View source for Plankalkül

{{Short description|Programming language designed 1942 to 1945}}
{{Distinguish|Plan Calcul}}
{{Use dmy dates|date=November 2023|cs1-dates=y}}
{{Use list-defined references|date=November 2023}}
{{Infobox programming language
| name = Plankalkül
| paradigm = [[Procedural programming|Procedural]]
| released = {{start date and age|1948}} – concept first published
| designer = [[Konrad Zuse]]
| latest release version = 
| latest release date = 
| implementations = ''Plankalkül-Compiler'' by the [[Free University of Berlin|FU Berlin]] in 2000
| influenced = [[Superplan]], [[ALGOL 58]]<ref name="Rojas-Hashagen_2002"/>
}}
'''Plankalkül''' ({{IPA|de|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.

''Kalkül'' (from Latin ''[[Calculus (disambiguation)|calculus]]'') is the [[German language|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.<ref name="Zenil_2012"/>

==History of programming==
In the domain of creating computing machines, Zuse was self-taught, and developed them without knowledge about other mechanical computing machines that existed already – although later on (building the [[Z3 (computer)|Z3]]) being inspired by [[David Hilbert|Hilbert]]'s and [[Wilhelm Ackermann|Ackermann]]'s book on elementary mathematical logic (see [[Principles of Mathematical Logic]]).<ref name="Hellige_2004"/>{{rp|pages=113, 152, 216}} To describe logical circuits, Zuse invented his own diagram and notation system, which he called "combinatorics of conditionals" ({{langx|de|Bedingungskombinatorik}}). After finishing the [[Z1 (computer)|Z1]] in 1938, Zuse discovered that the calculus he had independently devised already existed and was known as [[propositional calculus]].<ref name="Rojas-Göktekin-Friedland-Krüger-Kuniß-Langmack_2004"/>{{rp|page=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<ref name="Turing_2013"/>). In May 1939, he described his plans for the development of what would become Plankalkül.<ref name="Hellige_2004"/>{{rp|pages=113, 152, 216}} He wrote the following in his notebook:

{{Verse translation|lang=de
|1=Seit etwa einem halben Jahr allmähliches Einführen in die formale Logik. Viele meiner früheren Gedanken habe ich dort wiedergefunden. (Bedingungskombinatorik = Aussagenlogik; Lehre von den Intervallen = Gebietenkalkül). Ich plane jetzt die Aufsetzung des 'Plankalküls'. Hierzu sind eine Reihe von Begriffen zu klären.
|attr2=Konrad Zuse's notebook{{r|name="Rojas-Göktekin-Friedland-Krüger-Kuniß-Langmack_2004"|page=3}}
|2=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]]). I now plan the adoption of "Calculus of plans" onto this. A series of concepts need to be clarified for this.
}}

[[File:"Konrad Zuse-Haus" in Bruck 2.jpg|thumb|right|Historical marker on house in {{ill|Hinterstein|de}} where Zuse worked on Plankalkül]]

While working on his doctoral dissertation, Zuse developed the first known formal system of algorithm notation<ref name="Knuth-Pardo_1976"/>{{rp|page=9}} capable of handling branches and loops.<ref name="Giloi_1997"/>{{rp|page=18}}<ref name="Hellige_2004"/>{{rp|page=56}} In 1942 he began writing a [[computer chess|chess]] program in Plankalkül.<ref name="Hellige_2004"/>{{rp|pages=216-217}} In 1944, Zuse met with the German logician and philosopher [[Heinrich Scholz]], who expressed appreciation for Zuse's utilization of [[logical calculus]].<ref name="Petzold_1992"/> In 1945, Zuse described Plankalkül in an unpublished book.<ref name="Zuse_1945"/> The collapse of [[Nazi Germany]], however, prevented him from submitting his manuscript.<ref name="Giloi_1997"/>{{rp|page=18}}

At that time the only two working computers in the world were [[ENIAC]] and [[Harvard Mark I]], neither of which used a compiler, and ENIAC needed to be reprogrammed for each task by changing how the wires were connected.<ref name="Rojas-Göktekin-Friedland-Krüger-Kuniß-Langmack_2004"/>{{rp|page=3}}

Although most of his computers were destroyed by Allied bombs, Zuse was able to rescue one machine, the [[Z4 (computer)|Z4]], and move it to the Alpine village of [[Hinterstein]]<ref name="Knuth-Pardo_1976"/>{{rp|page=8}} (part of [[Bad Hindelang]]).

{{Cquote
|quote=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.
|author=[[Heinz Rutishauser]], creator of [[ALGOL]]}}

Unable to continue building computers – which was also forbidden by the Allied Powers<ref name="Coy_2004"/> – Zuse devoted his time to the development of a higher-level programming model and language.<ref name="Giloi_1997"/>{{rp|page=18}} In 1948, he published a paper in the ''[[Archiv der Mathematik]]'' and presented at the Annual Meeting of the [[GAMM]].<ref name="Hellige_2004"/>{{rp|page=89}} His work failed to attract much attention.{{Citation needed|date=September 2019}} In a 1957 lecture, Zuse expressed his hope that Plankalkül, "after some time as a [[Sleeping Beauty]], will yet come to life."<ref name="Rojas-Göktekin-Friedland-Krüger-Kuniß-Langmack_2004"/>{{rp|page=3}} He expressed disappointment that the designers of [[ALGOL 58]] never acknowledged the influence of Plankalkül on their own work.<ref name="Giloi_1997"/>{{rp|page=18}}<ref name="Knuth-Pardo_1976"/>{{rp|page=15}}

Plankalkül was republished with commentary in 1972.<ref name="Zuse_1972"/> The first compiler for Plankalkül was implemented by Joachim Hohmann in his 1975 dissertation.<ref name="Hohmann_1979"/> Other independent implementations followed in 1998<ref name="Mauerer_2016"/> and 2000 at the [[Free University of Berlin]].<ref name="Rojas-Göktekin-Friedland-Krüger-Kuniß-Langmack_2004"/>{{rp|page=2}}

==Description==
Plankalkül has drawn comparisons to the language [[APL (programming language)|APL]], and to [[relational algebra]]. It includes assignment statements, [[subroutine]]s, 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 (abstract data type)|graph]]'' ({{lang|de|verallgemeinerter Graph}}), which can be used to represent geometrical structures.<ref name="Giloi_1990"/>

Many features of the Plankalkül reappear in later programming languages; an exception is its idiosyncratic two-dimensional notation using multiple lines.  

Some features of the Plankalkül:<ref name="Hellige_2004"/>{{rp|page=217}}
* 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 [[binary digit|bit]] or [[Boolean data type|Boolean]] ({{langx|de|Ja-Nein-Werte}} – yes-no value in Zuse's terminology). It is denoted by the identifier <math>S0</math>. All the further data types are composite, and build up from primitive by means of "arrays" and "records".<ref name="Bauer-Wössner_1972"/>{{rp|page=679}}

So, a sequence of eight bits (which in modern computing could be regarded as [[byte]]) is denoted by <math>8 \times S0</math>, and Boolean matrix of size <math>m</math> by <math>n</math>&nbsp; is described by <math>m \times n \times S0</math>. There also exists a shortened notation, so one could write <math>S1 \cdot n</math> instead of <math>n \times S0</math>.<ref name="Bauer-Wössner_1972"/>{{rp|page=679}}

Type <math>S0</math> could have two possible values <math>0</math> and <math>L</math>. So 4-bit sequence could be written like L00L, but in cases where such a sequence represents a number, the programmer could use the decimal representation 9.<ref name="Bauer-Wössner_1972"/>{{rp|page=679}}

Record of two components <math>\sigma</math> and <math>\tau</math> is written as <math>(\sigma, \tau)</math>.<ref name="Bauer-Wössner_1972"/>{{rp|page=679}}

Type ({{langx|de|Art}}) in Plankalkül consists of 3 elements: structured value ({{langx|de|Struktur}}), pragmatic meaning ({{langx|de|Typ}}) and possible restriction on possible values ({{langx|de|Beschränkung}}).<ref name="Bauer-Wössner_1972"/>{{rp|page=679}} User defined types are identified by letter A with number, like <math>A1</math> – first user defined type.

====Examples====
Zuse used a lot of examples from chess theory:<ref name="Bauer-Wössner_1972"/>{{rp|page=680}}
{|cellpadding=5 style="border:1px solid #BBB; width:800px;"
|-
| <math>A1</math>
| <math>S1 \cdot 3</math>
| Coordinate of chess board (it has size 8x8 so 3 bits are just enough)
|-
| <math>A2</math>
| <math>2 \times A1</math>
| square of the board (for example L00, 00L denotes e2 in [[Algebraic notation (chess)|algebraic notation]])
|-
| <math>A3</math>
| <math>S1 \cdot 4</math>
| piece (for example, 00L0&nbsp;— white king)
|-
| <math>A4</math>
| <math>(A2, A3)</math>
| piece on a board (for example L00, 00L; 00L0&nbsp;— white king on e2)
|-
| <math>A5</math>
| <math>64 \times A3</math>
| board (pieces positions, describes which piece each of 64 squares contains)
|-
| <math>A10</math>
| <math>(A5, S0, S1 \cdot 4, A2)</math>
| game state (<math>A5</math>&nbsp;— board, <math>S0</math>&nbsp;— player to move, <math>S1 \cdot 4</math>&nbsp;— possibility of [[castling]] (2 for white and 2 for black), <math>A2</math>&nbsp;— information about cell on which ''[[en passant]]'' move is possible
|}

===Identifiers===
Identifiers are alphanumeric characters with a number.<ref name="Bauer-Wössner_1972"/>{{rp|page=679}} There are the following kinds of identifiers for variables:<ref name="Zuse_1945"/>{{rp|page=10}}

* Input values ({{langx|de|Eingabewerte, Variablen}})&nbsp;— marked with a letter V.
* Intermediate, temporary values ({{langx|de|Zwischenwerte}})&nbsp;— marked with a letter Z.
* Constants ({{langx|de|Constanten}})&nbsp;— marked with a letter С.
* Output values ({{langx|de|Resultatwerte}})&nbsp;— marked with a letter R.

Particular variable of some kind is identified by number, written under the kind.<ref name="Bauer-Wössner_1972"/>{{rp|page=679}} For example:

: <math>\begin{matrix} V \\ 0 \end{matrix}</math>, <math>\begin{matrix} Z \\ 2 \end{matrix}</math>, <math>\begin{matrix} C \\ 31 \end{matrix}</math> etc.

Programs and subprograms are marked with a letter P, followed by a program (and optionally a subprogram) number. For example <math>P13</math>, <math>P5 \cdot 7</math>.<ref name="Bauer-Wössner_1972"/>{{rp|page=679}}

Output value of program  <math>P13</math> saved there in variable <math>\begin{matrix} R \\ 0 \end{matrix}</math> is available for other subprograms under the identifier <math>\begin{matrix} R17 \\ 0 \end{matrix}</math>, and reading value of that variable also means executing related subprogram.<ref name="Bauer-Wössner_1972"/>{{rp|page=680}}

===Accessing elements by index===
Plankalkül allows access for separate elements of variable by using "component index" ({{langx|de|Komponenten-Index}}). When, for example, program receives input in variable <math>\begin{matrix} V \\ 0 \end{matrix}</math> of type <math>A10</math> (game state), then <math>\begin{matrix} V \\ 0 \\ 0 \end{matrix}</math>&nbsp;— gives board state, <math>\begin{matrix} V \\ 0 \\ 0 \cdot i \end{matrix}</math>&nbsp;— piece on square number i, and <math>\begin{matrix} V \\ 0 \\ 0 \cdot i \cdot j \end{matrix}</math> bit number j of  that piece.<ref name="Bauer-Wössner_1972"/>{{rp|page=680}}

In modern programming languages, that would be described by notation similar to <code>V0[0]</code>, <code>V0[0][i]</code>, <code>V0[0][i][j]</code> (although to access a single bit in modern programming languages a [[mask (computing)|bitmask]] is typically used).

===Two-dimensional syntax===
Because indexes of variables are written vertically, each Plankalkül instruction requires multiple rows to write down.{{citation needed|date=November 2016}}

First row contains variable kind, then variable number marked with letter V ({{langx|de|Variablen-Index}}), then indexes of variable subcomponents marked with K ({{langx|de|Komponenten-Index}}), and then ({{langx|de|Struktur-Index}}) marked with S, which describes variable type. Type is not required, but Zuse notes that this helps with reading and understanding the program.<ref name="Bauer-Wössner_1972"/>{{rp|page=681}}

In the line <math>S</math> types <math>S0</math> and <math>S1</math> could be shortened to <math>0</math> and <math>1</math>.<ref name="Bauer-Wössner_1972"/>{{rp|page=681}}

Examples:

{|cellpadding=5 style="border:1px solid #BBB; width:600px;"
|-
| <math>\begin{array}{r|l}
    & V \\ 
  V & 3 \\
  K & \\
  S & m \times 2 \times 1 \cdot n
 \end{array}</math>
| variable V3&nbsp;— list of <math>m</math> pairs of values of type <math>S1 \cdot n</math>
|-
| <math>\begin{array}{r|l}
    & V \\ 
  V & 3 \\
  S & m \times 2 \times 1 \cdot n
 \end{array}</math>
| Row K could be skipped when it is empty. Therefore, this expression means the same as above.
|-
| <math>\begin{array}{r|l}
    & V \\ 
  V & 3 \\
  K & i \cdot 0 \cdot 7 \\
  S & 0
 \end{array}</math>
| Value of eights bit (index 7), of first (index 0) pair, of і-th element of variable V3, has Boolean type (<math>S0</math>).
|}

Indexes could be not only constants. Variables could be used as indexes for other variables, and that is marked with a line, which shows in which component index would value of variable be used:

{|cellpadding=5 style="border:1px solid #BBB; width:600px;"
|-
| [[File:Plankalkül variable index.png|Using variable as index for other variable, in 2d Plankalül notation]]
| Z5-th element of variable V3. Equivalent to expression <code>V3[Z5]</code> in many modern programming languages.<ref name="Bauer-Wössner_1972"/>{{rp|page=681}}
|}

===Assignment operation===
Zuse introduced in his calculus an assignment operator, unknown in mathematics before him. He marked it with «<math>\Rightarrow</math>», and called it yields-sign ({{langx|de|Ergibt-Zeichen}}). Use of concept of assignment is one of the key differences between mathematics and computer science.<ref name="Knuth-Pardo_1976"/>{{rp|page=14}}

Zuse wrote that the expression:
: <math>\begin{array}{r|lll}
    & Z + 1 & \Rightarrow & Z\\ 
  V & 1     &             & 1\\
 \end{array}</math>

is analogous to the more traditional mathematical equation:

: <math>\begin{array}{r|lll}
    & Z + 1 & =  & Z\\ 
  V & 1     &    & 1\\
  K & i     &    & i + 1\\
 \end{array}</math>

There are claims that Konrad Zuse initially used the glyph [[File:Ergibt-Zeichen.png|frameless|25px]] as a sign for assignment, and started to use <math>\Rightarrow</math> under the influence of [[Heinz Rutishauser]].<ref name="Bauer-Wössner_1972"/>{{rp|page=681}} Knuth and Pardo believe that Zuse always wrote <math>\Rightarrow</math>, and that [[File:Ergibt-Zeichen.png|frameless|25px]] was introduced by publishers of «Über den allgemeinen Plankalkül als Mittel zur Formulierung schematisch-kombinativer Aufgaben» in 1948.<ref name="Knuth-Pardo_1976"/>{{rp|page=14}} In the [[ALGOL 58]] conference in Zürich, European participants proposed to use the assignment character introduced by Zuse, but the American delegation insisted on <code>:=</code>.<ref name="Bauer-Wössner_1972"/>{{rp|page=681}}

The variable that stores the result of an assignment ([[L-value (computer science)|l-value]]) is written to the right side of assignment operator.<ref name="Knuth-Pardo_1976"/>{{rp|page=14}} The first assignment to the variable is considered to be a declaration.<ref name="Bauer-Wössner_1972"/>{{rp|page=681}}

The left side of assignment operator is used for an expression ({{langx|de|Ausdruck}}), that defines which value will be assigned to the variable. Expressions could use arithmetic operators, Boolean operators, and comparison operators (<math>=, \neq, \leq</math> etc.).<ref name="Bauer-Wössner_1972"/>{{rp|page=682}}

The exponentiation operation is written similarly to the indexing operation - using lines in the two-dimensional notation:<ref name="Zuse_1945"/>{{rp|page=45}} 

[[File:Plankalkül-Potenzen.png|Exponentiation notation in Plankalkül]]

===Control flow===
Boolean values were represented as integers with {{code|1=FALSE=0}} and {{code|1=TRUE=1}}. Conditional control flow took the form of a guarded statement {{code|A -> B}}, which executed the block {{code|B}} if {{code|A}} was true. There was also an iteration operator, of the form {{code|W { A -> X; B -> Y }}} which repeats until all guards are false.<ref name="Rojas_2001"/>

===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]], something today would be called a [[translator (computing)|translator]] or [[compiler]].<ref name="Hellige_2004"/>{{rp|pages=45, 104, 105}}

===Example===
The original notation was two-dimensional.{{clarification needed|date=December 2019}} For a later implementation in the 1990s, a linear notation was developed.

The following example defines a function <code>max3</code> (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

==See also==
* [[History of programming languages]]
* [[Timeline of programming languages]]
* [[List of programming languages]]

==References==
{{reflist|refs=

<ref name="Zenil_2012">{{cite book |editor-first=Héctor |editor-last=Zenil |editor-link=:d:Q63660773 |date=2012 |title=A Computable Universe: Understanding and Exploring Nature As Computation - with a Foreword by Sir [[Roger Penrose]] |publication-place=Singapore |publisher=[[World Scientific Publishing Company]] |page=791}}</ref>
<ref name="Turing_2013">{{cite web |title=Why is propositional logic not Turing complete? |author= |date=2013-04-01 |work=StackExchange |department=Mathematics |url=https://math.stackexchange.com/a/348411/571313 |access-date=2023-11-02 |url-status=live |archive-url=https://web.archive.org/web/20231102131830/https://math.stackexchange.com/questions/348379/why-is-propositional-logic-not-turing-complete/348411#348411 |archive-date=2023-11-02}}</ref>
<ref name="Giloi_1990">{{citation |title=Konrad Zuses Plankalkül als Vorläufer moderner Programmiermodelle |language=de |author-first=Wolfgang K. |author-last=Giloi |author-link=:de:Wolfgang Giloi |date=November 1990}}</ref>
<ref name="Giloi_1997">{{cite journal |title=Konrad Zuse's Plankalkül: The First High-Level "non von Neumann" Programming Language |author-last=Giloi |author-first=Wolfgang K. |author-link=:de:Wolfgang Giloi |date=April–June 1997 |journal=[[IEEE Annals of the History of Computing]] |issn= |publisher=[[IEEE]] |volume=19 |issue=2 |doi=10.1109/85.586068 |pages=17–24 |url=http://doi.ieeecomputersociety.org/10.1109/85.586068}} (8 pages)</ref>
<ref name="Rojas_2001">{{cite encyclopedia |author-last=Rojas |author-first=Raúl |author-link=Raúl Rojas |title=Plankalkül |encyclopedia=Encyclopedia of computers and computer history |date=2001 |publisher=[[Fitzroy Dearborn Publishers]] |location=Chicago / London |isbn=1-57958235-4 |page=634 |url=http://page.mi.fu-berlin.de/rojas/pub/computer_history/m_z/plankalkuel.pdf |access-date=26 May 2023}}</ref>
<ref name="Rojas-Hashagen_2002">{{cite book |author-last1=Rojas |author-first1=Raúl |author-link1=Raúl Rojas |author-first2=Ulf |author-last2=Hashagen |author-link2=:de:Ulf Hashagen |date=2002 |title=The First Computers: History and Architectures |publisher=[[MIT Press]] |isbn=978-0-26268137-7 |edition= |page=292 |url=https://books.google.com/books?id=nDWPW9uwZPAC&dq=algol-68+konrad+zuse&pg=PA292 |access-date=2013-10-25}}</ref> 
<ref name="Petzold_1992">{{cite book |title=Moderne Rechenkünstler. Die Industrialisierung der Rechentechnik in Deutschland |language=de |author-first=Hartmut |author-last=Petzold |author-link=:de:Hartmut Petzold |publication-place=München, Germany |publisher=[[C.H. Beck Verlag]] |date=1992 |edition=}}</ref>
<ref name="Zuse_1945">{{cite book |title=Der Plankalkül (In der Fassung von 1945) |language=de |author-first=Konrad |author-last=Zuse |author-link=Konrad Zuse |editor-first1=Raúl |editor-last1=Rojas |editor-link1=Raúl Rojas |editor-first2=G. |editor-last2=Wagner |editor-first3=Ludmila |editor-last3=Scharf |editor-first4=Susanne |editor-last4=Schöttker-Söhl [Schötke-Suhl<!-- most probably typos in the document -->] |type=Manuscript |date=1946 |orig-date=1945 |publisher=Konrad Zuse Internet Archive |id=ZIA ID: 0233 |pages=10, 45 |url=http://zuse.zib.de/item/DB2j_t_w1fbxvaiq |access-date=2023-11-01 |url-status=live |archive-url=https://web.archive.org/web/20150416133441/http://zuse.zib.de/file/zuse_archive-0233.pdf;jsessionid=5F7002ED0507BF67BC4332A35F1DCDA5?id=http%3A//zuse.zib.de/file/1rUAfKDkirW8o3gT/21/1c/70/9e-d718-4b4e-be7b-ed9b620f5683/0/original/092be0ebdd0784fee570ef37eee273c7.pdf&download=1 |archive-date=2015-04-16}} (1+1+180 pages)</ref>
<ref name="Hohmann_1979">{{cite book |author-first=Joachim |author-last=Hohmann |title=Der PLANKALKÜL im Vergleich mit algorithmischen Sprachen |language=de |series=Reihe Informatik und Operations Research |volume=7 |publisher=[[S. Toeche-Mittler-Verlag]] (stmv) |publication-place=Darmstadt, Germany |date=1979 |edition=1 |isbn=3-87820-028-5}} (136 pages) [https://web.archive.org/web/20231030161043/https://external.dandelon.com/download/attachments/dandelon/ids/DE0049D0E905ED237EB1EC1257A0E0049AFDF.pdf Contents]</ref>
<ref name="Mauerer_2016">[https://web.archive.org/web/20161115175703/http://www.bytesex.de/mauerer/pk/README Description of Plankalkül-Compiler by Wolfgang Mauerer]; {{cite web |url=http://www.bytesex.de/mauerer/pk/ |title=Der Plankalkül von Konrad Zuse |author-last=Mauerer |author-first=Wolfgang |date=2016-06-03 |language=de |others=Implementation in German |archive-url=https://web.archive.org/web/20160603234257/http://www.bytesex.de/mauerer/pk/ |archive-date=2016-06-03 |access-date=2017-10-03}}</ref>
<ref name="Hellige_2004">{{cite book |editor-first=Hans Dieter |editor-last=Hellige |location=Bremen, Germany |title=Geschichten der Informatik. Visionen, Paradigmen, Leitmotive |language=de |publication-place=Berlin / Heidelberg, Germany |publisher=[[Springer-Verlag]] |edition=1 |date=January 2004 |orig-date=November 2002 |isbn=978-3-540-00217-8 |id={{ISBN|3-540-00217-0}} |doi=10.1007/978-3-642-18631-8 |pages=45, 56, 89, 104–105, 113, 152, 216–217}} (xii+514 pages)</ref>
<ref name="Coy_2004">{{cite book |author-first=Wolfgang |author-last=Coy |author-link=:de:Wolfgang Coy |editor-first=Hans Dieter |editor-last=Hellige |title=Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Teil 5: Wandel der Leitkonzepte in der Wissenschaftsdisziplin Informatik |language=de |title-link=#{{harvid|Hellige|2004}} |chapter=Was ist Informatik? Zur Entstehung des Faches an den deutschen Universitäten |publication-place=Berlin / Heidelberg, Germany |publisher=[[Springer-Verlag]] |edition=1 |date=January 2004 |orig-date=November 2002 |isbn=978-3-540-00217-8 |id={{ISBN|3-540-00217-0}} |doi=10.1007/978-3-642-18631-8_17 |pages=473–498 [474] |chapter-url=https://www.researchgate.net/publication/301184912}} [https://web.archive.org/web/20231102212758/https://edoc.hu-berlin.de/bitstream/handle/18452/9794/8.pdf?sequence=1]</ref>
<ref name="Rojas-Göktekin-Friedland-Krüger-Kuniß-Langmack_2004">{{cite book |author-first1=Raúl |author-last1=Rojas |author-link1=Raúl Rojas |author-first2=Cüneyt |author-last2=Göktekin |author-first3=Gerald |author-last3=Friedland |author-first4=Mike |author-last4=Krüger |author-first5=Ludmila |author-last5=Scharf |author-first6=Denis |author-last6=Kuniß |author-first7=Olaf |author-last7=Langmack |editor-first=Hans Dieter |editor-last=Hellige |title=Geschichten der Informatik. Visionen, Paradigmen, Leitmotive. Teil 3: Leitideen und Paradigmen in der Entwicklung der Programmiersprachen und der Programmierung |title-link=#{{harvid|Hellige|2004}} |chapter=Konrad Zuses Plankalkül — Seine Genese und eine moderne Implementierung |language=de |publication-place=Berlin / Heidelberg, Germany |publisher=[[Springer-Verlag]] |edition=1 |date=January 2004 |orig-date=November 2002 |doi=10.1007/978-3-642-18631-8_9 |isbn=978-3-642-62208-3 |pages=215–235 [2–4] |chapter-url=http://www.zib.de/zuse/Inhalt/Programme/Plankalkuel/Genese/Genese.pdf |archive-url=https://web.archive.org/web/20060501175217/http://www.zib.de/zuse/Inhalt/Programme/Plankalkuel/Genese/Genese.pdf |archive-date=2006-05-01}} (21 [24] pages)</ref>
<ref name="Knuth-Pardo_1976">{{cite web |title=The Early Development of Programming Languages |author-last1=Knuth |author-first1=Donald Ervin |author-link1=Donald Ervin Knuth |author-last2=Pardo |author-first2=Luis Isidoro Trabb |author-link2=:pt:Luis Trabb Pardo |date=August 1976 |pages=8, 9, 14, 15 |url=https://bitsavers.org/pdf/stanford/cs_techReports/STAN-CS-76-562_EarlyDevelPgmgLang_Aug76.pdf |publisher=Stanford University, Computer Science Department |access-date=2017-12-28 |url-status=dead |archive-url=https://web.archive.org/web/20170912102014/http://bitsavers.org/pdf/stanford/cs_techReports/STAN-CS-76-562_EarlyDevelPgmgLang_Aug76.pdf |archive-date=2017-09-12}}</ref>
<ref name="Bauer-Wössner_1972">{{cite journal |title=The "Plankalkül" of Konrad Zuse: A Forerunner of Today's Programming Languages |language=en |author-last1=Bauer |author-first1=Friedrich L. |author-link1=Friedrich L. Bauer |author-last2=Wössner |author-first2=Hans |date=1972 |journal=[[Communications of the ACM]] |issn= |volume=15 |issue=7 |doi=10.1145/361454.361515 |s2cid=17681101 |pages=678–685 |url=http://delivery.acm.org/10.1145/370000/361515/p678-bauer.pdf?key1=361515&key2=3342588511&coll=&dl=acm&CFID=15151515&CFTOKEN=6184618 |url-status=dead |archive-url=https://web.archive.org/web/20090220012346/http://delivery.acm.org/10.1145/370000/361515/p678-bauer.pdf?key1=361515&key2=3342588511&coll=&dl=acm&CFID=15151515&CFTOKEN=6184618 |archive-date=2009-02-20}} ([http://www.catb.org/retro/plankalkuel/ HTML])</ref>
<ref name="Zuse_1972">{{cite book |title=Der Plankalkül. Kommentierter Nachdruck der Fassung von 1945 |language=de |author-last=Zuse |author-first=Konrad |author-link=Konrad Zuse |date=1972 |publisher=[[Gesellschaft für Mathematik und Datenverarbeitung]] (GMD) / Bundesministerium für Bildung und Wissenschaft (BMBW) |publication-place=Sankt Augustin, Germany |volume=63<!-- or |number=? --> |id=BMBW-GMD-63}}</ref>
}}

==Further reading==
* {{cite book |title=Ansätze einer Theorie des allgemeinen Rechnens unter besonderer Berücksichtigung des Aussagenkalküls und dessen Anwendung auf Relaisschaltungen |language=de |trans-title=Inception of a universal theory of computation with special consideration of the propositional calculus and its application to relay circuits |author-last=Zuse |author-first=Konrad |author-link=Konrad Zuse |date=1943 |type=unpublished manuscript |id=Zuse Papers 045/018}}
* {{cite journal |title=Über den allgemeinen Plankalkül als Mittel zur Formulierung schematisch-kombinativer Aufgaben |language=de |trans-title= |author-last=Zuse |author-first=Konrad |author-link=Konrad Zuse |date=1948-12-06 |orig-date=November 1948 |journal=[[Archiv der Mathematik]] |issn=0003-889X |eissn=1420-8938 |location=Hopferau bei Füssen, Germany |publisher=[[Birkhäuser Verlag]] |publication-place=Karlsruhe / Stuttgart / Basel, Germany |volume=1 |issue=6 |doi=10.1007/BF02038459 |pages=441–449}} (9 pages)
* {{cite book |title=Plankalkül: The First High-Level Programming Language and its Implementation |language=en |author-last1=Rojas |author-first1=Raúl |author-link1=Raúl Rojas |author-first2=Cüneyt |author-last2=Göktekin |author-first3=Gerald |author-last3=Friedland |author-first4=Mike |author-last4=Krüger |author-first5=Denis |author-last5=Kuniß |author-first6=Olaf |author-last6=Langmack |date=February 2000 |publisher=Institut für Informatik, Freie Universität Berlin & Feinarbeit.de |location=Berlin, Germany |id=Technical Report B-3/2000 |url=https://www.researchgate.net/publication/250809396 |archive-url=https://web.archive.org/web/20060501175521/http://www.zib.de/zuse/Inhalt/Programme/Plankalkuel/Plankalkuel-Report/techreport.pdf |archive-date=2006-05-01}}[https://web.archive.org/web/20141018204625/http://www.zib.de:80/zuse/Inhalt/Programme/Plankalkuel/Plankalkuel-Report/Plankalkuel-Report.htm] (22 pages)
* {{cite web |title=Plankalkül |author-first=Bram |author-last=Bruines |date=2010-01-08 |type=Thesis |url=https://www.cs.ru.nl/bachelors-theses/2010/Bram_Bruines___0213837___Plankalkul.pdf |access-date=2023-11-02 |url-status=live |archive-url=https://web.archive.org/web/20231102210756/https://www.cs.ru.nl/bachelors-theses/2010/Bram_Bruines___0213837___Plankalkul.pdf |archive-date=2023-11-02}} (24 pages)

==External links==
* {{cite web |title=Plankalkül-Programme |language=de, en |date=2014-08-21 |website=Konrad Zuse Internet Archive |url=http://zuse.zib.de/ |access-date=2017-10-04 |url-status=dead |archive-url=https://web.archive.org/web/20140821215119/http://www.zib.de/zuse/Inhalt/Programme/Plankalkuel/ |archive-date=2014-08-21}} (NB. Plankalkül Java applets and documents.)

{{Authority control}}

{{DEFAULTSORT:Plankalkul}}
[[Category:Programming languages created in 1948]]
[[Category:Procedural programming languages]]
[[Category:Non-English-based programming languages]]
[[Category:German inventions of the Nazi period]]
[[Category:German inventions]]
[[Category:Konrad Zuse]]
[[Category:1940s establishments in Germany]]