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Abstract Data Types - Universal Algebra
(dt. Abstrakte Datentypen - Universelle Algebra)

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises as well as at least 2 presentations of the tasks.
Examination type: Oral or written examination
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Computer Sciences.
Original study programme M.Sc. Informatik / Vertiefungsbereich Informatik
One semester,
Alle 3-4 Semester
Person in charge of the module's outline Prof. Dr. H.-Peter Gumm


Mathematical theory of abstract data types:

  • Types, algebras, morphisms.
  • Substructures, congruences, products, images
  • terms, equations, equation calculus
  • Initial and free objects
  • Birkhoff's theorem
  • Maltsev Terms
  • Multi-sorted algebras
  • Hidden sorts, behavioral specifications

Qualification Goals

Students learn the concepts of data structures:

  • Abstract data types, morphisms, derived structures,
  • Freedom, Initiality and Induction,
  • Specifications by equations and implications,
  • Multi-sorted systems,
  • Hidden Specifications.


  • training of scientific skills (recognition, formulation, problem solving, abstraction),
  • oral communication skills in the lab sessions by practicing free speech and discussion in front of an audience.


None. The competences taught in the following modules are recommended: Logic, either Algorithms and Data Structures or Practical Informatics II: Data Structures and Algorithms for Pre-Service-Teachers.

Recommended Reading

  • Th. Ihringer: Allgemeine Algebra. Mit einem Anhang über Universelle Coalgebra von H.P.Gumm, Heldermann Verlag, 2003.
  • J. Martin: Data Types and Data Structures. Prentice Hall; 1986.
  • B. Liskov, S. Zilles: Programming with abstract data types. SIGPLAN; J. A. Goguen, J. W. Thatcher, E. W. Wagner: An Initial Algebra Approach to the Specification, Correctness and Implementation of Abstract Data Types.

Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2020/21. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.