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For questions on the formal system in mathematical logic for expressing effective functions, programs and computation, and proofs, using abstract notions of functions and combining them through binding and substitution.

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Algebraic structure generated by primitive graph operations

Perhaps this paper might be tangentially related to the ideas you are developing? Bilal Khan, Kiran Bhutani, Delaram Kahrobaei. A Graphic Generalization of Arithmetic, Electronic Journal of Combinato …