Plank calculus

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The Plankalkül is a programming language developed by Konrad Zuse between 1942 and 1946 . It was the first high-level programming language in the world.


The Plankalkül includes assignments , function calls , conditional statements , loops , floating point arithmetic , fields , compound data types and other special features such as targeted execution .

The notation of the programs was originally two-dimensional: Separate lines were provided for indices and type specifications. A linear transcription was developed for a later implementation in the 1990s.

The following example shows a program (in linear transcription) that implements the calculation of the maximum of three variables in the function max3 :

P1 max3 (V0[:8.0],V1[:8.0],V2[:8.0]) → R0[:8.0]
max(V0[:8.0],V1[:8.0]) → Z1[:8.0]
max(Z1[:8.0],V2[:8.0]) → R0[:8.0]
P2 max (V0[:8.0],V1[:8.0]) → R0[:8.0]
V0[:8.0] → Z1[:8.0]
(Z1[:8.0] < V1[:8.0]) → V1[:8.0] → Z1[:8.0]
Z1[:8.0] → R0[:8.0]


Konrad Zuse used the work on the lambda calculus by Alonzo Church and Stephen Kleene from the 1930s when developing the Plankalküls . He wanted to use the language on a successor to his Z3 computer system, but the events of the Second World War made it impossible.

Bibliography can be found as early as the late 1940s, but it wasn't until 1972 that the language was first published in full. The Plankalkül was described and implemented in 1975 by J. Hohmann as part of a dissertation. At the end of the 1990s, independent alternative implementations followed (in 1998 and two years later another at the Free University of Berlin ), including a syntax editor.

The Plankalkül is primarily of historical importance in the field of programming languages. The language was not used in practice.


  • Konrad Zuse: About the general plan calculus as a means of formulating schematic-combinative tasks . Arch. Math. 1, pp. 441-449, 1948/49.
  • Konrad Zuse: The Plankalkül. Society for Mathematics and Data Processing. No. 63, BMBW - GMD - 63, 1972
  • Joachim Hohmann: The Plankalkül compared with algorithmic languages . ISBN 978-3-87820-028-4 . Darmstadt, 1979
  • Wolfgang Giloi : Konrad Zuse's Plankalkül as a forerunner of modern programming models Konrad-Zuse-Center for Information Technology Berlin. Berlin 1990. (Technical report TR 90-13 )
  • Jürgen Alex: Grundzüge des Plankalküls , in: Drsb .: On the origin of the computer - From Alfred Tarski to Konrad Zuse […] - Tertium non datur, VDI-Verlag Düsseldorf 2007, pp. 215 to 233

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