Editing Plankalkül (section)

===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]]