This page describes how roles are implemented in GHC. If you're looking for how to use roles in a Haskell program, see Roles.
The Role datatype
The Role datatype, defined in CoAxiom to avoid mentioning it in an hs-boot file, is defined thusly:
data Role = Nominal | Representational | Phantom deriving (Eq, Data.Data, Data.Typeable)
Two types are nominally equal when they have the same name. This is the usual equality in Haskell or Core. Two types are representationally equal when they have the same representation. (If a type is higher-kinded, all nominally equal instantiations lead to representationally equal types.) Any two types are "phantomly" equal.
Roles on Coercions
Every coercion proves an equality at a certain role. There are subtle rules governing what compositions are allowed. See the core spec for the details, or look at coercionRole. To facilitate this, a few of the Coercion constructors needed to be changed:
- Refl now takes a role and a type, proving reflexive equality at the given role.
- TyConAppCo also takes a role. The choice of this role affects which roles the arguments must be at. If the role is nominal, all arguments must be nominal. If the role is phantom, all arguments must be phantom. But, if the role is representational, the argument roles must correspond to tyConRoles called on the tycon in the TyConAppCo. The idea is that different tycons have different requirements in order to prove representational equality. See the section below discussing roles with tycons. Note that, now, the interpretation of a TyConAppCo may differ from that of nested AppCos.
- CoVarCos extract their role from their type.
- UnivCo is a new "universal" coercion. It takes a role and two types and witnesses equality between those types at that role. It replaces the old UnsafeCo. UnivCo at role P is needed in TyConAppCos at role P.
- The role produced by NthCo is essentially the inverse of the TyConAppCo story. If NthCo's parameter is N or P, the result has the same role. If it's R, though, the result's role is determined by tyConRoles once again.
- SubCo implements sub-roling: its argument is N and it produces R.
Because coercions can be produced at any of the three roles, most functions that produce them now take a Role parameter, indicating what role to produce. These, in turn, make use of maybeSubCo2 and maybeSubCo, which convert among the roles; they are documented in the source.
The functions mkTyConAppCo (and, in turn mkFunCo) now have a bit of a delicate requirement on their arguments: the argument types must "match" the desired role. Thus, if the desired role is R, the arguments must have the roles indicated by tyConRoles. In practice, it is not hard to ensure this precondition, but you do have to be aware of it.
Roles on TcCoercions
The type checker operates solely on TcCoercions. What roles do these have? Because the type checker thinks only about nominal equality, it would make sense for all TcCoercions to have role N. But, sometimes the type checker needs to pass around a coercion produced by a newtype (for example, in implicit-parameter handling). So, they need to handle R coercions as well. But, we never lint a TcCoercion, so we don't quite need to be as careful with them.
The solution is that, when desugaring to Coercions, we pass in a Role parameter, indicating how we should interpret the TcCoercion. (Casts always use R equality.) Because we hopefully never ask for nominal equality from a newtype axiom, this works in practice. If a problem arises, it will most likely take the form of a maybeSubCo2 panic.
Roles with TyCons
Every TyCon's parameters are now each assigned a role. The interpretation is this: if a parameter a of tycon T has role r, then a coercion at role r can be lifted into a representational coercion of T a. Thus, N is the most restrictive, and P is the most permissive. These roles are user-visible, so they are described on the Roles page.
Kind variables are all assigned role N. We must be careful when comparing a tycon's roles against the role annotations, because role annotations are only on type variables, never kind variables. So, we often have to drop the kind-variable roles when doing the comparison.
eqPrimTyCon vs eqReprPrimTyCon
The type of a nominal coercion is headed by eqPrimTyCon, spelled ~#. In order to support NewtypeWrappers, we must also have a way of storing representational coercions. Their types are headed by eqReprPrimTyCon, spelled ~R#.