Plankalkül

Plankalkül (German pronunciation: [ˈplaːnkalkyːl]) is a programming language designed for engineering purposes by Konrad Zuse between 1942 and 1945. It was the first high-level programming language to be designed for a computer.

Not to be confused with Plan Calcul.
Plankalkül
ParadigmProcedural
Designed byKonrad Zuse
First appeared1948 (1948) – concept first published
Major implementations
Plankalkül-Compiler by the FU Berlin in 2000
Influenced by
Begriffsschrift
Influenced
Superplan by Heinz Rutishauser,
ALGOL 58[1]

Kalkül is the German term for a formal system—as in Hilbert-Kalkül, the original name for the Hilbert-style deduction system—so Plankalkül refers to a formal system for planning.[2]

History

In the domain of creating computing machines, Zuse was self-taught, and developed them without knowledge about other mechanical computing machines that existed already. To describe logical circuits, Zuse invented his own diagram and notation system, which he called "combinatorics of conditionals" (German: Bedingungskombinatorik). After finishing the Z1 in 1938, Zuse discovered that the calculus he had independently devised already existed and was known as propositional calculus.[3] What Zuse had in mind, however, needed to be much more powerful (propositional calculus is not Turing-complete and is not able to describe even simple arithmetic calculations[4]). In May 1939 he described his plans for the development of what would become Plankalkül.[5] He wrote following in his notebook:

Almost half a year of gradual introduction into formal logic. I rediscovered there lots of my previous thoughts. (combinatorics of conditionals = propositional calculus; study of intervals = lattice theory). Now I plan creation of "Calculus of plans". There are series of concepts needed to clarify for this.

Seit etwa einem halben Jahr allmähliches Einführen in die formale Logik. Viele meiner früheren Gedanken habe ich dort wieder gefunden. (Bedingungskombinatorik = Aussagenlogik; Lehre von den Intervallen = Gebietenkalkül). Ich plane jetzt die Aufsetzung des 'Plankalküls'. Hierzu sind eine Reihe von Begriffen zu klären.

—Konrad Zuse's notebook[3]
Table on house in Hinterstein where Zuse worked on Plankalkül

While working on his doctoral dissertation, Zuse developed the first known formal system of algorithm notation[6] capable of handling branches and loops.[7][8] In 1942 he began writing a chess program in Plankalkül.[9] In 1944, Zuse met with the German logician and philosopher Heinrich Scholz, who expressed appreciation for Zuse's utilization of logical calculus.[10] In 1945, Zuse described Plankalkül in an unpublished book.[11] The collapse of Nazi Germany, however, prevented him from submitting his manuscript.[7]

Original definition of language impresses with it's expressive constructs and it's modern flavour, so it feels like it was created a lot later than in the 1945. At that time the only two working computers in the world were ENIAC and Harvard Mark I, none of which used compiler, and ENIAC needed to be reprogrammed for each task by changing connection of wires.[12]

Although most of his computers were destroyed by Allied bombs, Zuse was able to rescue one machine, the Z4, and move it to the Alpine village of Hinterstein[13] (part of Bad Hindelang).

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.

— Heinz Rutishauser, creator of ALGOL

Unable to continue building computers -- which was also forbidden by the Allied Powers[14] -- Zuse devoted his time to the development of a higher-level programming model and language.[7] In 1948 he published a paper in the Archiv der Mathematik and presented at the Annual Meeting of the GAMM.[15] His work failed to attract much attention. In a 1957 lecture, Zuse expressed his hope that Plankalkül, "after some time as a Sleeping Beauty, will yet come to life." He expressed disappointment that the designers of ALGOL 58 never acknowledged the influence of Plankalkül on their own work.[7][16]

Plankalkül was more comprehensively published in 1972. The first compiler was implemented by Joachim Hohmann in his 1975 dissertation.[17] Other independent implementations followed in 1998 and 2000 at the Free University of Berlin.

Description

Plankalkül has drawn comparisons to the language APL, and to 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.[18]

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

Some features of the Plankalkül:[19]

  • 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

Data types

The only primitive data type in the Plankalkül is a single bit or boolean (in Zuses therms German: Ja-Nein-Werte - yes-no value). It is denoted by identifier. All the futher data types are composite, and build up from primitive by means of "arrays" and "records". So, sequence of eight bits (which in modern computing could be regarded as byte) is denoted by , and boolean matrix of size by  — .[20]

Terminology

Zuse called a single program a Rechenplan ("computation plan"). He envisioned what he called a Planfertigungsgerät ("plan assembly device"), which would automatically translate the mathematical formulation of a program into machine-readable punched film stock.[21]

Example

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

The following example defines a function max3 (in a linear transcription) that calculates the maximum of three variables:

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
gollark: Those are bad at transcoding and generally have slow storage.
gollark: I don't think your assumptions there are accurate. At all.
gollark: I disagree. Horses are not particularly cool animals.
gollark: Although we don't have the :transistor: emoji.
gollark: The transistor cult is still unofficially extant. You could always join that.

See also

Notes
  1. Rojas, Raúl; Hashagen, Ulf (2002). The First Computers: History and Architectures. MIT Press. p. 292. ISBN 978-0262681377. Retrieved October 25, 2013.
  2. 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.
  3. Rojas et al. 2004, p. 3.
  4. "Why is propositional logic not Turing complete?".
  5. Hans Dieter Hellige (ed.): Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. p. 216.
  6. Knuth & Pardo 1976, p. 9
  7. Giloi 1997
  8. Hans Dieter Hellige (ed.): Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. p. 56.
  9. Hans Dieter Hellige (ed.): Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. p. 216,217.
  10. Hartmut Petzold,Moderne Rechenkünstler. Die Industrialisierung der Rechentechnik in Deutschland. München. C.H. Beck Verlag 1992
  11. (full text of the 1945 manuscript)
  12. Rojas et al. 2000, p. 3.
  13. Knuth & Pardo 1976, p. 8
  14. Prof. Wolfgang Coy: Was ist Informatik? Zur Entstehung des Faches an den deutschen Universitäten, in: Hans Dieter Hellige (ed.): Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. p. 474.
  15. Hans Dieter Hellige (ed.): Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. p. 89.
  16. Knuth & Pardo 1976, p. 15
  17. 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.
  18. Prof. Wolfgang Giloi: Konrad Zuses Plankalkül als Vorläufer moderner Programmiermodelle, November 1990
  19. Hans Dieter Hellige (ed.): Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. p. 217.
  20. Bauer & Wössner 1972, p. 679.
  21. Hellige, Hans Dieter, Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Berlin, Springer 2004, ISBN 3-540-00217-0. pp. 45, 104, 105

References
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