Plankalkül

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Contents

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
x̄ (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

Translation Attempts

Here's some (probably badly mangled) attempts at translating some of Zuse's plankalkul papers. I'm gonna try running them through google translator and then manually cleaning them up afterwards.

Uber den Plankalkul

Notes

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

∧
∨
⇒
→
× ×

Hm. ∈σ

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