I was looking at an old post of mine on free monads and wondered what it would look like using operational. Here we go!

(Literate Haskell source for this blog post is here.)

First, some imports. We use GADTs for our instruction type.


module Note where

import Control.Monad
import Control.Monad.Operational
import Test.QuickCheck
import qualified Data.Map as M

We want to encode a few instructions that operate on a data store. For the moment we don’t care about the implementation, just the underlying actions that we can perform: create a value, list all values, retrieve a particular value, and delete a value.

Suppose we have an index of type i and values of type v. Then DataStoreInstruction is:

data DataStoreInstruction i v a where
    Create   :: v -> DataStoreInstruction i v i
    List     ::      DataStoreInstruction i v [v]
    Retrieve :: i -> DataStoreInstruction i v (Maybe v)
    Delete   :: i -> DataStoreInstruction i v ()

Intuitively, Create takes a value of type v and returns an instruction, which on interpretation gives a value of type i (the last type parameter).

List doesn’t take any argument and produces a list of type v, i.e. [v]. The only odd one is Delete which doesn’t return anything, so it has a () in the last type variable.

A sequence of DataStoreInstructions is a program, which we get using the Program constructor:

type DataStoreProgram i v a = Program (DataStoreInstruction i v) a

where the index has type i, the values have type v, and the overall result of the program has type a.

To more easily construct programs, use singleton:

create :: v -> DataStoreProgram i v i
create = singleton . Create

list :: DataStoreProgram i v [v]
list = singleton List

retrieve :: i -> DataStoreProgram i v (Maybe v)
retrieve = singleton . Retrieve

delete :: i -> DataStoreProgram i v ()
delete = singleton . Delete

Now we can write programs in this DSL! All the usual monad things are at our disposal:

-- Insert a few values and return a list
-- of all values:
doSomeThings :: DataStoreProgram Int Int [Int]
doSomeThings = do
    ix3 <- create 3
    ix4 <- create 4
    delete ix3
    ix5 <- create 5

-- Insert all the supplied values and
-- return a list of indexes as well as a
-- list of final values (which should be empty).
insertValues :: [Int] -> DataStoreProgram Int Int ([Int], [Int])
insertValues xs = do
    ixs <- forM xs create
    forM_ ixs delete -- delete everything
    final <- list

    return (ixs, final)

The last step is to write an interpreter. We do this using view and pattern matching on the constructors of DataStoreInstruction. We use :»= to break apart the program. As the documentation says, (someInstruction :>>= k) means someInstruction and the remaining program is given by the function k.

Here we interpret the program using a Map as the underlying data store:

interpretMap :: Ord a => DataStoreProgram a a b -> (M.Map a a -> b)
interpretMap = eval . view
    eval (Return x)          m = x
    eval (Create   v :>>= k) m = interpretMap (k v)              (M.insert v v m)
    eval (List       :>>= k) m = interpretMap (k (M.elems m))    m
    eval (Retrieve i :>>= k) m = interpretMap (k $ M.lookup i m) m
    eval (Delete   i :>>= k) m = interpretMap (k ())             (M.delete i m)

If we wanted to we could flatten a program out to a string:

interpretString :: (Show a, Show b) => DataStoreProgram a a b -> String
interpretString = eval . view
    eval (Return x)          = "Return "   ++ show x
    eval (Create   v :>>= k) = "Create("   ++ show v ++ "); "  ++ interpretString (k v)
    eval (List       :>>= k) = "List; "                        ++ interpretString (k [])
    eval (Retrieve i :>>= k) = "Retrieve(" ++ show i ++ "); "  ++ interpretString (k $ Just i)
    eval (Delete   i :>>= k) = "Delete("   ++ show i ++ "); "  ++ interpretString (k ())

Maybe we have some super-important business need for storing Int/Int key value maps with a Postgresql backend. We could target this by writing an interpreter that uses postgresql-simple:

data Connection = Connection -- cheating for this example

interprestPostgresql :: DataStoreProgram Int Int b -> (Connection -> IO b)
interprestPostgresql = eval . view
    eval (Return x)          _ = return x
    eval (Create   v :>>= k) c = interprestPostgresql (k v) (insertPsql c v)
    eval (List       :>>= k) c = do allValues <- getAllPsql c
                                    interprestPostgresql (k allValues) c
    eval (Retrieve i :>>= k) c = do v <- lookupPsql c i
                                    interprestPostgresql (k v) c
    eval (Delete   i :>>= k) c = deletePsql c i >> interprestPostgresql (k ()) c

    -- Exercises for the reader.
    insertPsql c v = undefined
    getAllPsql c   = undefined
    lookupPsql c i = undefined
    deletePsql c i = undefined

Running the programs:

*Note> interpretMap doSomeThings M.empty

*Note> interpretString doSomeThings
"Create(3); Create(4); Delete(3); Create(5); List; Return []"

*Note> interpretMap (insertValues [1..10]) M.empty

*Note> interpretString (insertValues [1..10])
"Create(1); Create(2); Create(3); Create(4); Create(5); Create(6);
 Create(7); Create(8); Create(9); Create(10); Delete(1); Delete(2);
 Delete(3); Delete(4); Delete(5); Delete(6); Delete(7); Delete(8);
 Delete(9); Delete(10); List; Return ([1,2,3,4,5,6,7,8,9,10],[])"


It’s always good to write some tests:

prop_insert_then_delete :: [Int] -> Bool
prop_insert_then_delete xs = null $ interpretMap (f xs) M.empty
    f :: [Int] -> DataStoreProgram Int Int [Int]
    f is = do
        ixs <- forM is create
        forM_ ixs delete

prop_create :: Positive Int -> Bool
prop_create (Positive n) = let ns = [1..n] in ns == interpretMap (f ns) M.empty
    f = mapM create
*Note> quickCheck prop_insert_then_delete
+++ OK, passed 100 tests.

*Note> quickCheck prop_create
+++ OK, passed 100 tests.

Over time we find out that the interpreter that uses Map is too slow, so we write a new one using a fancy data structure:

-- Uses fancy tuned data structure.
interpretMapFast :: Ord a => DataStoreProgram a a b -> (M.Map a a -> b)
interpretMapFast = undefined -- So fancy!

Now we can compare implementations using QuickCheck. Nice!

prop_fast_inserts :: [Int] -> Bool
prop_fast_inserts xs = (interpretMapFast xs' M.empty) == (interpretMap xs' M.empty)
    xs' = f xs

    f :: [Int] -> DataStoreProgram Int Int [Int]
    f is = do
        ixs <- forM is create

Use of operational in larger projects

Here are a few samples of the operational package in action. For more, see the reverse dependencies on Hackage.


I first heard about operational from this talk at the New York Haskell meetup: Conquering Hadoop with Haskell and Ozgun Ataman.

Here is the ConI type from Hadron.Controller:

data ConI a where
    Connect :: forall i o. MapReduce i o
            -> [Tap i] -> Tap o
            -> Maybe String
            -> ConI ()

    MakeTap :: Protocol' a -> ConI (Tap a)

        :: FilePath
        -> (FilePath -> Bool)
        -> ConI (Tap (FilePath, B.ByteString))

    ConIO :: IO a -> ConI a

    OrchIO :: IO a -> ConI ()
    -- Only the orchestrator performs action

    NodeIO :: IO a -> ConI a
    -- Only the nodes perform action

    SetVal :: String -> B.ByteString -> ConI ()

    GetVal :: String -> ConI (Maybe B.ByteString)

    RunOnce :: Serialize a => IO a -> ConI a
    -- Only run on orchestrator, then make available to all the
    -- nodes via HDFS.

There is the distinction between the single orchestrator node, which runs OrchIO and can’t run NodeIO, and worker nodes that can’t run OrchIO but can run NodeIO. In the orchestrate, trying to evaluate a NodeIO results in an error:

    :: (MonadMask m, MonadIO m, Applicative m)
    => Controller a
    -> RunContext
    -> RerunStrategy
    -> ContState
    -> m (Either String a)
orchestrate (Controller p) settings rr s = do
      (liftIO $ openFile "hadron.log" AppendMode)
      (liftIO . hClose)
      (\_h -> do echoInfo ()  "Initiating orchestration..."
                 evalStateT (runExceptT (go p)) s)
      go = eval . O.view

      eval (Return a) = return a
      eval (i :>>= f) = eval' i >>= go . f

      eval' :: (Functor m, MonadIO m) => ConI a -> ExceptT String (StateT ContState m) a
      eval' (ConIO  f) = liftIO f
      eval' (OrchIO f) = void $ liftIO f
      eval' (NodeIO _) = return (error "NodeIO can't be used in the orchestrator decision path")

Meanwhile, worker nodes ignore an OrchIO and lift the NodeIO action.


The Graphics.Rendering.Chart.Backend.Impl module defines the the backend instructions:

data ChartBackendInstr a where
  StrokePath :: Path -> ChartBackendInstr ()
  FillPath   :: Path -> ChartBackendInstr ()
  GetTextSize :: String -> ChartBackendInstr TextSize
  DrawText    :: Point -> String -> ChartBackendInstr ()
  GetAlignments :: ChartBackendInstr AlignmentFns
  WithTransform  :: Matrix ->  Program ChartBackendInstr a -> ChartBackendInstr a
  WithFontStyle  :: FontStyle -> Program ChartBackendInstr a -> ChartBackendInstr a
  WithFillStyle  :: FillStyle -> Program ChartBackendInstr a -> ChartBackendInstr a
  WithLineStyle  :: LineStyle -> Program ChartBackendInstr a -> ChartBackendInstr a
  WithClipRegion :: Rect -> Program ChartBackendInstr a -> ChartBackendInstr a

type BackendProgram a = Program ChartBackendInstr a

Then the Graphics.Rendering.Chart.Backend.Cairo module provides a way to run a BackendProgram for the cairo graphics engine:

runBackend' :: CEnv -> BackendProgram a -> C.Render a
runBackend' env m = eval env (view m)
    eval :: CEnv -> ProgramView ChartBackendInstr a -> C.Render a
    eval env (Return v)= return v
    eval env (StrokePath p :>>= f) = cStrokePath env p >>= step env f
    eval env (FillPath p :>>= f) = cFillPath env p >>= step env f
    eval env (GetTextSize s :>>= f) = cTextSize s >>= step env f
    eval env (DrawText p s :>>= f) = cDrawText env p s >>= step env f
    eval env (GetAlignments :>>= f) = return (ceAlignmentFns env) >>= step env f
    eval env (WithTransform m p :>>= f) = cWithTransform env m p >>= step env f
    eval env (WithFontStyle font p :>>= f) = cWithFontStyle env font p >>= step env f
    eval env (WithFillStyle fs p :>>= f) = cWithFillStyle env fs p >>= step env f
    eval env (WithLineStyle ls p :>>= f) = cWithLineStyle env ls p >>= step env f
    eval env (WithClipRegion r p :>>= f) = cWithClipRegion env r p >>= step env f

Meanwhile, Graphics.Rendering.Chart.Backend.Diagrams does the same but for diagrams:

runBackend' tr m = eval tr $ view $ m
    eval :: (D.Renderable (D.Path V2 (N b)) b, D.Renderable t b, D.TypeableFloat (N b))
         => TextRender b t -> ProgramView ChartBackendInstr a
         -> DState (N b) (D.QDiagram b V2 (N b) Any, a)
    eval tr (Return v) = return (mempty, v)
    eval tr (StrokePath p   :>>= f) = dStrokePath  p   <># step tr f
    eval tr (FillPath   p   :>>= f) = dFillPath    p   <># step tr f
    eval tr@TextRenderSvg    (DrawText   p s :>>= f) = dDrawTextSvg    p s <># step tr f
    eval tr@TextRenderNative (DrawText   p s :>>= f) = dDrawTextNative p s <># step tr f
    eval tr (GetTextSize  s :>>= f) = dTextSize      s <>= step tr f
    eval tr (GetAlignments  :>>= f) = dAlignmentFns    <>= step tr f
    eval tr (WithTransform m p :>>= f)  = dWithTransform  tr m  p <>= step tr f
    eval tr (WithFontStyle fs p :>>= f) = dWithFontStyle  tr fs p <>= step tr f
    eval tr (WithFillStyle fs p :>>= f) = dWithFillStyle  tr fs p <>= step tr f
    eval tr (WithLineStyle ls p :>>= f) = dWithLineStyle  tr ls p <>= step tr f
    eval tr (WithClipRegion r p :>>= f) = dWithClipRegion tr r  p <>= step tr f


The Data.Redis.Command module defines heaps of commands:

data Command :: * -> * where
    -- Connection
    Ping   :: Resp -> Command ()
    Echo   :: FromByteString a => Resp -> Command a
    Auth   :: Resp -> Command ()
    Quit   :: Resp -> Command ()
    Select :: Resp -> Command ()

    -- Many more here.

type Redis  = ProgramT Command

and Database.Redis.IO.Client, an internal module of redis-io, defines how to interpret the redis commands:

eval f conn red = run conn [] red
    run :: Connection -> [IO ()] -> Redis IO a -> IO (a, [IO ()])
    run h ii c = do
        r <- viewT c
        case r of
            Return a -> return (a, ii)

            -- Connection
            Ping   x :>>= k -> f h x (matchStr "PING" "PONG") >>= \(a, i) -> run h (i:ii) $ k a
            Echo   x :>>= k -> f h x (readBulk "ECHO")        >>= \(a, i) -> run h (i:ii) $ k a
            Auth   x :>>= k -> f h x (matchStr "AUTH" "OK")   >>= \(a, i) -> run h (i:ii) $ k a
            Quit   x :>>= k -> f h x (matchStr "QUIT" "OK")   >>= \(a, i) -> run h (i:ii) $ k a
            Select x :>>= k -> f h x (matchStr "SELECT" "OK") >>= \(a, i) -> run h (i:ii) $ k a

            -- Many more here, snipped


The internal module Puppet.Interpreter.Types of language-puppet defines an interpreter instruction type:

data InterpreterInstr a where
    GetNativeTypes      :: InterpreterInstr (Container NativeTypeMethods)
    GetStatement        :: TopLevelType -> Text -> InterpreterInstr Statement
    ComputeTemplate     :: Either Text T.Text -> InterpreterState -> InterpreterInstr T.Text
    ExternalFunction    :: Text -> [PValue] -> InterpreterInstr PValue
    GetNodeName         :: InterpreterInstr Text
    HieraQuery          :: Container Text -> T.Text -> HieraQueryType -> InterpreterInstr (Maybe PValue)
    GetCurrentCallStack :: InterpreterInstr [String]
    IsIgnoredModule     :: Text -> InterpreterInstr Bool
    IsExternalModule    :: Text -> InterpreterInstr Bool
    IsStrict            :: InterpreterInstr Bool
    PuppetPaths         :: InterpreterInstr PuppetDirPaths
    -- Many more here, snipped.

Then Puppet.Interpreter.IO provides:

-- The internal (not exposed) eval function
eval :: Monad m
     => InterpreterReader m
     -> InterpreterState
     -> ProgramViewT InterpreterInstr (State InterpreterState) a
     -> m (Either PrettyError a, InterpreterState, InterpreterWriter)
eval _ s (Return x) = return (Right x, s, mempty)
eval r s (a :>>= k) =
    let runInstr = interpretMonad r s . k -- run one instruction
        thpe = interpretMonad r s . throwPosError . getError
        pdb = r^.readerPdbApi
        strFail iof errf = iof >>= \case
            Left rr -> thpe (errf (string rr))
            Right x -> runInstr x
        canFail iof = iof >>= \case
            S.Left err -> thpe err
            S.Right x -> runInstr x
        canFailX iof = runExceptT iof >>= \case
            Left err -> thpe err
            Right x -> runInstr x
        logStuff x c = (_3 %~ (x <>)) <$> c
    in  case a of
            IsStrict                     -> runInstr (r ^. readerIsStrict)
            ExternalFunction fname args  -> case r ^. readerExternalFunc . at fname of
                                                Just fn -> interpretMonad r s ( fn args >>= k)
                                                Nothing -> thpe (PrettyError ("Unknown function: " <> ttext fname))
            GetStatement topleveltype toplevelname
                                         -> canFail ((r ^. readerGetStatement) topleveltype toplevelname)
            ComputeTemplate fn stt       -> canFail ((r ^. readerGetTemplate) fn stt r)
            WriterTell t                 -> logStuff t (runInstr ())
            WriterPass _                 -> thpe "WriterPass"
            WriterListen _               -> thpe "WriterListen"
            PuppetPaths                  -> runInstr (r ^. readerPuppetPaths)
            GetNativeTypes               -> runInstr (r ^. readerNativeTypes)
            ErrorThrow d                 -> return (Left d, s, mempty)
            ErrorCatch _ _               -> thpe "ErrorCatch"
            GetNodeName                  -> runInstr (r ^. readerNodename)
            -- More cases here, snipped.

Since InterpreterInstr is a normal data type, it’s possible to write an instance of Pretty so that warnings or error messages look nicer:

-- Puppet.Interpreter.PrettyPrinter

instance Pretty (InterpreterInstr a) where


    pretty (ExternalFunction fn args)  = pf (ttext fn) (map pretty args)
    pretty GetNodeName                 = pf "GetNodeName" []
    pretty (HieraQuery _ q _)          = pf "HieraQuery" [ttext q]
    pretty GetCurrentCallStack         = pf "GetCurrentCallStack" []
    pretty (ErrorThrow rr)             = pf "ErrorThrow" [getError rr]
    pretty (ErrorCatch _ _)            = pf "ErrorCatch" []
    pretty (WriterTell t)              = pf "WriterTell" (map (pretty . view _2) t)
    pretty (WriterPass _)              = pf "WriterPass" []