$\mu\lambda\epsilon\delta$-Calculus: A Self Optimizing Language that Seems to Exhibit Paradoxical Transfinite Cognitive Capabilities
Ronie Salgado

TL;DR
This paper introduces a novel self-optimizing language based on a paradoxical transfinite calculus that exhibits fractal-like structures and potential cognitive modeling capabilities.
Contribution
It presents a new calculus, $orce ext{ extmu}orce$, with extensions for modeling self-awareness and demonstrates its properties through a fractal-based optimizer.
Findings
The optimizer produces geometrical fractals resembling black holes.
The calculus always terminates and maintains program isomorphism.
Fractal structures act as efficient program compressors.
Abstract
Formal mathematics and computer science proofs are formalized using Hilbert-Russell-style logical systems which are designed to not admit paradoxes and self-refencing reasoning. These logical systems are natural way to describe and reason syntactic about tree-like data structures. We found that Wittgenstein-style logic is an alternate system whose propositional elements are directed graphs (points and arrows) capable of performing paraconsistent self-referencing reasoning without exploding. Imperative programming language are typically compiled and optimized with SSA-based graphs whose most general representation is the Sea of Node. By restricting the Sea of Nodes to only the data dependencies nodes, we attempted to stablish syntactic-semantic correspondences with the Lambda-calculus optimization. Surprisingly, when we tested our optimizer of the lambda calculus we performed a natural…
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Taxonomy
TopicsEvolutionary Algorithms and Applications · Computability, Logic, AI Algorithms
