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Plucking Constraints
source link: https://www.parsonsmatt.org/2020/01/03/plucking_constraints.html
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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:
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
:
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
.
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 :: ( 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 IO
for m
in program
.
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!
The mtl
library gives us a type that’s sole responsibility is discharging the MonadReader
instance: ReaderT
.
Let’s check out the runReaderT
function:
runReaderT :: ReaderT r m a -> r -> m a
runReaderT
says:
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 :: ( 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 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' :: ( 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 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' :: ( 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 ()
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' :: ( 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 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 ... 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.
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 :: ( 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 ()
Plucking Constraints!
The general pattern here is:
- A function has many constraints.
- You can pluck a single constraint off by making the type a little more concrete.
- 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 :: ( 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 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:
newtype ReaderT r m a -- or, with explicit kinds, newtype ReaderT (r :: Type) (m :: Type -> Type) (a :: Type) class MonadReader r m | r -> m 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:
-- [1] ReaderT r :: (Type -> Type) -> (Type -> Type) -- [2] ReaderT r m :: (Type -> Type) -- [3] ReaderT r m a :: Type
-
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 onPlayer
s to an entireGameState
. -
With an
m
and anr
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 them
parameter has. - Finally, we have a regular old value that has runtime types.
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.
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.
Hopefully you find this concept as useful as I have. Best of luck in your adventures!
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