The Church2 test gives a rather confusing error with the HEAD:

Church2.hs:27:14:
    Couldn't match expected type `CNat'
           against inferred type `(a -> a) -> a -> a'
      Expected type: CNat -> CNat
      Inferred type: CNat -> CNat
    In the first argument of `n', namely `(mul m)'
    In the expression: n (mul m) n1

In particular the lines

      Expected type: CNat -> CNat
      Inferred type: CNat -> CNat

are confusing, and I'm not sure why it's giving two expected/inferred pairs of types.