This is one of the most magical things about Prolog. From my functional/imperative programming experience, when originally picking up Prolog, I conceptualized

This is one of the most magical things about Prolog. From my functional/imperative programming experience, when originally picking up Prolog, I conceptualized the kind of operations you describe (e.g., “all splits”) as “running the function backwards” — going from output L to inputs X, Y. But as you write, the truth is that Prolog is modeling the relation of concatenation.