architecture-independent programming Set@l programming language Alternative set theory Aspect-oriented paradigm 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ilya I. Levin
    • 1
  • Alexey I. Dordopulo
    • 2
    Email author
  • Ivan V. Pisarenko
    • 2
  • Andrey K. Melnikov
    • 3
  1. 1.Southern Federal University, Academy for Engineering and Technology, Institute of Computer Technologies and Information SecurityTaganrogRussia
  2. 2.Supercomputers and Neurocomputers Research CenterTaganrogRussia
  3. 3.“InformInvestGroup” CJSCMoscowRussia

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