GADT monad

gadt-monad.hs

{-# LANGUAGE GADTs, LambdaCase #-}

import Control.Monad

-- Model the problem with a simple GADT:

data Foo a where
  GetInput :: Foo String
  WriteOutput :: String -> Foo ()
  Pure :: a -> Foo a
  Bind :: Foo a -> (a -> Foo b) -> Foo b

-- Implement instances trivially:  

instance Monad Foo where (>>=) = Bind; return = Pure
instance Applicative Foo where (<*>) = ap; pure = return
instance Functor Foo where fmap = liftM

-- Write an interpreter for the GADT:

interpretFoo :: Foo a -> IO a
interpretFoo =
  \case
    GetInput -> getLine
    WriteOutput s -> putStrLn s
    Pure a -> pure a
    Bind m f -> interpretFoo m >>= interpretFoo . f

-- You can write other, pure, interpreters, or anything else.