In the world of Haskell, the -> arrow embeds a GC (with runtime overhead) into the genrated code. A similar interface to Rust's borrow checker in Haskell (no runtime overhead) would be the ⊸ arrow from LinearTypes (in a future where GHC's GC is able to take advantage of this).
It looks, to me, like the arrow (⊸) notation is a lot simpler inteface to a no-runtime-overhead garbage collector -- or the absense of a traditional GC, in other words -- than Rust's borrow checker. But I'm looking forward to seeing how it plays out (it will probably take years before it becomes reality).