interactive input-output monad

Not to be confused with the standard IO monad.

data IO i o a
  = Return a
  | Input (i -> IO i o a)
  | Output o (IO i o a)

A value of type IO i o a is really an intensional description of a function of type [i] -> ([o], a).

runIO :: IO i o a -> [i] -> ([o], a)
runIO (Return a)   _        = x
runIO (Input k)    (i : is) = runIO (k i) is
runIO (Output o m) is       = (o : os, a)
  where ~(os, a) = runIO m