Working out the details of a type indexed free monad

Question

I\'ve been using a free monad to build a DSL. As part of the language, there is an input command, the goal is to reflect what types are expected by the input primit

Answer 1

If you're willing to sacrifice the implicit ordering and use explicit accessors instead, your Action '[Int, Int] could be implemented using ReaderT (HList '[Int, Int]). If you use an existing library like vinyl that provides lenses, you could write something like this:

-- Implemented with pseudo-vinyl
-- X and Y are Int fields, with accessors xField and yField
addTwo :: ReaderT (PlainRec '[X, Y]) Output ()
addTwo = do
  x <- view (rGet xField)
  y <- view (rGet yField)
  lift . output $ show (x + y) -- output :: String -> Output ()

Type safety is enforced by constraint propagation: rGet xField introduces a requirement that X be a member of the record.

For a simpler illustration without the type-level machinery, compare:

addTwo :: ReaderT (Int, Int) IO ()
addTwo = do
  x <- view _1
  y <- view _2
  lift . putStrLn $ show (x + y)

We lose the ordering property, which is significant loss, particularly if the ordering is meaningful, e.g. represents the order of user interaction.

Furthermore, we now have to use runReaderT (~ eval). We can't, say, interleave user input with output.