From the error below, I'm inferring that the RHS of the associated type definition can only contain type variables from the instance head, not the instance context. I didn't explicitly see this restriction when reading the GHC/Type_families entry.
Could perhaps the "a b -> bn" functional dependency of the TypeEq class lift this restriction for bn? This isn't my ball park, but that idea has my hopes up :). <haskell> {-# LANGUAGE TypeFamilies #-} import TypeEq -- Attempting to encapsulate TypeEq behind an associated type. class EQ a b where type BN a b instance TypeEq a b bn => EQ a b where type BN a b = bn </haskell> results in an error <ghci> /tmp/Test.hs:9:16: Not in scope: type variable `bn' Failed, modules loaded: none. </ghci>