1. Combinators as primitives of function composition The discussion treats combinators as the basic building blocks for higher‑order functions, often illustrated with “bird” names (K, I, W, etc.).
"Many primitives in array languages match the behaviour of certain combinators..." – leethomp
2. Practical impact in array languages like APL/BQN
Users note that these ideas give array languages a terse, compositional syntax, turning whole numeric algorithms into a few symbols.
"It's more like a recipe (for functions)." – Zhyl > "Combinators are math, and a little like Lisp – building functions from primitives..." – observationist
3. Theoretical significance of the Y combinator The Y combinator is highlighted as the classic example that enables recursion without named functions and ties into deeper computability theory.
"Or better yet, the y combinator is this: W S (Q (S I I))" – momentoftop
These three themes capture the core of the conversation: the definitional role of combinators, their concrete use in terse array languages, and their foundational place in computability theory.