Algorithms and algebra

  • F. L. Bauer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 122)


The algebraic definition of an algorithm given above is wider than the classical one. It is an abstract definition based on a signature only, and allows interpretation by any computational structure of this signature. Even introducing a set of properties does not necessarily determine the interpretation completely. This freedom is an advantage, it allows to treat a number of related algorithms under one single roof. Moreover, even for a given monomorphic type algorithms can be non-deterministic. This freedom allows to go to special descendants which show increased efficiency, including deterministic ones.

Both degrees of freedom can be used in a program development process in order to delay design decisions.

In particular, such an abstract algebraic definition of algorithms (in conjunction with the abstract definition of types and of congruence relations in the term algebra giving representants of the computational structures of such a type) is a step to become liberated from the notational pressure that has darkened so much the genuine issues of programming.


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© Springer-Verlag Berlin Heidelberg 1981

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  • F. L. Bauer

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