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Not to be confused with Plan Calcul.
Paradigm Procedural
Designed by Konrad Zuse
First appeared 1948; 67 years ago (1948) – concept first published
Major implementations
Plankalkül-Compiler by the FU Berlin in 2000
Influenced by
Superplan by Heinz Rutishauser,
ALGOL 58[1]

Plankalkül (German pronunciation: [ˈplaːnkalkyːl], "Plan Calculus") is a programming language designed for engineering purposes by Konrad Zuse between 1943 and 1945. It was the first high-level non-von Neumann programming language to be designed for a computer. Also, notes survive with scribblings about such a plan calculation dating back to 1941. Plankalkül was not published at that time owing to a combination of factors such as conditions in wartime and postwar Germany and his efforts to commercialise the Z3 computer and its successors. In 1944 Zuse met with the German logician and philosopher Heinrich Scholz and they discussed Zuse's Plankalkül. In March 1945 Scholz personally expressed his deep appreciation for Zuse's utilization of the logical calculus.[2]

By 1946, Zuse had written a book on the subject[3] but this remained unpublished. In 1948 Zuse published a paper about the Plankalkül in the "Archiv der Mathematik" but still did not attract much feedback – for a long time to come programming a computer would only be thought of as programming with machine code. The Plankalkül was eventually more comprehensively published in 1972 and the first compiler for it was implemented in 1975 in a dissertation by Joachim Hohmann.[4] Other independent implementations followed in 1998 and then in 2000 by the Free University of Berlin.

"Kalkül" means formal system – the Hilbert-style deduction system is for example originally called "Hilbert-Kalkül", so Plankalkül means "formal system for planning".


Plankalkül has drawn comparisons to APL and relational algebra. It includes assignment statements, subroutines, conditional statements, iteration, floating point arithmetic, arrays, hierarchical record structures, assertions, exception handling, and other advanced features such as goal-directed execution. The Plankalkül provides a data structure called general graph (verallgemeinerter Graph), which can be used to represent geometrical structures.[5]

Plankalkül shared an idiosyncratic notation using multiple lines with Frege's Begriffsschrift of 1879 (dealing with mathematical logic).[clarification needed]


A single program was called by Zuse a Rechenplan (i.e. computation plan) and already in 1944 Zuse envisioned a device that should read and then automatically translate a mathematical formulation of a program into machine readable punched film stock – a device which he called Planfertigungsgerät (i.e. plan construction device).[6]


The original notation was two dimensional. For the first real implementation in the 1990s, a linear notation was developed.

The following example shows a program (in a linear transcription), which calculates the maximum of three variables by calling the function max 3:

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]


In a lecture in 1957 Zuse mentioned his hope that the Plankalkül "after some time as a Sleeping Beauty, will yet come to life."

Heinz Rutishauser, one of the founders of ALGOL:

"The very first attempt to devise an algorithmic language was undertaken in 1948 by K. Zuse. His notation was quite general, but the proposal never attained the consideration it deserved."

See also[edit]


  1. ^ Rojas, Raúl; Hashagen, Ulf (2002). The First Computers: History and Architectures. MIT Press. p. 292. ISBN 978-0262681377. Retrieved October 25, 2013. 
  2. ^ Hartmut Petzold,Moderne Rechenkünstler. Die Industrialisierung der Rechentechnik in Deutschland. München. C.H. Beck Verlag 1992
  3. ^ (full text of the 1945 manuscript)
  4. ^ Joachim Hohmann: Der Plankalkül im Vergleich mit algorithmischen Sprachen. Reihe Informatik und Operations Research, S. Toeche-Mittler Verlag, Darmstadt 1979, ISBN 3-87820-028-5.
  5. ^ Prof. Wolfgang Giloi: Konrad Zuses Plankalkül als Vorläufer moderner Programmiermodelle, November 1990
  6. ^ Hellige, Hans Dieter, Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. pp. 45, 104, 105
  • Zuse, Konrad (1943), "Ansätze einer Theorie des allgemeinen Rechnens unter besonderer Berücksichtigung des Aussagenkalküls und dessen Anwendung auf Relaisschaltungen", (i.e. Inception of a universal theory of computation with special consideration of the propositional calculus and its application to relay circuits.) unpublished manuscript, Zuse Papers 045/018.
  • Zuse, Konrad (1948/49). "Über den allgemeinen Plankalkül als Mittel zur Formulierung schematisch-kombinativer Aufgaben". Arch. Math. 1, pp. 441–449, 1948/49.
  • Zuse, Konrad (1972). "Der Plankalkül". Gesellschaft für Mathematik und Datenverarbeitung. Nr. 63, BMBW - GMD - 63, 1972.
  • Giloi, Wolfgang, K. (1997). "Konrad Zuse's Plankalkül: The First High-Level "non von Neumann" Programming Language". IEEE Annals of the History of Computing, vol. 19, no. 2, pp. 17–24, April–June, 1997. (abstract)

External links[edit]