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.
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.
>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.
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:
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.
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.
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/bl...