Plankalkul Interpreter

The first high-level programming language, running again.

Plankalkul ("Plan Calculus") was designed by Konrad Zuse between 1942-1945. Building on the pioneering work of Rojas et al. (FU Berlin, 2000) who created the first implementation, this package provides an accessible Python interface.

Installation

pip install plankalkul

Quick Start

from plankalkul import run

# Calculate factorial
result = run('''
    P1 factorial (V0[:8.0]) => R0[:8.0]
        1 => R0[:8.0]
        1 => Z0[:8.0]
        W [ Z0[:8.0] * R0[:8.0] => R0[:8.0]
            Z0[:8.0] + 1 => Z0[:8.0] ] (Z0[:8.0] <= V0[:8.0])
    END
''', 5)

print(result['R0'])  # 120

Or run from command line:

plankalkul  # Runs demo programs

Why This Matters

Feature	Plankalkul (1945)	First "Modern" Language
Data structures	Yes	C (1972): 27 years later
User-defined types	Yes	C (1972): 27 years later
Assertions	Yes	Eiffel (1986): 41 years later
Structured control	Yes	ALGOL (1960): 15 years later

The first language had features that took decades to "reinvent".

Language Syntax

Program Structure

P<number> <name> (<parameters>) => <returns>
    <statements>
END

Variables

Prefix	Meaning
V0, V1...	Input parameters
Z0, Z1...	Local/intermediate variables
R0, R1...	Return values

Type Annotations

[:8.0]      ; 8-bit integer
[:1.0]      ; 1-bit (boolean)
[:16.0]     ; 16-bit integer
[:n×m.0]    ; n×m array

Operations

Operation	Symbol	ASCII Alternative
Assignment	→	=>
Multiply	×	*
Divide	:	/
Not equal	≠	!=
Less/equal	≤	<=
Greater/equal	≥	>=
Logical AND	∧	&
Logical OR	∨	|
Logical NOT	¬	!

Control Flow

Conditional:

(condition) => statement

While loop:

W [ statements ] (condition)

Counted loop (W1):

W1 (count) => counter_var { statements }

The W1 loop iterates from 0 to count-1, storing the current iteration in counter_var. This syntax was reconstructed from academic implementations based on Zuse's manuscripts.

Example Programs

Maximum of Two Numbers (Zuse's Original)

P1 max (V0[:8.0], V1[:8.0]) => R0[:8.0]
    V0[:8.0] => R0[:8.0]
    (R0[:8.0] < V1[:8.0]) => V1[:8.0] => R0[:8.0]
END

Factorial

P2 factorial (V0[:8.0]) => R0[:8.0]
    1 => R0[:8.0]
    1 => Z0[:8.0]
    W [ Z0[:8.0] * R0[:8.0] => R0[:8.0]
        Z0[:8.0] + 1 => Z0[:8.0] ] (Z0[:8.0] <= V0[:8.0])
END

Sum of 1 to N

P3 sum (V0[:8.0]) => R0[:8.0]
    0 => R0[:8.0]
    1 => Z0[:8.0]
    W [ R0[:8.0] + Z0[:8.0] => R0[:8.0]
        Z0[:8.0] + 1 => Z0[:8.0] ] (Z0[:8.0] <= V0[:8.0])
END

Factorial using W1 (Advanced Syntax)

P Factorial(V0[:8.0]) => R0[:8.0]
    1 => R0[:8.0]
    W1 (V0[:8.0]) => Z0[:8.0] {
        R0[:8.0] * (Z0[:8.0] + 1) => R0[:8.0]
    }
END

This advanced syntax comes from the Hovestar implementation, reconstructed from Zuse's manuscripts.

Historical Context

Timeline

Year	Event
1936	Zuse builds Z1 (mechanical computer)
1941	Z3 completed (first programmable computer)
1942-45	Plankalkül designed
1943	Z3 destroyed in Allied bombing
1945	WWII ends, Zuse flees with Z4
1948	Zuse writes manuscript "Der Plankalkül"
1972	Plankalkül published
2000	First implementation (FU Berlin)
2025	This implementation (The Ian Index)

Why It Was Forgotten

1. War: Designed during WWII, destroyed in bombing
2. Language barrier: Written in German
3. Isolation: Zuse didn't know about Turing or von Neumann
4. Politics: Work in Nazi Germany carried stigma
5. Commercial failure: No resources to implement

What Zuse Got Right

Plankalkul had features that took decades to "reinvent":

• Data structures (like C structs): reinvented 27 years later
• User-defined types: reinvented 27 years later
• Assertions: reinvented 41 years later
• Strong typing: reinvented 25 years later
• Structured control flow: reinvented 15 years later

Technical Details

Architecture

Source Code → Lexer → Tokens → Parser → AST → Interpreter → Result

Implementation

• Lexer: Handles both Unicode (→, ×, ≤) and ASCII (=>, *, <=) notation
• Parser: Recursive descent parser
• Interpreter: Tree-walking interpreter with variable scoping
• Type System: Basic type checking (integers, booleans, arrays)

License

MIT License — completing Zuse's public domain vision.

Related Projects

🎮 Zuse Chess (1942) — Play Konrad Zuse's chess algorithm in your browser. The first chess program ever written, reconstructed from 78 pages of original manuscripts.

References

1. Zuse, K. (1948). "Der Plankalkül"
2. Rojas, R. et al. (2000). "Plankalkül: The First High-Level Programming Language and its Implementation"
3. Bauer, F.L. & Wössner, H. (1972). "The 'Plankalkül' of Konrad Zuse: A Forerunner of Today's Programming Languages"

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"The significance of Plankalkül lies not in what it became, but in what it could have been."

Konrad Zuse deserves to be remembered.