Plankalkül

Translated tables (Zuze pp 114-117)

Character table

Symbol	German	Translation	Notes
A	Angabenart	Record type*
B	Beschränkungszeichen	Limitation mark*
C	Constante	Take a guess, brainiac
E	Existenz-Operator
F, G	Funktionszeichen, allgemein	Function markers, universal
I, i, j	Index
K	Komponente	Component indicator
L	Listenzeichen	List marker*
m, n	Gliedzahl von Angaben	Record part indicators*
N	Anzahl der Glieder einer Liste	Number of parts in a list
P	Planzeichen	Plan sign	As in program, as in function
R	Resultatwert	Result value	Write-only
S	Struktur	Structure	Ie array
T	Angabentyp	Record type*
U	Unterplan	Sub-plan
V, v	Variable	Variable	Ie. temporary
W	Wiederholungsplan	Repeat plan*	wiederholen = bring back; this is essentially the looping construct. It might be more like Ruby's inject than a traditional loop though
x, y	gebundne Variable, auch allgemeine Variable	Bound variables and also universal variables
z	Zwischenwert	Temporary value*
α	variables Angabenartzeichen	Variable record type indicators*
ε	laufend veränderliche Hilfsgröße eines Rechenplanes	Constantly variable help size of a program*	what the christ
κ	variabler Komponentindex	Variable component index
λ	"das Letzte"	"the latest"	Ie. previous
μ	"das Nächste"	"the next"
π	variables Planzeichen	Variable plan marker*
σ, τ	variables Strukturzeichen	Variable structure markers
∏	Produkt
∑	Summe	Sum

* = Possibly worthless translation

Operator table

Operator	German	Translation	Notes
□ (box)	Allgemeines Leerstellenzeichen	Universal empty space mark
∨	Disjunktion	Disjunction	http://en.wikipedia.org/wiki/Logical_disjunction
∧	Konjunktion	Conjunction	http://en.wikipedia.org/wiki/Logical_conjunction
̄x (with macron)	Negation	Negation	Im Sinne des Aussagenkalküls
→	Implikation	Implication	Ie. conditional
≁ (not tilde)	Disvalenz	Not equal
∼	Äquivalenz	Equal
TO	BE	FUCKING	CONTINUED

Spec

Variables

V	parameters (r/o)
Z	temporaries (r/w)
R	results (w/o)
C	constants (?)

Variables are initialized the first time they're assigned to, subsequent assignments are simply normal assignments.

2D syntax 'sidebar'

In the 2D notation there is a vertical column on the right where the value of elements in that row is indicated:

 |Main Line
V|Variable Number
K|Component Number (Komponenten-Index)
S|Comment Line (Struktur-Index)

So, as an example:

 |Z  ^ Z
V|4    2
K|2.3
S|0    0

(from page 8 in the Zuse PDF). This is (probably) equivalent to:

Z4[2.3] ^ Z2

in the linear notation.

Note: not quite sure what the operator means yet, possibly greater-than.

Primitives

The only primitive type is boolean (or a bit). They are denoted by S0.

Arrays

Arrays can be made up of any other data type. For example:

8 × S0

is an array of 8 bits whereas:

n × 4 × S0

is an n-length array with each element being a 4-length array of bits.

Arrays can be subscripted:

 |V
V|0
K|1

means the 1st component of V0 (linear syntax is V0[1]).

Records

Page 2 of Bauer alludes to 'records' of the form (A2, A3). We need more info here.

Operators

Note that this list is vastly incomplete.

=	Equality test
=>	Assignment
+	Addition
-	Subtraction (inferred, may not exist)

The µ operator

 µx(x ∈ V ^ R(x))
        0

Apparently this means 'The next element of V0 for which the procedure call R returns true'.

Conditionals

Conditionals are of the form expression -> statement. There is no else clause. There is also no 'or' for the expression.

Loops

Loops are initiated using the letter W. I don't really understand anything beyond that.

Questions

• Are S (and maybe A) variables or types or constants or what? We know S0 is the boolean bit, S1 is an array of boolean bits and apparently S2 is a constant of some type.

• What is the difference between S and A?

• How is a function declared? The Bauer PDF gives this syntax:

P17 |R(V) => (R, R)
   V|  0      0  1
   S|  α      α  0

but.. how is this function called?, how do you actually define stuff to occur in the function, is the 'FIN' end symbol used?

• Are the S lines actually taken into account? Do they define the structure of the index?

Implementation

Is the 2d syntax representable in ascii in some obvious way? What are the advantages of the 2d syntax?

Links

• The Life and Work of Konrad Zuse (by Horst Zuse) Part 5: Konrad Zuse's Plankakül Programming Language (1942-1945/6)
• Konrad Zuse Internet Archive

Notes

I'm looking through my character map for some useful HTML entities:

∧	∧
∨	∨
⇒	⇒
→	→
×	×

Hm. ∈σ