Haskell: type-safe sprintf

Sprintf.hs

-- Source: Fun with Type Functions

data L
data V a
data f1 :<>: f2

type Parser a = String -> [(a, String)]
type Printer a = a -> String

data F f where
  L :: String -> F L
  V :: Parser a -> Printer a -> F (V a)
  (:<>:) :: F f1 -> F f2 -> F (f1 :<>: f2)
infixr 7 :<>:

instance IsString (F L) where
  fromString = L

type Sprintf f = TPrinter f String

type family TPrinter f x where
  TPrinter L x = x
  TPrinter (V a) x = a -> x
  TPrinter (f1 :<>: f2) x = TPrinter f1 (TPrinter f2 x)

sprintf :: F f -> Sprintf f
sprintf fmt = printer fmt id
  where
    printer :: F f -> (String -> a) -> TPrinter f a
    printer (L str) k = k str
    printer (V _ show) k = \a -> k $ show a
    printer (f1 :<>: f2) k = printer f1 $ \str1 -> printer f2 $ \str2 -> k (str1 ++ str2)

d# :: F (V Int)
d# = V reads show

f# :: F (V Double)
f# = V reads show

main :: IO ()
main = do
  print $ 
    sprintf ("I am " :<>: d# :<>: " years old.") 26