6.4.21. Roles

Using GeneralizedNewtypeDeriving (Generalised derived instances for newtypes), a programmer can take existing instances of classes and “lift” these into instances of that class for a newtype. However, this is not always safe. For example, consider the following:

newtype Age = MkAge { unAge :: Int }

type family Inspect x
type instance Inspect Age = Int
type instance Inspect Int = Bool

class BadIdea a where
  bad :: a -> Inspect a

instance BadIdea Int where
  bad = (> 0)

deriving instance BadIdea Age    -- not allowed!

If the derived instance were allowed, what would the type of its method bad be? It would seem to be Age -> Inspect Age, which is equivalent to Age -> Int, according to the type family Inspect. Yet, if we simply adapt the implementation from the instance for Int, the implementation for bad produces a Bool, and we have trouble.

The way to identify such situations is to have roles assigned to type variables of datatypes, classes, and type synonyms.

Roles as implemented in GHC are a from a simplified version of the work described in Generative type abstraction and type-level computation, published at POPL 2011.

6.4.21.1. Nominal, Representational, and Phantom

The goal of the roles system is to track when two types have the same underlying representation. In the example above, Age and Int have the same representation. But, the corresponding instances of BadIdea would not have the same representation, because the types of the implementations of bad would be different.

Suppose we have two uses of a type constructor, each applied to the same parameters except for one difference. (For example, T Age Bool c and T Int Bool c for some type T.) The role of a type parameter says what we need to know about the two differing type arguments in order to know that the two outer types have the same representation (in the example, what must be true about Age and Int in order to show that T Age Bool c has the same representation as T Int Bool c).

GHC supports three different roles for type parameters: nominal, representational, and phantom. If a type parameter has a nominal role, then the two types that differ must not actually differ at all: they must be identical (after type family reduction). If a type parameter has a representational role, then the two types must have the same representation. (If T's first parameter’s role is representational, then T Age Bool c and T Int Bool c would have the same representation, because Age and Int have the same representation.) If a type parameter has a phantom role, then we need no further information.

Here are some examples:

data Simple a = MkSimple a          -- a has role representational

type family F
type instance F Int = Bool
type instance F Age = Char

data Complex a = MkComplex (F a)    -- a has role nominal

data Phant a = MkPhant Bool         -- a has role phantom

The type Simple has its parameter at role representational, which is generally the most common case. Simple Age would have the same representation as Simple Int. The type Complex, on the other hand, has its parameter at role nominal, because Complex Age and Complex Int are not the same. Lastly, Phant Age and Phant Bool have the same representation, even though Age and Bool are unrelated.

6.4.21.2. Role inference

What role should a given type parameter should have? GHC performs role inference to determine the correct role for every parameter. It starts with a few base facts: (->) has two representational parameters; (~) has two nominal parameters; all type families’ parameters are nominal; and all GADT-like parameters are nominal. Then, these facts are propagated to all places where these types are used. The default role for datatypes and synonyms is phantom; the default role for classes is nominal. Thus, for datatypes and synonyms, any parameters unused in the right-hand side (or used only in other types in phantom positions) will be phantom. Whenever a parameter is used in a representational position (that is, used as a type argument to a constructor whose corresponding variable is at role representational), we raise its role from phantom to representational. Similarly, when a parameter is used in a nominal position, its role is upgraded to nominal. We never downgrade a role from nominal to phantom or representational, or from representational to phantom. In this way, we infer the most-general role for each parameter.

Classes have their roles default to nominal to promote coherence of class instances. If a C Int were stored in a datatype, it would be quite bad if that were somehow changed into a C Age somewhere, especially if another C Age had been declared!

There is one particularly tricky case that should be explained:

data Tricky a b = MkTricky (a b)

What should Tricky’s roles be? At first blush, it would seem that both a and b should be at role representational, since both are used in the right-hand side and neither is involved in a type family. However, this would be wrong, as the following example shows:

data Nom a = MkNom (F a)   -- type family F from example above

Is Tricky Nom Age representationally equal to Tricky Nom Int? No! The former stores a Char and the latter stores a Bool. The solution to this is to require all parameters to type variables to have role nominal. Thus, GHC would infer role representational for a but role nominal for b.

6.4.21.3. Role annotations

RoleAnnotations

Since:

7.8.1

Allow role annotation syntax.

Sometimes the programmer wants to constrain the inference process. For example, the base library contains the following definition:

data Ptr a = Ptr Addr#

The idea is that a should really be a representational parameter, but role inference assigns it to phantom. This makes some level of sense: a pointer to an Int really is representationally the same as a pointer to a Bool. But, that’s not at all how we want to use Ptrs! So, we want to be able to say

type role Ptr representational
data Ptr a = Ptr Addr#

The type role (enabled with RoleAnnotations) declaration forces the parameter a to be at role representational, not role phantom. GHC then checks the user-supplied roles to make sure they don’t break any promises. It would be bad, for example, if the user could make BadIdea's role be representational.

As another example, we can consider a type Set a that represents a set of data, ordered according to a's Ord instance. While it would generally be type-safe to consider a to be at role representational, it is possible that a newtype and its base type have different orderings encoded in their respective Ord instances. This would lead to misbehavior at runtime. So, the author of the Set datatype would like its parameter to be at role nominal. This would be done with a declaration

type role Set nominal

Role annotations can also be used should a programmer wish to write a class with a representational (or phantom) role. However, as a class with non-nominal roles can quickly lead to class instance incoherence, it is necessary to also specify IncoherentInstances to allow non-nominal roles for classes.

The other place where role annotations may be necessary are in hs-boot files (How to compile mutually recursive modules), where the right-hand sides of definitions can be omitted. As usual, the types/classes declared in an hs-boot file must match up with the definitions in the hs file, including down to the roles. The default role for datatypes is representational in hs-boot files, corresponding to the common use case.

Role annotations are allowed on data, newtype, and class declarations. A role annotation declaration starts with type role and is followed by one role listing for each parameter of the type. (This parameter count includes parameters implicitly specified by a kind signature in a GADT-style data or newtype declaration.) Each role listing is a role (nominal, representational, or phantom) or a _. Using a _ says that GHC should infer that role. The role annotation may go anywhere in the same module as the datatype or class definition (much like a value-level type signature). Here are some examples:

type role T1 _ phantom
data T1 a b = MkT1 a     -- b is not used; annotation is fine but unnecessary

type role T2 _ phantom
data T2 a b = MkT2 b     -- ERROR: b is used and cannot be phantom

type role T3 _ nominal
data T3 a b = MkT3 a     -- OK: nominal is higher than necessary, but safe

type role T4 nominal
data T4 a = MkT4 (a Int) -- OK, but nominal is higher than necessary

type role C representational _   -- OK, with -XIncoherentInstances
class C a b where ...    -- OK, b will get a nominal role

type role X nominal
type X a = ...           -- ERROR: role annotations not allowed for type synonyms