There’s a Haskell trick that I’ve observed in a few settings, and I’ve never seen a name put to it. I’d like to write a post about the technique and give it a name. It’s often useful to write in a type class constrained manner, but at some point you need to discharge (or satisfy?) those constraints. You can pluck a single constraint at a time.
This technique is used primarily used in
mtl (or other effect libraries), but it also has uses in error handling.
We can easily gather constraints by using functions that require them.
Here’s a function that has a
MonadReader Int constraint:
number :: (MonadReader Int m) => m Int number = ask
Here’s another function that has a
MonadError String constraint:
woops :: (MonadError String m) => m void woops = throwError "woops!"
And yet another function with a
MonadState Char constraint:
update :: (MonadState Char m) => m () update = modify succ
We can seamlessly write a program that uses all of these functions together:
program = do number woops update
GHC will happily infer the type of
program :: ( MonadReader Int m , MonadError String m , MonadState Char m ) => m ()
At some point, we’ll need to actually use this.
Virtually all Haskell code that gets used is called from
main :: IO ().
Let’s try just using it directly:
main :: IO () main = program
GHC is going to complain about this. It’s going to say something like:
No instance for `MonadReader Int IO` arising from a use of `program` .... No instance for `MonadState Char IO` arising from a use of `program` .... Couldn't match type `IOException` with type `String` ....
This is GHC’s way of telling us that it doesn’t know how to run our program in
IO type is not powerful enough to do all the stuff we want as-is.
And it has a conflicting way to throw errors - the
MonadError instance is for the
IOException type, not the
String that we’re trying to use.
So we have to do something differently.
Let’s try figuring out what GHC is doing with
main = program.
First, we’ll look at the equations:
program :: ( MonadReader Int m , MonadError String m , MonadState Char m ) => m () main :: IO ()
GHC sees that the “shape” of these types is similar.
It can substitute
Does that work?
program :: ( MonadReader Int IO , MonadError String IO , MonadState Char IO ) => IO ()
Yeah! That looks okay so far.
Now, we have a totally concrete constraint:
MonadReader Int IO doesn’t have any type variables.
So let’s look it up and see if we can find an instance
. . .
Unfortunately, there’s no instance defined like this.
If there’s no instance for
IO, then how are we going to satisfy that constraint?
We need to get rid of it and discharge it somehow!
mtl library gives us a type that’s sole responsibility is discharging the
Let’s check out the
runReaderT :: ReaderT r m a -> r -> m a
My first argument is a
ReaderT r m a. My second argument is the
renvironment. And then I’ll take off the
ReaderTbusiness on the type, returning only
We’re going to pluck off that
MonadReader constraint by turning it into a concrete type.
runReaderT is one way to do that plucking.
GHC inferred a pretty general type for
program earlier, but we can pick a more concrete type.
program :: ( MonadError String n , MonadState Char n ) => ReaderT Int n ()
Notice how we’ve shifted a constraint into a concrete type.
We’ve fixed the type of
m to be
ReaderT Int n, and all the other constraints got delegated down to this new type variable
We don’t need to pick this concrete type at our definition site of
Indeed, we can provide that annotation somewhere else, like in
main :: IO () main = let program' :: ( MonadError String n , MonadState Char n ) => ReaderT Int n () program' = program in runReaderT program' 3
We’re literally saying “
program' is exactly like
program but we’re making it a tiny bit more concrete.”
Now, GHC still isn’t happy.
It’s going to complain that there’s no instance for
MonadState Char IO and that
String isn’t equal to
So we have a little more work to do.
mtl library gives us types for plucking these constraints off too.
runStateT can be used to pluck off a
MonadState constraint, as well as
program'', which will use
StateT to ‘pluck’ the
MonadState Char constraint off.
main :: IO () main = let program' :: ( MonadError String n , MonadState Char n ) => ReaderT Int n () program' = program program'' :: (MonadError String n) => ReaderT Int (StateT Char n) () program'' = program' programRead :: (MonadError String n) => StateT Char n () programRead = runReaderT program'' 3 in runStateT programRead 'c'
GHC still isn’t happy - it’s going to complain that
((), Char) aren’t the same types.
Also we still haven’t dealt with
String being different.
So let’s use
ExceptT to pluck out that final constraint.
main :: IO () main = let program' :: ( MonadError String n , MonadState Char n ) => ReaderT Int n () program' = program program'' :: (MonadError String n) => ReaderT Int (StateT Char n) () program'' = program' program''' :: (Monad m) => ReaderT Int (StateT Char (ExceptT String m) () -> m () program''' = program'' -- ... snip ...
Okay, so I’m going to snip here and talk about something interesting.
When we plucked the
MonadError constraint out, we didn’t totally remove it.
Instead, we’re left with a
We’ll get into this later.
But first, let’s look at the steps that happen when we run the program, one piece at a time.
-- ... snip ... programRead :: (Monad m) => StateT Char (ExceptT String m) () programRead = runReaderT program''' 3 programStated :: (Monad m) => ExceptT String m ((), Char) programStated = runStateT programRead 'a' programExcepted :: (Monad m) => m (Either String ((), Char)) programExcepted = runExceptT programStated programInIO :: IO (Either String ((), Char)) programInIO = programExcepted in do result <- programInIO case result of Left err -> do fail err Right ((), endState) -> do print endState pure ()
GHC doesn’t error on this!
When we finally get to
programExcepted, we have a type that GHC can happily accept.
IO type has an instance of
Monad, and so we can just substitute
(Monad m) => m () and
IO () without any fuss.
These are all of the steps, laid out explicitly, but we can condense them significantly.
program :: ( MonadReader Int m , MonadError String m , MonadState Char m ) => m () program = do number woops update main :: IO () main = do result <- runExceptT (runStateT (runReaderT program 3) 'a') case result of Left err -> do fail err Right ((), endState) -> do print endState pure ()
The general pattern here is:
We don’t need to only do this in
Suppose we want to discharge the
MonadReader Int inside of
program :: ( MonadState Char m , MonadError String m ) => m () program = do i <- gets fromEnum runReaderT number i woops update
We plucked the
MonadReader constraint off of
number directly and discharged it right there.
So you don’t have to just collect constraints until you discharge them in
You can pluck them off one-at-a-time as you need to, or as it becomes convenient to do so.
Let’s look at
MonadReader to see how the type and class are designed for plucking.
We don’t need to worry about the implementations, just the types:
newtype ReaderT r m a -- or, with explicit kinds, newtype ReaderT (r :: Type) (m :: Type -> Type) (a :: Type) class MonadReader r m | m -> r instance (Monad m) => MonadReader r (ReaderT r m) instance (MonadError e m) => MonadError e (ReaderT r m) instance (MonadState s m) => MonadState s (ReaderT r m)
ReaderT, partially applied, as a few different readings:
--  ReaderT r :: (Type -> Type) -> (Type -> Type) --  ReaderT r m :: (Type -> Type) --  ReaderT r m a :: Type
rapplied, we have a ‘monad transformer.’ Don’t worry if this is tricky: just notice that we have something like
(a -> a) -> (a -> a). At the value level, this might look something like:
updatePlayer :: (Player -> Player) -> GameState -> GameState
Where we can call
updatePlayer to ‘lift’ a function that operates on
Players to an entire
rapplied, we have a ‘monad.’ Again, don’t worry if this is tricky. Just notice that we have something that fits the same shape that the
The important bit here is the ‘delegation’ type variable. For the class we know how to handle, we can write a ‘base case’:
instance (Monad m) => MonadReader r (ReaderT r m)
And for the classes that we don’t know how to handle, we can write ‘recursive cases’:
instance (MonadError e m) => MonadError e (ReaderT r m) instance (MonadState s m) => MonadState s (ReaderT r m)
Now, GHC has all the information it needs to pluck a single constraint off and delegate the rest.
I mentioned that this technique can also be applied to errors. First, we need to write classes that work for our errors. Let’s say we have database, HTTP, and filesystem errors:
class AsDbError err where liftDbError :: DbError -> err isDbError :: err -> Maybe DbError class AsHttpError err where liftHttpError :: HttpError -> err isHttpError :: err -> Maybe HttpError class AsFileError err where liftFileError :: FileError -> err isFileError :: err -> Maybe FileError
Obviously, our ‘base case’ instances are pretty simple.
instance AsDbError DbError where liftDbError = id isDbError = Just instance AsHttpError HttpError where liftHttpError = id isHttpError = Just -- etc...
But we need a way of “delegating.” So let’s write our ‘error transformer’ type for each error:
data DbErrorOr err = IsDbErr DbError | DbOther err data HttpErrorOr err = IsHttpErr HttpError | HttpOther err data FileErrorOr err = IsFileErr FileError | FileOther err
Now, we can write an instance for
instance AsDbError (DbErrorOr err) where liftDbError dbError = IsDbErr dbError isDbError (IsDbErr e) = Just e isDbError (DbOther _) = Nothing
This one is pretty simple - it is also a ‘base case.’ Let’s write the recursive case:
instance AsHttpError err => AsHttpError (DbErrorOr err) where liftHttpError httpError = DbOther (liftHttpError httpError) isHttpError (IsDbErr _) = Nothing isHttpError (DbOther err) = isHttpError err
Here, we’re just writing some boilerplate code to delegate to the underlying
We’d want to repeat this for every permutation, of course.
Now, we can compose programs that throw varying errors:
program :: (AsHttpError e, AsDbError e) => Either e () program = do Left (liftHttpError HttpError) Left (liftDbError DbError)
The constraints collect exactly as nicely as you’d want, and the type class machinery allows you to easily go from the single type to the concrete type.
Let’s ‘pluck’ the constraint. We’ll ‘pick’ a concrete type and delegate the other constraint to the type variable:
program' :: (AsHttpError e) => Either (DbErrorOr e) () program' = program
GHC is pretty happy about this. All the instances work out, and it solves the problem of how to delegate everything for you.
We can pattern match directly on this, which allows us to “catch” individual errors and discharge them:
handleLeft :: Either err a -> (err -> Either err' a) -> Either err' a handleLeft (Right r) _ = Right r handleLeft (Left l) f = f l program'' :: AsHttpError e => Either e () program'' = handleLeft program $ \err -> case err of IsDbErr dbError -> Right () DbOther dbOther -> Left dbOther
Voila! We’ve “handled” the database error, but we’ve delegated handling the HTTP error. The technique of ‘constraint plucking’ works out here.
Now, an astute reader might note that this technique is so boring. There’s so much boilerplate code!! SO MUCH!!!
Come on, y’all.
It’s exactly the same amount of boilerplate code as the
mtl library requires.
Is it really that bad?
Okay, yeah, it’s pretty bad.
This encoding is primarily here to present the ‘constraint plucking’ technique.
You can do a more general and ergonomic approach to handling errors like this, but describing it is out of scope for this post.
I’ve published a library named
plucky that captures this pattern, and the module documentation covers it pretty extensively.
Hopefully you find this concept as useful as I have. Best of luck in your adventures!