I don't think this is the same. My C++ is getting rusty, so correct me if I'm wrong, but making a function const is mostly about making the "this" pointer const. A const function can still mutate global variables or call non-const functions, such as operator<< on cout. A pure D function can do neither of those things.

That's fair. C++ has const methods on objects, but I think nothing at global scope. But you shouldn't have global mutable state :-)