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# Update to Roles

It has become (somewhat) clear that the Roles mechanism as implemented in GHC 7.8 is insufficient. (See examples below.) This page is dedicated to creating a new design for roles that might fix the problems.

## Problem examples

We have three known examples of where current roles are failing us.

### Adding `join` to `Monad`

As part of the Applicative-Monad Proposal, we wish to add `join` to `Monad`, thus:

class Applicative m => Monad m where ... join :: forall a. m (m a) -> m a

This is all well and good, and would work with GeneralizedNewtypeDeriving (GND) most of the time. But, consider this:

newtype T m a = T (m a) deriving (Functor, Applicative, Monad) readRef :: MonadIO m => IORef a -> T m a readRef = T . liftIO . readIORef

The designer of `T` will export it abstractly, allowing only the reading of `IORef`s in the `T` monad but not other operations.

Sadly, the use of GND fails here, with `join` in the `Monad` class. Here is the relevant generated code:

instance Monad m => Monad (T m) where ... join = coerce (join :: m (m a) -> m a) :: forall a. T m (T m a) -> T m a

Thus, GHC must derive `Coercible (m (m a) -> m a) (T m (T m a) -> T m a)`. This requirement reduces (in part) to `Coercible (m (m a)) (T m (T m a))`. We try to solve this by applying a newtype-unwrapping instance, `Coercible x (m a) => Coercible x (T m a)`. Then, we must solve `Coercible (m (m a)) (m (T m a))`. And here, we are stuck. We do know `Coercible (m a) (T m a)`, but we don't know the role of `m`'s parameter, and must assume (for safety) that it could be nominal. Thus, we can't solve for `Coercible (m (m a)) (m (T m a))`.

This problem would occur if `join` were in `Monad` and a programmer used GND on any monad transformer. This is a common enough idiom to make us want to fix the situation.

### The `MVector` class

A redesign of the `vector` package is underway, introducing the `Vector` class, among other changes. Here is the offending method:

class (...) => Vector v a where basicUnsafeIndexM :: Monad m => v a -> Int -> m a ...

Here, `a` is the type of the thing stored in the vector, and it is natural to want to coerce a vector of `Int`s to a vector of `Age`s. But, GND would not work here, for very similar reasons to the case above -- we won't be able to coerce `m Int` to `m Age`, because we don't know enough about `m`.

### The `acme-schoenfinkel` package

This next example is the one known case of type-safe code that existed before GHC 7.8 that does not work with GHC 7.8's roles. The package `acme-schoenfinkel-0.1.1` package (by Ertugrul Söylemez) defines

WrappedSchoenfinkel { unwrapSchoenfinkel :: cat a b } deriving (Alternative, Applicative, Arrow, ArrowApply, ArrowChoice, ArrowLoop, ArrowPlus, ArrowZero, Category, Functor)

GND fails on `ArrowApply`:

class Arrow a => ArrowApply (a :: * -> * -> *) where app :: forall b c. a (a b c, b) c

The problem here echoes the `join` problem quite closely.

## The best known solution

Edward Kmett initially described an approach in an email, roughly as follows (names subject to bikeshedding, as always):

Currently, `Data.Type.Coercion` makes this definition:

data Coercion a b where Coercion :: Coercible a b => Coercion a b

Building on that, define a class `Rep` like this:

class Rep (f :: k1 -> k2) where co :: Coercible a b => Coercion (f a) (f b)

The idea is that a type is in the `Rep` class if its *next* parameter is representational. Thus, we would have instances `Rep Maybe`, `Rep []`, `Rep Either`, `Rep (Either a)`, etc. We would *not* have `Rep G`, where `G` is a GADT.

Using this, we can define GND over `join` thus (continuing the example above):

instance (Rep m, Monad m) => Monad (T m) where ... join = case co :: Coercion (m (m a)) (m (T m a)) of Coercion -> coerce (join :: m (m a) -> m a) :: forall a. T m (T m a) -> T m a

This compiles without difficulty.

Of course, we need to bake this reasoning into the compiler and the existing `Coercible` solver, essentially with a `Coercible` "instance" like

instance (Rep f, Coercible a b) => Coercible (f a) (f b)

We also would want automatic generation of instances of `Rep`, not unlike the generation of instances for `Coercible`.

### Open user-facing design questions

- How far should instance generation go? For example, for the type

newtype ReaderT r m a = ReaderT (r -> m a)

the instance

instance Rep m => Rep (ReaderT r m)

can be written. Should this be inferred? I (Richard) can imagine a beefed up role inference algorithm which could figure this out. But, perhaps there exist harder cases that would not be inferrable.

- Should users be able to write instances for
`Rep`by hand? They cannot do so for`Coercible`.

- What should the method in
`Rep`be?`Coercion a b -> Coercion (f a) (f b)`,`Coercible a b => Coercion (f a) (f b)`, and`Coercible a b => Coercible (f a) (f b)`(definable internally) are all contenders.

- Should we do something analogous for phantom roles?

### Open implementation questions

- Currently, all coercions (including representational ones) are unboxed (and thus take up exactly 0 bits) in a running program. (We ignore
`-fdefer-type-errors`here.) But, Core has no way of expressing*functions*in the coercion language, and the`co`method above essentially desugars to a coercion function. Either we have to add functions to the language of coercions, or we have to keep the coercions generated by`Rep`instances boxed at runtime, taking of the space of a pointer and potentially an unevaluated thunk.

- The
`ReaderT`example defined`ReaderT`as a newtype. The`Rep`instance shown is indeed writable by hand, right now. But, if`ReaderT`were defined as a*data*type, the`Rep`instance would be impossible to write, as there are no newtype-unwrapping instances. It seems a new form of axiom would be necessary to implement this trick for data types. This axiom would have to be produced at the data type definition, much like how newtype axioms are produced with newtype definitions.