There are a lot of other Haskell features you can use. Term-level recursion works: f :: a -> b f = f Type-level recursion works, even without explicit ter

There are a lot of other Haskell features you can use. Term-level recursion works: f :: a -> b f = f Type-level recursion works, even without explicit term-level recursion: data T a b = C (T a b -> (a -> b)) q :: T a b -> (T a b -> (a -> b)) q (C f) = f w :: T a b -> (a -> b) w x = (q x) x f :: a -> b f = w (C w) This is basically encoding Russell's paradox at the type level. You can write out f explicitly, just so that it doesn't look like you might somehow still be applying w to itself recursively: g :: a -> b g = (\x -> ((\(C f) -> f) x) x) (C (\x -> ((\(C f) -> f) x) x)) There are even ways of doing this using highly impredicative definitions involving GADTs and type families, without involving any explicit recursion at all: http://okmij.org/ftp/Haskell/impredicativity-bites.html http://okmij.org/ftp/Haskell/impredicativity-bites.html The GADT example no longer seems to work, so changes to GADT type checking might have eliminated it, but the type family one still does.