Plucking In, Plucking Out

In plucking constraints, I talked about a way to shrink a set of constraints by partially concretizing it. At the end of the article, I show how to use it for errors. The plucky package documents the technique, and my upcoming library prio embed plucking into run-time exceptions, effectively solving the trouble with typed errors. Figuring that out has been bothering me for two and a half years!

This got me thinking. Michael Snoyman’s rio package is an alternative Prelude which bakes the ReaderT Design Pattern in to the base monad RIO r a, and then encourages users to write in a polymorphic style.

-- Concrete, monomorphic:
foo :: Int -> RIO AppEnv String

-- Abstract, polymorphic:
, HasThing env, HasOtherThing env
)
=> Int
-> m String


The abstract foo specifies exactly what the env must satisfy. With a concrete type, the AppEnv type is almost certainly too big - it probably needs to support all kinds of things, and foo is only a small part of that.

In The Trouble With Typed Errors, I argue that an error type that is too big is a major problem. But I’ve never really been bothered with an env type that is too big. Why is that?

Profunctors

If I combine prio’s CheckedT e m a for checked runtime exceptions and rio’s RIO r a, I get this neat type:

newtype App r e a = App
{ unApp :: CheckedT e (RIO r a)
}
deriving
newtype
-- etc
)


Let’s simplify. Instead of runtime exceptions with CheckedT, we’ll use Either e. We’ll inline the transformers, too.

newtype App r e a = App
{ unApp :: r -> IO (Either e a)
}
deriving
via (ReaderT r (ExceptT e IO))
-- etc
)


If you squint a little, this is a Profunctor with an input of type r and an output of type Either e a. Either e a is even just a way of “blessing” one possible output as the “bind” output while the e is a “short-circuit” output. Profunctor is a fancy math word that makes me think about category theory. If I apply some sloppy category theory thinking, maybe I can satisfactorily answer “Why is a too-big output bad, while a too-big input is fine?”

The Problem With catch

The problem with catch is that it doesn’t change the error set at all.

catch
:: Either e a
-> (e -> Either e a)
-> Either e a


There is no type-level evidence that anything has changed. Alexis King would call this validation, not parsing.

The Correct type of catch is something like:

catch
:: forall input small rest
. ( Contains small input
, rest ~ Delete small input
)
=> Either input a
-> (small -> Either rest a)
-> Either rest a


The big difference here is that the small type of problem has been handled, and we’re only left with the rest. Using Constraint Plucking, this signature is simply:

catch
:: Either (Either small rest) a
-> (small -> Either rest a)
-> Either rest a


Since catch is our Big Problem with the output, we should get to our Big Problem with the input by taking the dual of this function. Taking the dual means flipping the arrows and replacing sums with products. (Real category theory experts will yell at me for this, I Will Not Log Off, but I will accept a PR linking to a better explanation).

-- Provide alias names to help with flipping the arrows
catch0 :: start -> handler -> result

-- Let's do start now. We'll just convert Either to Tuple.
start ~ Either (Either small rest) a
start0 ~ ( (small, rest), a )

-- Handler:
handler ~ (small -> Either rest a)
-- Flip arrow
handler0 ~ (Either rest a -> small)
-- Tuplize
handler1 ~ ((rest, a) -> small)

-- Result
result ~ Either rest a
-- Tuplize
result ~ (rest, a)

cocatch0
:: start
-> handler
-> result
-- substitute our named expressions
cocatch
:: ((small, rest), a)
-> ((rest, a) -> small)
-> (rest, a)
cocatch ((small, rest), a) k =
(rest, a)


Huh. This is totally useless. I suspect I have performed the flipping of arrows incorrectly. Edward Yang has a really good post on category theory and flipping arrows, so I’ll read that and come back to this.

catch is really like a bind on the e parameter of Either e a. Just compare the signatures:

bind
:: Either e a
-> (a -> Either e a)
-> Either e a

catch
:: Either e a
-> (e -> Either e a)
-> Either e a


This makes me think: Monad is the wrong approach. I want to look at the equivalent Comonad. The dual of Either e a is (e, a) - the Env comonad. So let’s look at cobind on Env:

cobind
:: Env e a
-> (Env e a -> b)
-> Env e b

cocatch
:: Env e a
-> (Env e a -> x)
-> Env x a


Now we’re getting somewhere. Let’s rewrite as a tuple:

cocatch
:: (e, a)
-> ((e, a) -> x)
-> (x, a)
cocatch (e, a) k =
(k (e, a), a)


Hmm. Let’s curry that second argument.

cocatch
:: (e, a)
-> (e -> a -> x)
-> (x, a)
cocatch (e, a) k = (k e a, a)


Looks a lot like censor from MonadWriter:

censor :: (w -> w) -> Writer w a -> Writer w a
censor f (Writer x) = Writer $cocatch (\w _ -> f w) x  It’s really a more specialized variant of mapWriter: cocatch w f = mapWriter (\(e, a) -> (f e a, a)) w  Well, that’s interesting, but it doesn’t answer my question. The dual of the Either monad is the Env comonad, which is equivalent to the Writer monad, not the Reader monad. Maybe I need to get back to the Profunctor approach - inspect why the contravariant part of the functor is OK to be too big. Inputs and Outputs With App r e a , we have two output types and an input type. We have a few tools for working on these type parameters. fmap :: (a -> b) -> App r e a -> App r e b fmapL :: (e -> f) -> App r e a -> App r f a local :: (r -> x) -> App x e a -> App r e a  local is like our contramap function, but it won’t work because the kinds aren’t right. We can introduce effectful variants: bind :: (a -> App r e b) -> App r e a -> App r e b catch :: (e -> App r f b) -> App r e a -> App r f a what :: (r -> App x e a) -> App x e a -> App r e a  Okay, what has my interest. It can’t be defined. We never have an x, so there’s no way we can discharge it. Maybe we can translate this and flip arrows slightly differently… -- unwrap the newtypes: local :: (r -> x) -> (x -> Either e a) -> (r -> Either e a) localM :: (r -> x -> Either e a) -> (x -> Either e a) -> (r -> Either e a)  Okay, this is obviously wrong. The x is in the wrong spot! We’re not supposed to be accepting an x as input, we’re supposed to be producing one. Let’s try that again. localM :: (r -> Either e x) -- App r e x -> (x -> Either e a) -- App x e a -> (r -> Either e a) -- App r e a  This looks much more feasible. localM :: App r e x -> App x e a -> App r e a localM mkX withX = do x <- mkX localApp (\_ -> x) withX  Well, this is a bit of a weird one. If we can produce an x from an App r e, then we can run an App x e a action into App r e a. Plucking with catch is about incrementally removing constraints that add cases to a type. So plucking with localM is about incrementally adding types to the environment product. localMPluck :: App r e x -> App (x, r) e a -> App r e a localMPluck mkX withXR = do x <- mkX localApp (\r -> (x, r)) withXR  The tuple type works OK for a constraint plucking interface, but I don’t really like it, so let’s define a nested product. data a :* b = a :* b infixr 7 :*  The pattern for a plucking interface is to write a class that can delegate to a type parameter. class Has t env where get :: env -> t instance Has x x where get = id instance {-# overlapping #-} Has x (x :* y) where get (a :* _) = a instance {-# overlappable #-} Has x y => Has x (a :* y) where get (_ :* b) = get b  And, let’s give it a nicer name - provide. It’s providing some new bit of information to the environment. provide :: App r e new -> App (new :* r) e a -> App r e a  A Man Provides Let’s run App into IO. We’ll guarantee via RankNTypes that it doesn’t need anything and doesn’t throw anything. runApp :: (forall r e. App r e a) -> IO a runApp action = do eitherVoidA <- runExceptT$ runReaderT (unApp action) ()
case eitherVoidA of
Left v -> absurd v
Right a -> pure a


Since we’re requiring a value that can work with any r, we can provide a () value. And, likewise, since we’re requiring that the e error type is any type we want, we can select Void. We get a guarantee that all checked exceptions are handled and we don’t need anything from the environment.

Now, let’s use this stuff. We’re going to need a logger, first of all.

data Logger = Logger

mkLogger :: App r e Logger
mkLogger = pure Logger

logInfo :: (Has Logger r) => String -> App r e ()
liftIO $putStrLn msg main :: IO () main = do runApp$ do


Our main fails with an error: No instance for (Has Logger r). So we need to provide one.

main :: IO ()
main = do
runApp $do provide mkLogger$ do


We can pass provide mkLogger to runApp because mkLogger has no requirements on the e or r types. Now, let’s make a database handle. This one is going to require logging.

data DbHandle = DbHandle

mkDbHandle :: (Has Logger r) => App r e DbHandle
mkDbHandle = do
pure DbHandle

getUserIds :: (Has DbHandle r) => App r e [Int]
getUserIds = do
pure [1,2,3]


We can’t call this next to logInfo above, because we haven’t provided it. The following code black fails with an error No isntance for (Has DbHandle r).

main :: IO ()
main = do
runApp $do provide mkLogger$ do
ids <- getUserIds
forM_ ids $\id -> do logInfo (show id)  We can fix it by providing one: main :: IO () main = do runApp$ do
provide mkLogger $do logInfo "asdf" provide mkDbHandle$ do
ids <- getUserIds
forM_ ids $\id -> do logInfo (show id)  This works just fine. What about throwing errors? Plucking Errors We need to pluck a sum type. data a || b = This a | That b class lil :< big where inject :: lil -> big project :: big -> Maybe lil instance lil :< lil where inject = id project = Just instance {-# overlapping #-} lil :< (lil || rest) where inject = This project x = case x of This a -> Just a _ -> Nothing instance {-# overlappable #-} (lil :< rest) => lil :< (not || rest) where inject = That . inject project x = case x of This _ -> Nothing That a -> project a throw :: lil :< big => lil -> App r big a throw = throwError . inject catch :: App r (lil || rest) a -> (lil -> App r rest a) -> App r rest a catch action handler = ReaderT$ \r ->
runReaderT action r catchE \lilOrRest ->
case lilOrRest of
This lil ->
That rest ->
throwE rest


Let’s suppose that creating a database handle actually has a PgError exception associated with it.

data DbExn = DbExn

mkDbHandle :: (Has Logger r, DbExn :< e) => App r e DbHandle
mkDbHandle = do
if 3 == 4
then pure DbHandle
else throw DbExn


Now, our main no longer compiles! GHC complains about No instance for (DbExn :< e) arising from a use of mkDbHandle. So we need to discharge that exception in the above block.

We’ll define handle as a shorthand (handle = flip catch), and we can discharge the error:

main :: IO ()
main = do
runApp $do provide mkLogger$ do
handle (\DbExn -> logInfo "uh oh")
$provide mkDbHandle$ do
ids <- getUserIds
forM_ ids $\id -> do logInfo (show id)  This now compiles. But I suspect the handle f . provide mk pattern is common enough to factor it out. providing :: (lil -> App r rest a) -> App r (lil || rest) x -> App (x :* r) (lil || rest) a -> App r rest a providing handler provider = handle handler . provide provider main :: IO () main = do runApp$ do
provide mkLogger $do logInfo "asdf" providing (\DbExn -> logInfo "uh oh") mkDbHandle$ do
ids <- getUserIds
forM_ ids \$ \id -> do


Neat!

Wait, where were we?

Right. Right. I’m trying to figure out why a big type for an error is a Problem, but a big type for an environment isn’t. In doing so, I figured out how to make composable, growing environments that play nicely with constraints.

If I don’t have a composable, growing environment that plays nicely with constraints, then what do I have? Usually just a big AppEnv type that has everythign I ever need. Functions may be defined in terms of constraints, but usually are just defined in:

newtype App a = App { unApp :: ReaderT AppEnv IO a }


When do I need to get away from App? Only when I want to use a function in another context. It can be frustrating to provide an entire AppEnv when I only need a database handle. But it rarely bites me in a way that is frustrating. Why?

Ignoring inputs is safe. But ignoring outputs is dangerous.

fine :: (Int, String) -> Int
fine (i, _) = i



fine throws away the input. It’s wasteful, but it’s not lying. bad, however, encodes partiality - it says it might have an Int or a String, but it definitely doesn’t have a String. It’s not lying, or even wrong, it’s just not helpful. If you want to use the Int inside, you gotta handle the Right String case.

useBad :: (String -> Int) -> Int


Now, fine has a problem: it’s too specific about it’s requirements. If I want to call fine with the result of useBad, then I have to come up with a String from somewhere. I don’t know whether or not it actually uses the String or not, so I have no idea if it matters what String I use. We can make fine’s type more precise:

fine :: (Int, unused) -> Int
fine (i, _) = i


Now, since unused is a type variable that I get to pick, I can pass () to satisfy the type checker.

Likewise, we can refine bad’s type to make it more specific to what it has:

bad :: Either Int Void


Now we know we’re never getting a Right out of it, so we don’t have to worry about it. Our calling code is much simpler:

useBad :: Int