|Designed by||Konrad Zuse|
|First appeared||1948– concept first published|
|Plankalkül-Compiler by the FU Berlin in 2000|
|Superplan by Heinz Rutishauser, |
Plankalkül (German pronunciation: [ˈplaːnkalkyːl], "Plan Calculus") is a programming language designed for engineering purposes by Konrad Zuse between 1942 and 1945. It was the first high-level (non-von Neumann) programming language to be designed for a computer.
After finishing the Z1 in 1938 Zuse started to study academic logic literature, where he found that the calculus, that he devised on his own already existed and was called propositional calculus -- though what Zuse had in mind had to be much more powerful and in May 1939 he first wrote about the project to develop the Plankalkül.
While working on his intended doctoral dissertation, Konrad Zuse developed a formal system of notation for algorithms because no such system was yet known. This notation could only handle linear (unbranched and unlooped) calculation plans. Zuse's formal system on the other hand did include branched and looped calculation. He had intended to submit an early manuscript, written in 1944, as a PhD thesis, but the collapse of Nazi Germany made this impossible.
Near the end of the Second World War, most of the computers Zuse was building were destroyed by Allied bombs. He was able to rescue one machine, the Z4, and move it to the small Alpine village of Hinterstein. After the war it was not possible for Zuse to continue building his computers, so he devoted his time to the development of a higher level programming model and language for them called the Plankalkül.
Notes survive with scribblings about such a plan calculation dating back to May 1939 and in 1942 Zuse began writing a computer chess program in Plankalkül. 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. Plankalkül was not published at that time owing to a combination of factors such as conditions in World War II and postwar Germany and his efforts to commercialise the Z3 computer and its successors.
In 1945, Zuse wrote an unpublished book about the Plankalkül and in 1948 he published a paper in the "Archiv der Mathematik" and introduced his programming language at the Annual Meeting of the GAMM. His work did not attract much attention, and for a long time to come programming a computer would only be thought of as using machine code.
The Plankalkül was more comprehensively published in 1972 and the first compiler for it was implemented in 1975 in a dissertation by Joachim Hohmann. Other independent implementations followed in 1998 and then in 2000 by the Free University of Berlin.
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 generalized graph (verallgemeinerter Graph), which can be used to represent geometrical structures.
Some features of the Plankalkül:
- only local variables
- functions do not support recursion
- only supports call by value
- composite types are arrays and tuples
- contains conditional expressions
- contains a for loop and a while loop
- no goto
The only primitive data type in the Plankalkül is a single bit, denoted by S0. Further data types can be built up from these.
Zuse called a single program a Rechenplan (i.e. computation plan), and in 1944 he already 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).
The original notation was two dimensional. For a later 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
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] END 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] END
In a lecture in 1957 Zuse mentioned his hope that the Plankalkül "after some time as a Sleeping Beauty, will yet come to life".
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.
- Rojas, Raúl; Hashagen, Ulf (2002). The First Computers: History and Architectures. MIT Press. p. 292. ISBN 978-0262681377. Retrieved October 25, 2013.
- Hector Zenil (ed.), 2012. A Computable Universe: Understanding and Exploring Nature As Computation with a Foreword by Sir Roger Penrose. Singapore: World Scientific Publishing Company. Page 791.
- Hans Dieter Hellige (ed.): Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. p. 216.
- Knuth & Pardo 1976, p. 9
- Giloi 1997
- Hans Dieter Hellige (ed.): Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. p. 56.
- Knuth & Pardo 1976, p. 8
- Hans Dieter Hellige (ed.): Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. p. 216,217.
- Hartmut Petzold,Moderne Rechenkünstler. Die Industrialisierung der Rechentechnik in Deutschland. München. C.H. Beck Verlag 1992
- (full text of the 1945 manuscript)
- Hans Dieter Hellige (ed.): Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. p. 89.
- 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.
- Knuth & Pardo 1976, p. 15
- Prof. Wolfgang Giloi: Konrad Zuses Plankalkül als Vorläufer moderner Programmiermodelle, November 1990
- Hans Dieter Hellige (ed.): Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. p. 217.
- Hellige, Hans Dieter, Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. pp. 45, 104, 105
- Giloi, Wolfgang (1997), "Konrad Zuse's Plankalkül: The First High-Level "non von Neumann" Programming Language", IEEE Annals of the History of Computing, 19 (2): 17–24, doi:10.1109/85.586068
- Knuth, Donald Ervin; Pardo, Luis Trabb (1976), The Early Development of Programming Languages (PDF), Stanford University, Computer Science Department, archived from the original (PDF) on 2017-09-12, retrieved 2017-12-28
- 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 (1997). "Konrad Zuse's Plankalkül: The First High-Level "non von Neumann" Programming Language". IEEE Annals of the History of Computing. 19 (2): 17–24. doi:10.1109/85.586068.
- The "Plankalkül" of Konrad Zuse: A Forerunner of Today's Programming Languages by Friedrich L. Bauer (alternative source)
- Rojas, Raúl, et al. (2000). "Plankalkül: The First High-Level Programming Language and its Implementation". Institut für Informatik, Freie Universität Berlin, Technical Report B-3/2000. (full text)(archived)
- Mauerer, Wolfgang (2016-06-03). "Der Plankalkül von Konrad Zuse" (in German). Implementation in German. Archived from the original on 2016-06-03. Retrieved 2017-10-03.
- "Plankalkül". Konrad Zuse Internet Archive. Archived page with Plankalkül java applets (non functioning) and several documents (German/English). 2014-08-21. Archived from the original on 2014-08-21. Retrieved 2017-10-04.CS1 maint: others (link)
- Bram Bruines: Plankalkul(2010) - Plankalkül described in a formal way