[D66] Genesis: A Symbolic Extension of the Turing Machine

[René Oudeweg]

[the way forward?]


A Type System for Genesis:
Structural Modes Beyond the Turing Machine
Anonymous

Abstract

This paper presents a type system for Genesis, a structural extension of 
the Turing machine augmented with four primitive operators: □, △, ◦, and 
. . .
Unlike traditional type systems, Genesis types classify both values and 
modes of computation. We define the typing judgments,
modal kinds, subtyping relations, and safety properties of the system, 
and show that it is sound, stratified, and erasable to a classical 
Turing-complete core.


RO

On 12/27/25 11:22, René Oudeweg wrote:
> [een niet insignificante bijdrage aan de computerwetenschap... /RO]
> 
> 
> 
> 
>   Genesis: A Structural Extension of the Turing Machine
> 
> Anonymous
> 
> 
> Abstract
> The Turing machine provides a minimal and robust model of computation, 
> yet it treats structure, self-reference, and non-halting processes only 
> indirectly. This paper introduces Genesis, a conservative extension of 
> the Turing machine augmented with four primitive operators: □,△, ◦, 
> and . . .
> We define the formal semantics of Genesis, prove its relation to 
> classical Turing computation, and demonstrate how it captures structural 
> persistence, generativity, reflection,and open-ended execution within a 
> single computational framework.
> 
> 
> 
>   RO
> 
> ------------------------------------------------------------------------
> 
> □ state invariant
> △ derive rule R from context
> ○ reflect delta
> … continue
> 
> 
> ------------------------------------------------------------------------
> 
> 
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