255:
2674:
2624:
3224:
223:
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
2408:
2616:
2523:
2159:
2367:
2284:
2743:
3444:
335:
Unable to continue building computers – which was also forbidden by the Allied Powers – Zuse devoted his time to the development of a higher-level programming model and language. In 1948, he published a paper in the
357:
Plankalkül was republished with commentary in 1972. The first compiler for
Plankalkül was implemented by Joachim Hohmann in his 1975 dissertation. Other independent implementations followed in 1998 and 2000 at the
1909:
178:
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
1855:
2400:
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:
215:
and is not able to describe even simple arithmetic calculations). In May 1939, he described his plans for the development of what would become
Plankalkül. He wrote the following in his notebook:
1807:
1691:
1536:
1742:
1653:
1501:
1466:
3477:
3064:
319:
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.
3345:
2534:
1258:
273:
While working on his doctoral dissertation, Zuse developed the first known formal system of algorithm notation capable of handling branches and loops. In 1942 he began writing a
594:
3629:
793:
2733:
2465:
2085:
2669:
2645:
2446:
3104:
1166:
976:
652:
519:
2210:
1592:
1335:
1039:
917:
623:
1107:
741:
387:
2295:
2218:
761:
3615:
1765:
1618:
1563:
1195:
2392:
2032:
2009:
1362:
1306:
1283:
1136:
1068:
1009:
946:
887:
851:
678:
483:
3643:
3012:
Geschichten der
Informatik. Visionen, Paradigmen, Leitmotive. Teil 3: Leitideen und Paradigmen in der Entwicklung der Programmiersprachen und der Programmierung
2181:
2072:
2052:
1986:
718:
698:
559:
539:
720:. 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.
2407:
406:
Many features of the
Plankalkül reappear in later programming languages; an exception is its idiosyncratic two-dimensional notation using multiple lines.
3567:(1948-12-06) . Written at Hopferau bei Füssen, Germany. "Über den allgemeinen Plankalkül als Mittel zur Formulierung schematisch-kombinativer Aufgaben".
3310:
2703:), that defines which value will be assigned to the variable. Expressions could use arithmetic operators, Boolean operators, and comparison operators (
3291:
3712:
3003:
231:
Almost half a year of gradual introduction into formal logic. I rediscovered there lots of my previous thoughts. (combinatorics of conditionals =
2681:
conference in Zürich, European participants proposed to use the assignment character introduced by Zuse, but the
American delegation insisted on
1965:) marked with S, which describes variable type. Type is not required, but Zuse notes that this helps with reading and understanding the program.
2677:
was introduced by publishers of «Über den allgemeinen
Plankalkül als Mittel zur Formulierung schematisch-kombinativer Aufgaben» in 1948. In the
3702:
3553:
Ansätze einer
Theorie des allgemeinen Rechnens unter besonderer Berücksichtigung des Aussagenkalküls und dessen Anwendung auf Relaisschaltungen
3717:
3557:
Inception of a universal theory of computation with special consideration of the propositional calculus and its application to relay circuits
1860:
3256:
Geschichten der
Informatik. Visionen, Paradigmen, Leitmotive. Teil 5: Wandel der Leitkonzepte in der Wissenschaftsdisziplin Informatik
3707:
195:). To describe logical circuits, Zuse invented his own diagram and notation system, which he called "combinatorics of conditionals" (
3732:
3623:. Berlin, Germany: Institut für Informatik, Freie Universität Berlin & Feinarbeit.de. Technical Report B-3/2000. Archived from
3669:
3151:
3111:
1812:
300:, neither of which used a compiler, and ENIAC needed to be reprogrammed for each task by changing how the wires were connected.
2692:) is written to the right side of assignment operator. The first assignment to the variable is considered to be a declaration.
346:. His work failed to attract much attention. In a 1957 lecture, Zuse expressed his hope that Plankalkül, "after some time as a
2793:("plan assembly device"), which would automatically translate the mathematical formulation of a program into machine-readable
3276:
3032:
2965:
1542:
Programs and subprograms are marked with a letter P, followed by a program (and optionally a subprogram) number. For example
2738:
The exponentiation operation is written similarly to the indexing operation - using lines in the two-dimensional notation:
2884:
2823:
P1 max3 (V0,V1,V2) → R0 max(V0,V1) → Z1 max(Z1,V2) → R0 END P2 max (V0,V1) → R0 V0 → Z1 (Z1 < V1) → V1 → Z1 Z1 → R0 END
2870:
2917:
2742:
1770:
78:
1658:
2539:
2470:
1938:
Because indexes of variables are written vertically, each
Plankalkül instruction requires multiple rows to write down.
1506:
1712:
1623:
1471:
1436:
3636:
3356:
3337:
3286:
2975:
2837:
2813:
The original notation was two-dimensional. For a later implementation in the 1990s, a linear notation was developed.
3002:; Göktekin, Cüneyt; Friedland, Gerald; Krüger, Mike; Scharf, Ludmila; Kuniß, Denis; Langmack, Olaf (January 2004) .
3522:
2832:
1381:
Identifiers are alphanumeric characters with a number. There are the following kinds of identifiers for variables:
192:
2611:{\displaystyle {\begin{array}{r|lll}&Z+1&=&Z\\V&1&&1\\K&i&&i+1\\\end{array}}}
239:). I now plan the adoption of "Calculus of plans" onto this. A series of concepts need to be clarified for this.
135:
3362:
163:
2428:
Zuse introduced in his calculus an assignment operator, unknown in mathematics before him. He marked it with «
386:, arrays, hierarchical record structures, assertions, exception handling, and other advanced features such as
3503:
2842:
485:. All the further data types are composite, and build up from primitive by means of "arrays" and "records".
2371:
Value of eights bit (index 7), of first (index 0) pair, of і-th element of variable V3, has Boolean type (
1201:
3514:
207:
in 1938, Zuse discovered that the calculus he had independently devised already existed and was known as
3038:
2456:). Use of concept of assignment is one of the key differences between mathematics and computer science.
564:
303:
Although most of his computers were destroyed by Allied bombs, Zuse was able to rescue one machine, the
3722:
2689:
981:
393:
371:
3328:. Reihe Informatik und Operations Research (in German). Vol. 7 (1 ed.). Darmstadt, Germany:
2518:{\displaystyle {\begin{array}{r|lll}&Z+1&\Rightarrow &Z\\V&1&&1\\\end{array}}}
2154:{\displaystyle {\begin{array}{r|l}&V\\V&3\\K&\\S&m\times 2\times 1\cdot n\end{array}}}
3452:
766:
383:
359:
146:
89:
3614:; Göktekin, Cüneyt; Friedland, Gerald; Krüger, Mike; Kuniß, Denis; Langmack, Olaf (February 2000).
3329:
2706:
2300:
2223:
2090:
122:
2911:
A Computable Universe: Understanding and Exploring Nature As Computation - with a Foreword by Sir
2654:
2630:
2431:
1142:
211:. What Zuse had in mind, however, needed to be much more powerful (propositional calculus is not
952:
628:
495:
2798:
2186:
1568:
1430:
Particular variable of some kind is identified by number, written under the kind. For example:
1311:
1015:
893:
599:
232:
208:
39:
2362:{\displaystyle {\begin{array}{r|l}&V\\V&3\\K&i\cdot 0\cdot 7\\S&0\end{array}}}
2279:{\displaystyle {\begin{array}{r|l}&V\\V&3\\S&m\times 2\times 1\cdot n\end{array}}}
3569:
2288:
Row K could be skipped when it is empty. Therefore, this expression means the same as above.
1074:
726:
338:
3727:
746:
127:
34:
3578:
8:
3110:. Stanford University, Computer Science Department. pp. 8, 9, 14, 15. Archived from
3100:
1747:
1600:
1545:
1177:
2374:
2014:
1991:
1344:
1288:
1265:
1118:
1050:
991:
928:
869:
833:
660:
465:
3590:
3469:
3440:
3223:(Manuscript) (in German). Konrad Zuse Internet Archive. pp. 10, 45. ZIA ID: 0233.
3183:
3147:"Konrad Zuse's Plankalkül: The First High-Level "non von Neumann" Programming Language"
3146:
3096:
2794:
2166:
2057:
2037:
1971:
1701:
Plankalkül allows access for separate elements of variable by using "component index" (
703:
683:
544:
524:
375:
3624:
3598:
3518:
3387:
3333:
3282:
3272:
3250:
3142:
3028:
2994:
2992:
2990:
2988:
2986:
2971:
2961:
2880:
2648:
451:
324:
188:
3473:
254:
3582:
3461:
3264:
3191:
3164:
3020:
2953:
1927:
282:
2983:
277:
program in Plankalkül. In 1944, Zuse met with the German logician and philosopher
3268:
3260:
3246:
3056:
3016:
2949:
2866:
2696:
2449:
1958:
1950:
1942:
1702:
1419:
1408:
1397:
1386:
823:
815:
807:
799:
455:
347:
278:
212:
196:
151:
46:
3445:"The "Plankalkül" of Konrad Zuse: A Forerunner of Today's Programming Languages"
3024:
1914:
In modern programming languages, that would be described by notation similar to
3188:
Moderne Rechenkünstler. Die Industrialisierung der Rechentechnik in Deutschland
297:
274:
264:
236:
3251:"Was ist Informatik? Zur Entstehung des Faches an den deutschen Universitäten"
2957:
1693:, and reading value of that variable also means executing related subprogram.
3696:
3602:
3594:
2912:
1941:
First row contains variable kind, then variable number marked with letter V (
488:
So, a sequence of eight bits (which in modern computing could be regarded as
420:
312:
304:
285:. In 1945, Zuse described Plankalkül in an unpublished book. The collapse of
204:
184:
180:
155:
3617:
Plankalkül: The First High-Level Programming Language and its Implementation
3611:
3499:
3214:
2999:
2862:
2820:(in a linear transcription) that calculates the maximum of three variables:
1170:
board (pieces positions, describes which piece each of 64 squares contains)
350:, will yet come to life." He expressed disappointment that the designers of
3313:(GMD) / Bundesministerium für Bildung und Wissenschaft (BMBW). BMBW-GMD-63.
3218:
447:
286:
3465:
2906:
3564:
3548:
3486:
3302:
3210:
3004:"Konrad Zuses Plankalkül — Seine Genese und eine moderne Implementierung"
308:
259:
131:
51:
20:
2944:
Hellige, Hans Dieter, ed. (January 2004) . Written at Bremen, Germany.
3586:
1366:
462:– yes-no value in Zuse's terminology). It is denoted by the identifier
379:
3168:
1111:
piece on a board (for example L00, 00L; 00L0 — white king on e2)
921:
Coordinate of chess board (it has size 8x8 so 3 bits are just enough)
2876:
102:
3366:
2802:
2678:
1926:(although to access a single bit in modern programming languages a
1338:
830:). User defined types are identified by letter A with number, like
351:
106:
354:
never acknowledged the influence of Plankalkül on their own work.
3392:
Konrad Zuses Plankalkül als Vorläufer moderner Programmiermodelle
2673:
2623:
1904:{\displaystyle {\begin{matrix}V\\0\\0\cdot i\cdot j\end{matrix}}}
3559:] (unpublished manuscript) (in German). Zuse Papers 045/018.
3217:; Wagner, G.; Scharf, Ludmila; Schöttker-Söhl , Susanne (eds.).
2761:. Conditional control flow took the form of a guarded statement
2695:
The left side of assignment operator is used for an expression (
292:
At that time the only two working computers in the world were
596:. There also exists a shortened notation, so one could write
328:
293:
3610:
3307:
Der Plankalkül. Kommentierter Nachdruck der Fassung von 1945
2998:
2946:
Geschichten der Informatik. Visionen, Paradigmen, Leitmotive
2773:
was true. There was also an iteration operator, of the form
2528:
is analogous to the more traditional mathematical equation:
3160:
2621:
There are claims that Konrad Zuse initially used the glyph
489:
446:
The only primitive data type in the Plankalkül is a single
435:
343:
1850:{\displaystyle {\begin{matrix}V\\0\\0\cdot i\end{matrix}}}
806:) in Plankalkül consists of 3 elements: structured value (
403:), which can be used to represent geometrical structures.
1949:), then indexes of variable subcomponents marked with K (
1709:). When, for example, program receives input in variable
289:, however, prevented him from submitting his manuscript.
3326:
Der PLANKALKÜL im Vergleich mit algorithmischen Sprachen
3259:(in German) (1 ed.). Berlin / Heidelberg, Germany:
3015:(in German) (1 ed.). Berlin / Heidelberg, Germany:
2948:(in German) (1 ed.). Berlin / Heidelberg, Germany:
1655:
is available for other subprograms under the identifier
980:
square of the board (for example L00, 00L denotes e2 in
2413:
Z5-th element of variable V3. Equivalent to expression
281:, who expressed appreciation for Zuse's utilization of
3677:
3435:
3433:
3431:
3429:
3427:
3425:
3423:
3421:
3357:
Description of Plankalkül-Compiler by Wolfgang Mauerer
2688:
The variable that stores the result of an assignment (
1865:
1817:
1775:
1717:
1663:
1628:
1511:
1476:
1441:
3419:
3417:
3415:
3413:
3411:
3409:
3407:
3405:
3403:
3401:
3365:(in German). Implementation in German. Archived from
2789:("computation plan"). He envisioned what he called a
2709:
2657:
2633:
2537:
2468:
2434:
2377:
2298:
2221:
2189:
2169:
2088:
2060:
2040:
2017:
1994:
1974:
1863:
1815:
1773:
1750:
1715:
1661:
1626:
1603:
1571:
1548:
1509:
1474:
1439:
1347:
1314:
1291:
1268:
1204:
1180:
1145:
1121:
1077:
1053:
1018:
994:
955:
931:
896:
872:
836:
769:
749:
729:
706:
686:
663:
631:
602:
567:
547:
527:
498:
468:
3309:(in German). Vol. 63. Sankt Augustin, Germany:
3676:(in German and English). 2014-08-21. Archived from
2952:. pp. 45, 56, 89, 104–105, 113, 152, 216–217.
1802:{\displaystyle {\begin{matrix}V\\0\\0\end{matrix}}}
3398:
3091:
3089:
3087:
3085:
3083:
3081:
2855:
2727:
2663:
2639:
2610:
2517:
2440:
2386:
2361:
2278:
2204:
2175:
2153:
2066:
2046:
2026:
2003:
1980:
1903:
1849:
1801:
1759:
1736:
1686:{\displaystyle {\begin{matrix}R17\\0\end{matrix}}}
1685:
1647:
1612:
1586:
1557:
1530:
1495:
1460:
1356:
1329:
1300:
1277:
1252:
1189:
1160:
1130:
1101:
1062:
1033:
1003:
970:
940:
911:
881:
845:
787:
755:
735:
712:
692:
672:
646:
617:
588:
553:
533:
513:
477:
390:. The Plankalkül provides a data structure called
3311:Gesellschaft für Mathematik und Datenverarbeitung
3057:"Why is propositional logic not Turing complete?"
2753:Boolean values were represented as integers with
2651:. Knuth and Pardo believe that Zuse always wrote
1531:{\displaystyle {\begin{matrix}C\\31\end{matrix}}}
370:Plankalkül has drawn comparisons to the language
3694:
3105:"The Early Development of Programming Languages"
1737:{\displaystyle {\begin{matrix}V\\0\end{matrix}}}
1648:{\displaystyle {\begin{matrix}R\\0\end{matrix}}}
1496:{\displaystyle {\begin{matrix}Z\\2\end{matrix}}}
1461:{\displaystyle {\begin{matrix}V\\0\end{matrix}}}
3078:
861:Zuse used a lot of examples from chess theory:
822:) and possible restriction on possible values (
3511:Encyclopedia of computers and computer history
2939:
2937:
2935:
2933:
2931:
2929:
2927:
2872:The First Computers: History and Architectures
1696:
191:'s book on elementary mathematical logic (see
3577:(6). Karlsruhe / Stuttgart / Basel, Germany:
2861:
2627:as a sign for assignment, and started to use
3689:(NB. Plankalkül Java applets and documents.)
3439:
3350:
3317:
3137:
3135:
3133:
3131:
2777:} which repeats until all guards are false.
1043:piece (for example, 00L0 — white king)
398:
3205:
3203:
3201:
3176:
2924:
342:and presented at the Annual Meeting of the
3492:
3380:
3095:
3049:
2672:
2622:
16:Programming language designed 1942 to 1945
3295:
3128:
2899:
2816:The following example defines a function
1933:
173:
3239:
3220:Der Plankalkül (In der Fassung von 1945)
3198:
1364: — information about cell on which
253:
170:refers to a formal system for planning.
134:between 1942 and 1945. It was the first
3713:Non-English-based programming languages
3634:
3360:
3323:
3254:
3182:
3152:IEEE Annals of the History of Computing
3010:
2943:
2423:
307:, and move it to the Alpine village of
3695:
2417:in many modern programming languages.
1857: — piece on square number i, and
3703:Programming languages created in 1948
3498:
3386:
3141:
2905:
425:composite types are arrays and tuples
382:, conditional statements, iteration,
378:. It includes assignment statements,
130:designed for engineering purposes by
121:
3718:German inventions of the Nazi period
3563:
3547:
3301:
3209:
2797:, something today would be called a
1253:{\displaystyle (A5,S0,S1\cdot 4,A2)}
431:contains a for loop and a while loop
217:
3245:
2918:World Scientific Publishing Company
13:
3541:
589:{\displaystyle m\times n\times S0}
416:functions do not support recursion
14:
3744:
3662:
3253:. In Hellige, Hans Dieter (ed.).
3009:. In Hellige, Hans Dieter (ed.).
2838:Timeline of programming languages
409:Some features of the Plankalkül:
3708:Procedural programming languages
3363:"Der Plankalkül von Konrad Zuse"
3361:Mauerer, Wolfgang (2016-06-03).
2833:History of programming languages
2741:
2459:Zuse wrote that the expression:
2406:
2402:
2079:
1426:) — marked with a letter R.
1415:) — marked with a letter С.
1404:) — marked with a letter Z.
1396:Intermediate, temporary values (
1393:) — marked with a letter V.
863:
428:contains conditional expressions
193:Principles of Mathematical Logic
3733:1940s establishments in Germany
3649:from the original on 2023-11-02
3227:from the original on 2015-04-16
3190:(in German). München, Germany:
3067:from the original on 2023-11-02
2785:Zuse called a single program a
2774:
2770:
2766:
2762:
2758:
2754:
2748:
1341:(2 for white and 2 for black),
788:{\displaystyle (\sigma ,\tau )}
680:could have two possible values
269:where Zuse worked on Plankalkül
138:to be designed for a computer.
136:high-level programming language
2780:
2658:
2634:
2485:
2448:», and called it yields-sign (
2435:
1376:
1247:
1205:
1096:
1078:
782:
770:
365:
258:Historical marker on house in
164:Hilbert-style deduction system
1:
2848:
2843:List of programming languages
2728:{\displaystyle =,\neq ,\leq }
1911:bit number j of that piece.
521:, and Boolean matrix of size
441:
3674:Konrad Zuse Internet Archive
3635:Bruines, Bram (2010-01-08).
3269:10.1007/978-3-642-18631-8_17
2664:{\displaystyle \Rightarrow }
2640:{\displaystyle \Rightarrow }
2441:{\displaystyle \Rightarrow }
162:, the original name for the
7:
3515:Fitzroy Dearborn Publishers
3025:10.1007/978-3-642-18631-8_9
2826:
2765:, which executed the block
2163:variable V3 — list of
1809: — gives board state,
1697:Accessing elements by index
1161:{\displaystyle 64\times A3}
856:
853:– first user defined type.
63:; 76 years ago
10:
3749:
2808:
971:{\displaystyle 2\times A1}
647:{\displaystyle n\times S0}
514:{\displaystyle 8\times S0}
18:
3453:Communications of the ACM
3324:Hohmann, Joachim (1979).
3101:Pardo, Luis Isidoro Trabb
2958:10.1007/978-3-642-18631-8
2205:{\displaystyle S1\cdot n}
1597:Output value of program
1587:{\displaystyle P5\cdot 7}
1330:{\displaystyle S1\cdot 4}
1034:{\displaystyle S1\cdot 4}
912:{\displaystyle S1\cdot 3}
723:Record of two components
618:{\displaystyle S1\cdot n}
384:floating-point arithmetic
360:Free University of Berlin
101:
96:
84:
76:
72:– concept first published
57:
45:
33:
3443:; Wössner, Hans (1972).
3330:S. Toeche-Mittler-Verlag
2775:W { A -> X; B -> Y
2183:pairs of values of type
1620:saved there in variable
1308: — player to move,
248:—Konrad Zuse's notebook
221:
19:Not to be confused with
2647:under the influence of
1391:Eingabewerte, Variablen
1337: — possibility of
1102:{\displaystyle (A2,A3)}
736:{\displaystyle \sigma }
561: is described by
400:verallgemeinerter Graph
388:goal-directed execution
235:; study of intervals =
203:). After finishing the
123:[ˈplaːnkalkyːl]
3670:"Plankalkül-Programme"
2729:
2700:
2665:
2641:
2612:
2519:
2453:
2442:
2388:
2363:
2280:
2206:
2177:
2155:
2068:
2048:
2034:could be shortened to
2028:
2005:
1982:
1962:
1954:
1946:
1934:Two-dimensional syntax
1905:
1851:
1803:
1761:
1738:
1706:
1687:
1649:
1614:
1588:
1559:
1532:
1497:
1462:
1423:
1412:
1401:
1390:
1358:
1331:
1302:
1279:
1254:
1191:
1162:
1132:
1103:
1064:
1035:
1005:
972:
942:
913:
883:
847:
827:
819:
814:), pragmatic meaning (
811:
803:
789:
757:
737:
714:
694:
674:
648:
619:
590:
555:
535:
515:
479:
459:
399:
333:
270:
233:propositional calculus
229:
209:propositional calculus
201:Bedingungskombinatorik
200:
174:History of programming
3570:Archiv der Mathematik
3466:10.1145/361454.361515
3263:. pp. 473–498 .
3019:. pp. 215–235 .
2730:
2666:
2642:
2613:
2520:
2443:
2389:
2364:
2281:
2207:
2178:
2156:
2069:
2049:
2029:
2006:
1983:
1906:
1852:
1804:
1762:
1739:
1688:
1650:
1615:
1589:
1560:
1533:
1498:
1463:
1359:
1332:
1303:
1280:
1255:
1192:
1163:
1133:
1104:
1065:
1036:
1006:
973:
943:
914:
884:
848:
790:
758:
756:{\displaystyle \tau }
738:
715:
695:
675:
649:
620:
591:
556:
536:
516:
480:
339:Archiv der Mathematik
317:
257:
224:Begriffen zu klären.
119:German pronunciation:
3513:. Chicago / London:
2707:
2655:
2631:
2535:
2466:
2432:
2424:Assignment operation
2375:
2296:
2219:
2187:
2167:
2086:
2058:
2038:
2015:
1992:
1972:
1930:is typically used).
1861:
1813:
1771:
1748:
1713:
1659:
1624:
1601:
1569:
1546:
1507:
1472:
1437:
1345:
1312:
1289:
1266:
1202:
1178:
1143:
1119:
1075:
1051:
1016:
992:
953:
929:
894:
870:
834:
767:
747:
727:
704:
684:
661:
629:
600:
565:
545:
525:
496:
466:
413:only local variables
183:) being inspired by
128:programming language
3441:Bauer, Friedrich L.
3145:(April–June 1997).
3097:Knuth, Donald Ervin
2791:Planfertigungsgerät
1767:(game state), then
1760:{\displaystyle A10}
1613:{\displaystyle P13}
1558:{\displaystyle P13}
1190:{\displaystyle A10}
86:Plankalkül-Compiler
58:First appeared
30:
3587:10.1007/BF02038459
3388:Giloi, Wolfgang K.
3143:Giloi, Wolfgang K.
2795:punched film stock
2725:
2661:
2637:
2608:
2606:
2515:
2513:
2438:
2387:{\displaystyle S0}
2384:
2359:
2357:
2276:
2274:
2202:
2173:
2151:
2149:
2064:
2044:
2027:{\displaystyle S1}
2024:
2004:{\displaystyle S0}
2001:
1978:
1901:
1899:
1847:
1845:
1799:
1797:
1757:
1734:
1732:
1683:
1681:
1645:
1643:
1610:
1584:
1555:
1528:
1526:
1493:
1491:
1458:
1456:
1357:{\displaystyle A2}
1354:
1327:
1301:{\displaystyle S0}
1298:
1278:{\displaystyle A5}
1275:
1250:
1187:
1158:
1131:{\displaystyle A5}
1128:
1099:
1063:{\displaystyle A4}
1060:
1031:
1004:{\displaystyle A3}
1001:
982:algebraic notation
968:
941:{\displaystyle A2}
938:
909:
882:{\displaystyle A1}
879:
846:{\displaystyle A1}
843:
785:
753:
733:
710:
690:
673:{\displaystyle S0}
670:
644:
615:
586:
551:
531:
511:
478:{\displaystyle S0}
475:
376:relational algebra
271:
28:
3723:German inventions
3579:Birkhäuser Verlag
3390:(November 1990),
3278:978-3-540-00217-8
3249:(January 2004) .
3169:10.1109/85.586068
3034:978-3-642-62208-3
2967:978-3-540-00217-8
2649:Heinz Rutishauser
2421:
2420:
2398:
2397:
2176:{\displaystyle m}
2067:{\displaystyle 1}
2047:{\displaystyle 0}
1981:{\displaystyle S}
1955:Komponenten-Index
1707:Komponenten-Index
1374:
1373:
1370:move is possible
713:{\displaystyle L}
693:{\displaystyle 0}
554:{\displaystyle n}
534:{\displaystyle m}
325:Heinz Rutishauser
252:
251:
112:
111:
3740:
3688:
3686:
3685:
3657:
3655:
3654:
3648:
3641:
3628:
3622:
3606:
3560:
3535:
3534:
3532:
3531:
3508:
3496:
3490:
3484:
3482:
3476:. Archived from
3449:
3437:
3396:
3395:
3384:
3378:
3377:
3375:
3374:
3354:
3348:
3343:
3321:
3315:
3314:
3299:
3293:
3290:
3243:
3237:
3235:
3233:
3232:
3207:
3196:
3195:
3192:C.H. Beck Verlag
3184:Petzold, Hartmut
3180:
3174:
3172:
3139:
3126:
3125:
3123:
3122:
3116:
3109:
3093:
3076:
3075:
3073:
3072:
3053:
3047:
3045:
3043:
3037:. Archived from
3008:
2996:
2981:
2979:
2941:
2922:
2921:
2903:
2897:
2896:
2894:
2893:
2886:978-0-26268137-7
2859:
2819:
2776:
2772:
2768:
2764:
2760:
2756:
2745:
2734:
2732:
2731:
2726:
2684:
2676:
2670:
2668:
2667:
2662:
2646:
2644:
2643:
2638:
2626:
2617:
2615:
2614:
2609:
2607:
2593:
2575:
2541:
2524:
2522:
2521:
2516:
2514:
2506:
2472:
2447:
2445:
2444:
2439:
2416:
2410:
2403:
2393:
2391:
2390:
2385:
2368:
2366:
2365:
2360:
2358:
2302:
2285:
2283:
2282:
2277:
2275:
2225:
2211:
2209:
2208:
2203:
2182:
2180:
2179:
2174:
2160:
2158:
2157:
2152:
2150:
2117:
2092:
2080:
2073:
2071:
2070:
2065:
2053:
2051:
2050:
2045:
2033:
2031:
2030:
2025:
2010:
2008:
2007:
2002:
1987:
1985:
1984:
1979:
1925:
1921:
1917:
1910:
1908:
1907:
1902:
1900:
1856:
1854:
1853:
1848:
1846:
1808:
1806:
1805:
1800:
1798:
1766:
1764:
1763:
1758:
1743:
1741:
1740:
1735:
1733:
1692:
1690:
1689:
1684:
1682:
1654:
1652:
1651:
1646:
1644:
1619:
1617:
1616:
1611:
1593:
1591:
1590:
1585:
1564:
1562:
1561:
1556:
1537:
1535:
1534:
1529:
1527:
1502:
1500:
1499:
1494:
1492:
1467:
1465:
1464:
1459:
1457:
1363:
1361:
1360:
1355:
1336:
1334:
1333:
1328:
1307:
1305:
1304:
1299:
1284:
1282:
1281:
1276:
1259:
1257:
1256:
1251:
1196:
1194:
1193:
1188:
1167:
1165:
1164:
1159:
1137:
1135:
1134:
1129:
1108:
1106:
1105:
1100:
1069:
1067:
1066:
1061:
1040:
1038:
1037:
1032:
1010:
1008:
1007:
1002:
977:
975:
974:
969:
947:
945:
944:
939:
918:
916:
915:
910:
888:
886:
885:
880:
864:
852:
850:
849:
844:
794:
792:
791:
786:
762:
760:
759:
754:
742:
740:
739:
734:
719:
717:
716:
711:
699:
697:
696:
691:
679:
677:
676:
671:
653:
651:
650:
645:
624:
622:
621:
616:
595:
593:
592:
587:
560:
558:
557:
552:
540:
538:
537:
532:
520:
518:
517:
512:
492:) is denoted by
484:
482:
481:
476:
402:
331:
283:logical calculus
268:
218:
125:
120:
71:
69:
64:
47:Designed by
31:
27:
3748:
3747:
3743:
3742:
3741:
3739:
3738:
3737:
3693:
3692:
3683:
3681:
3668:
3665:
3652:
3650:
3646:
3639:
3620:
3544:
3542:Further reading
3539:
3538:
3529:
3527:
3525:
3517:. p. 634.
3506:
3497:
3493:
3480:
3447:
3438:
3399:
3385:
3381:
3372:
3370:
3355:
3351:
3340:
3322:
3318:
3300:
3296:
3279:
3261:Springer-Verlag
3244:
3240:
3236:(1+1+180 pages)
3230:
3228:
3208:
3199:
3181:
3177:
3140:
3129:
3120:
3118:
3114:
3107:
3103:(August 1976).
3094:
3079:
3070:
3068:
3059:. Mathematics.
3055:
3054:
3050:
3041:
3035:
3017:Springer-Verlag
3006:
2997:
2984:
2980:(xii+514 pages)
2968:
2950:Springer-Verlag
2942:
2925:
2904:
2900:
2891:
2889:
2887:
2879:. p. 292.
2860:
2856:
2851:
2829:
2824:
2817:
2811:
2783:
2751:
2708:
2705:
2704:
2682:
2656:
2653:
2652:
2632:
2629:
2628:
2605:
2604:
2592:
2587:
2581:
2580:
2574:
2569:
2563:
2562:
2557:
2552:
2538:
2536:
2533:
2532:
2512:
2511:
2505:
2500:
2494:
2493:
2488:
2483:
2469:
2467:
2464:
2463:
2433:
2430:
2429:
2426:
2414:
2376:
2373:
2372:
2356:
2355:
2350:
2344:
2343:
2326:
2320:
2319:
2314:
2308:
2307:
2299:
2297:
2294:
2293:
2273:
2272:
2249:
2243:
2242:
2237:
2231:
2230:
2222:
2220:
2217:
2216:
2188:
2185:
2184:
2168:
2165:
2164:
2148:
2147:
2124:
2118:
2116:
2110:
2109:
2104:
2098:
2097:
2089:
2087:
2084:
2083:
2059:
2056:
2055:
2039:
2036:
2035:
2016:
2013:
2012:
1993:
1990:
1989:
1973:
1970:
1969:
1947:Variablen-Index
1936:
1923:
1919:
1915:
1898:
1897:
1879:
1878:
1872:
1871:
1864:
1862:
1859:
1858:
1844:
1843:
1831:
1830:
1824:
1823:
1816:
1814:
1811:
1810:
1796:
1795:
1789:
1788:
1782:
1781:
1774:
1772:
1769:
1768:
1749:
1746:
1745:
1731:
1730:
1724:
1723:
1716:
1714:
1711:
1710:
1699:
1680:
1679:
1673:
1672:
1662:
1660:
1657:
1656:
1642:
1641:
1635:
1634:
1627:
1625:
1622:
1621:
1602:
1599:
1598:
1570:
1567:
1566:
1547:
1544:
1543:
1525:
1524:
1518:
1517:
1510:
1508:
1505:
1504:
1490:
1489:
1483:
1482:
1475:
1473:
1470:
1469:
1455:
1454:
1448:
1447:
1440:
1438:
1435:
1434:
1418:Output values (
1379:
1346:
1343:
1342:
1313:
1310:
1309:
1290:
1287:
1286:
1285: — board,
1267:
1264:
1263:
1203:
1200:
1199:
1179:
1176:
1175:
1144:
1141:
1140:
1120:
1117:
1116:
1076:
1073:
1072:
1052:
1049:
1048:
1017:
1014:
1013:
993:
990:
989:
954:
951:
950:
930:
927:
926:
895:
892:
891:
871:
868:
867:
859:
835:
832:
831:
768:
765:
764:
748:
745:
744:
728:
725:
724:
705:
702:
701:
685:
682:
681:
662:
659:
658:
630:
627:
626:
601:
598:
597:
566:
563:
562:
546:
543:
542:
526:
523:
522:
497:
494:
493:
467:
464:
463:
444:
368:
348:Sleeping Beauty
332:
323:
279:Heinrich Scholz
262:
241:
226:
213:Turing-complete
176:
118:
79:implementations
67:
65:
62:
24:
17:
12:
11:
5:
3746:
3736:
3735:
3730:
3725:
3720:
3715:
3710:
3705:
3691:
3690:
3664:
3663:External links
3661:
3660:
3659:
3632:
3627:on 2006-05-01.
3608:
3561:
3543:
3540:
3537:
3536:
3523:
3491:
3483:on 2009-02-20.
3460:(7): 678–685.
3397:
3379:
3349:
3338:
3316:
3294:
3277:
3238:
3197:
3175:
3127:
3077:
3063:. 2013-04-01.
3048:
3044:on 2006-05-01.
3033:
2982:
2966:
2923:
2920:. p. 791.
2909:, ed. (2012).
2898:
2885:
2853:
2852:
2850:
2847:
2846:
2845:
2840:
2835:
2828:
2825:
2822:
2810:
2807:
2782:
2779:
2750:
2747:
2724:
2721:
2718:
2715:
2712:
2660:
2636:
2619:
2618:
2603:
2600:
2597:
2594:
2591:
2588:
2586:
2583:
2582:
2579:
2576:
2573:
2570:
2568:
2565:
2564:
2561:
2558:
2556:
2553:
2551:
2548:
2545:
2542:
2540:
2526:
2525:
2510:
2507:
2504:
2501:
2499:
2496:
2495:
2492:
2489:
2487:
2484:
2482:
2479:
2476:
2473:
2471:
2454:Ergibt-Zeichen
2437:
2425:
2422:
2419:
2418:
2411:
2396:
2395:
2383:
2380:
2369:
2354:
2351:
2349:
2346:
2345:
2342:
2339:
2336:
2333:
2330:
2327:
2325:
2322:
2321:
2318:
2315:
2313:
2310:
2309:
2306:
2303:
2301:
2290:
2289:
2286:
2271:
2268:
2265:
2262:
2259:
2256:
2253:
2250:
2248:
2245:
2244:
2241:
2238:
2236:
2233:
2232:
2229:
2226:
2224:
2213:
2212:
2201:
2198:
2195:
2192:
2172:
2161:
2146:
2143:
2140:
2137:
2134:
2131:
2128:
2125:
2123:
2120:
2119:
2115:
2112:
2111:
2108:
2105:
2103:
2100:
2099:
2096:
2093:
2091:
2063:
2043:
2023:
2020:
2000:
1997:
1977:
1963:Struktur-Index
1935:
1932:
1896:
1893:
1890:
1887:
1884:
1881:
1880:
1877:
1874:
1873:
1870:
1867:
1866:
1842:
1839:
1836:
1833:
1832:
1829:
1826:
1825:
1822:
1819:
1818:
1794:
1791:
1790:
1787:
1784:
1783:
1780:
1777:
1776:
1756:
1753:
1729:
1726:
1725:
1722:
1719:
1718:
1698:
1695:
1678:
1675:
1674:
1671:
1668:
1665:
1664:
1640:
1637:
1636:
1633:
1630:
1629:
1609:
1606:
1583:
1580:
1577:
1574:
1554:
1551:
1540:
1539:
1523:
1520:
1519:
1516:
1513:
1512:
1488:
1485:
1484:
1481:
1478:
1477:
1453:
1450:
1449:
1446:
1443:
1442:
1428:
1427:
1416:
1405:
1394:
1385:Input values (
1378:
1375:
1372:
1371:
1353:
1350:
1326:
1323:
1320:
1317:
1297:
1294:
1274:
1271:
1260:
1249:
1246:
1243:
1240:
1237:
1234:
1231:
1228:
1225:
1222:
1219:
1216:
1213:
1210:
1207:
1197:
1186:
1183:
1172:
1171:
1168:
1157:
1154:
1151:
1148:
1138:
1127:
1124:
1113:
1112:
1109:
1098:
1095:
1092:
1089:
1086:
1083:
1080:
1070:
1059:
1056:
1045:
1044:
1041:
1030:
1027:
1024:
1021:
1011:
1000:
997:
986:
985:
978:
967:
964:
961:
958:
948:
937:
934:
923:
922:
919:
908:
905:
902:
899:
889:
878:
875:
858:
855:
842:
839:
784:
781:
778:
775:
772:
763:is written as
752:
732:
709:
689:
669:
666:
643:
640:
637:
634:
614:
611:
608:
605:
585:
582:
579:
576:
573:
570:
550:
530:
510:
507:
504:
501:
474:
471:
443:
440:
439:
438:
432:
429:
426:
423:
419:only supports
417:
414:
367:
364:
321:
298:Harvard Mark I
250:
249:
246:
243:
242:
237:lattice theory
227:
175:
172:
160:Hilbert-Kalkül
110:
109:
99:
98:
94:
93:
82:
81:
74:
73:
59:
55:
54:
49:
43:
42:
37:
15:
9:
6:
4:
3:
2:
3745:
3734:
3731:
3729:
3726:
3724:
3721:
3719:
3716:
3714:
3711:
3709:
3706:
3704:
3701:
3700:
3698:
3680:on 2014-08-21
3679:
3675:
3671:
3667:
3666:
3645:
3638:
3633:
3630:
3626:
3619:
3618:
3613:
3609:
3604:
3600:
3596:
3592:
3588:
3584:
3580:
3576:
3573:(in German).
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3393:
3389:
3383:
3369:on 2016-06-03
3368:
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3339:3-87820-028-5
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3287:3-540-00217-0
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3247:Coy, Wolfgang
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3117:on 2017-09-12
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2916:. Singapore:
2915:
2914:
2913:Roger Penrose
2908:
2907:Zenil, Héctor
2902:
2888:
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2874:
2873:
2868:
2867:Hashagen, Ulf
2864:
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1956:
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1424:Resultatwerte
1421:
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1402:Zwischenwerte
1399:
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721:
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687:
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612:
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583:
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472:
469:
461:
460:Ja-Nein-Werte
457:
453:
449:
437:
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430:
427:
424:
422:
421:call by value
418:
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313:Bad Hindelang
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156:formal system
153:
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3682:. Retrieved
3678:the original
3673:
3651:. Retrieved
3637:"Plankalkül"
3625:the original
3616:
3574:
3568:
3565:Zuse, Konrad
3556:
3552:
3549:Zuse, Konrad
3528:. Retrieved
3524:1-57958235-4
3510:
3504:"Plankalkül"
3494:
3478:the original
3457:
3451:
3391:
3382:
3371:. Retrieved
3367:the original
3352:
3344:(136 pages)
3325:
3319:
3306:
3303:Zuse, Konrad
3297:
3255:
3241:
3229:. Retrieved
3219:
3211:Zuse, Konrad
3187:
3178:
3156:
3150:
3119:. Retrieved
3112:the original
3069:. Retrieved
3060:
3051:
3039:the original
3011:
2945:
2910:
2901:
2890:. Retrieved
2871:
2857:
2815:
2812:
2790:
2786:
2784:
2752:
2749:Control flow
2740:
2737:
2694:
2687:
2620:
2527:
2458:
2427:
2399:
2076:
1968:In the line
1967:
1940:
1937:
1913:
1700:
1596:
1541:
1429:
1380:
1365:
1262:game state (
860:
828:Beschränkung
797:
722:
656:
487:
445:
408:
405:
392:generalized
391:
369:
356:
337:
334:
318:
302:
291:
287:Nazi Germany
272:
230:
222:
177:
167:
159:
145:
144:(from Latin
141:
140:
114:
113:
85:
25:
3728:Konrad Zuse
3612:Rojas, Raúl
3581:: 441–449.
3500:Rojas, Raúl
3394:(in German)
3215:Rojas, Raúl
3046:(21 pages)
3000:Rojas, Raúl
2863:Rojas, Raúl
2781:Terminology
2671:, and that
1407:Constants (
1377:Identifiers
625:instead of
380:subroutines
366:Description
309:Hinterstein
263: [
260:Hinterstein
154:term for a
132:Konrad Zuse
52:Konrad Zuse
21:Plan Calcul
3697:Categories
3684:2017-10-04
3658:(24 pages)
3653:2023-11-02
3642:(Thesis).
3631:(22 pages)
3530:2023-05-26
3373:2017-10-03
3231:2023-11-01
3121:2017-12-28
3071:2023-11-02
2892:2013-10-25
2849:References
2799:translator
2787:Rechenplan
2077:Examples:
1413:Constanten
1367:en passant
442:Data types
168:Plankalkül
115:Plankalkül
97:Influenced
40:Procedural
29:Plankalkül
3607:(9 pages)
3603:0003-889X
3595:1420-8938
3213:(1946) .
3173:(8 pages)
3163:: 17–24.
2877:MIT Press
2763:A -> B
2723:≤
2717:≠
2659:⇒
2635:⇒
2486:⇒
2436:⇒
2338:⋅
2332:⋅
2267:⋅
2261:×
2255:×
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2142:⋅
2136:×
2130:×
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1886:⋅
1838:⋅
1579:⋅
1322:⋅
1233:⋅
1150:×
1026:⋅
960:×
904:⋅
780:τ
774:σ
751:τ
731:σ
636:×
610:⋅
578:×
572:×
503:×
374:, and to
311:(part of
189:Ackermann
150:) is the
103:Superplan
90:FU Berlin
3644:Archived
3551:(1943).
3502:(2001).
3474:17681101
3346:Contents
3332:(stmv).
3305:(1972).
3225:Archived
3186:(1992).
3065:Archived
2869:(2002).
2827:See also
2803:compiler
2701:Ausdruck
2679:ALGOL 58
1744:of type
1339:castling
857:Examples
812:Struktur
352:ALGOL 58
322:—
147:calculus
107:ALGOL 58
35:Paradigm
2809:Example
2755:FALSE=0
2735:etc.).
2690:l-value
1928:bitmask
452:Boolean
187:'s and
185:Hilbert
158:—as in
126:) is a
92:in 2000
88:by the
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2759:TRUE=1
2697:German
2450:German
1988:types
1959:German
1951:German
1943:German
1703:German
1420:German
1409:German
1398:German
1387:German
824:German
816:German
808:German
800:German
798:Type (
456:German
197:German
152:German
142:Kalkül
77:Major
3647:(PDF)
3640:(PDF)
3621:(PDF)
3591:eISSN
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3470:S2CID
3448:(PDF)
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3115:(PDF)
3108:(PDF)
3042:(PDF)
3007:(PDF)
657:Type
394:graph
329:ALGOL
294:ENIAC
275:chess
267:]
3599:ISSN
3519:ISBN
3487:HTML
3334:ISBN
3283:ISBN
3273:ISBN
3161:IEEE
3029:ISBN
2972:ISBN
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2818:max3
2757:and
2054:and
2011:and
1538:etc.
743:and
700:and
490:byte
436:goto
344:GAMM
296:and
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