# Plucking Constraints

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.

# Gathering Constraints

We can easily gather constraints by using functions that require them. Here’s a function that has a MonadReader Int constraint:

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:

program
)
=> 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

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. Perhaps the 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.

# Unify

Let’s try figuring out what GHC is doing with main = program. First, we’ll look at the equations:

program
)
=> m  ()
main
:: IO ()

GHC sees that the “shape” of these types is similar. It can substitute IO for m in program. Does that work?

program
)
=> 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!

-> r
-> m a

My first argument is a ReaderT r m a. My second argument is the r environment. And then I’ll take off the ReaderT business on the type, returning only m.

We’re going to pluck off that MonadReader constraint by turning it into a concrete type. And 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
)

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 n. We don’t need to pick this concrete type at our definition site of program. Indeed, we can provide that annotation somewhere else, like in main:

main :: IO ()
main =
let
program'
)
program' =
program
in

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 IOException. So we have a little more work to do.

Fortunately, the mtl library gives us types for plucking these constraints off too. StateT and runStateT can be used to pluck off a MonadState constraint, as well as ExceptT and runExceptT.

Let’s write program'', which will use StateT to ‘pluck’ the MonadState Char constraint off.

main :: IO ()
main =
let
program'
)
program' =
program

program''
=> ReaderT Int (StateT Char n) ()
program'' =
program'

=> StateT Char n ()
in

GHC still isn’t happy - it’s going to complain that () and ((), Char) aren’t the same types. Also we still haven’t dealt with IOException and String being different.

So let’s use ExceptT to pluck out that final constraint.

main :: IO ()
main =
let
program'
)
program' =
program

program''
=> ReaderT Int (StateT Char n) ()
program'' =
program'

program'''
=> 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 Monad constraint. 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 ...
=> StateT Char (ExceptT String m) ()

programStated
=> ExceptT String m ((), Char)
programStated =

programExcepted
=> 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. The 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
)
=> 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 ()

# Plucking Constraints!

The general pattern here is:

1. A function has many constraints.
2. You can pluck a single constraint off by making the type a little more concrete.
3. The rest of the constraints are delegated to the new type.

We don’t need to only do this in main. Suppose we want to discharge the MonadReader Int inside of program:

program
)
=> m ()
program = do
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 main. You can pluck them off one-at-a-time as you need to, or as it becomes convenient to do so.

# How does it work?

Let’s look at ReaderT and MonadReader to see how the type and class are designed for plucking. We don’t need to worry about the implementations, just the types:

-- or, with explicit kinds,
(r :: Type)
(m :: Type -> Type)
(a :: Type)

-- [1]
ReaderT r       :: (Type -> Type) -> (Type -> Type)
-- [2]
ReaderT r m                       :: (Type -> Type)
-- [3]
ReaderT r m a                              :: Type
1. With just an r applied, 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 GameState.

2. With an m and an r applied, 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 m parameter has.
3. Finally, we have a regular old type that has runtime values.

The important bit here is the ‘delegation’ type variable. For the class we know how to handle, we can write a ‘base case’:

And for the classes that we don’t know how to handle, we can write ‘recursive cases’:

Now, GHC has all the information it needs to pluck a single constraint off and delegate the rest.

# Plucking Errors

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 DbErrorOr.

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 err variable. 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?

YESSSS!!!

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!