[nyssos]

Here's a less galactic version. Suppose you're implementing a binary tree where every leaf has to have the same height - a toy model of a self-balancing search tree.

Here's an implementation using GADTs and type-level addition

    data Node (level :: Nat) (a :: Type) where
        Leaf :: a -> Node Zero a
        Interior :: a -> (Node l a, Node l a) -> Node (l + 1) a

It's impossible to construct an unbalanced node, since `Interior` only takes two nodes of the same level, and every `Leaf` is of level 0.