3 ms·

Great notes! I think it’s also worth noting that Barry Jay has a particularly strong vantage point for unearthing this particular foundational candidate. Firs

• peter_d_sherman 12d ago
  >Great notes! Thank you! >I think it’s also worth noting that Barry Jay has a particularly strong vantage point for unearthing this particular foundational candidate. First, his advisor was Joachim Lambek, who’s responsible for adding Category Theory in the Curry-Howard-Lambek correspondence. Curry-Howard-Lambek correspondence is a very important point, I'm glad you brought it up! >If one looks at Barry’s body of work over his lifetime, it’s no surprise it would culminate into an elegantly beautiful system capable of self-reflection. No, it's not surprising indeed! >I think his 2025 PEPM paper did a great job explaining the ideas to a regular programmer / wannabe academic like myself: https://github.com/barry-jay-personal/typed_tree_calculus/blob/main/typed_program_analysis.pdf https://github.com/barry-jay-personal/typed_tree_calculus/bl... Excellent link! Random thought: From the paper: "The operator [Triangle] (pronounced "node") is a ternary operator)..." I wonder if Tree Calculus (and/or binary trees in general!) could be related to, and/or applied to the Ternary Tau and/or the Balanced Phinary number systems: https://neuraloutlet.wordpress.com/tag/ternary-tau-system/ https://neuraloutlet.wordpress.com/tag/ternary-tau-system/ https://en.wikipedia.org/wiki/Balanced_ternary https://en.wikipedia.org/wiki/Balanced_ternary