This page describes how roles are implemented in GHC. If you're looking for how to use roles in a Haskell program, see Roles.
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.
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:
Reflnow takes a role and a type, proving reflexive equality at the given role.
TyConAppCoalso 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
tyConRolescalled 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
TyConAppComay differ from that of nested
CoVarCos extract their role from their type.
UnivCois a new "universal" coercion. It takes a role and two types and witnesses equality between those types at that role. It replaces the old
UnivCoat role P is needed in
TyConAppCos at role P.
- The role produced by
NthCois essentially the inverse of the
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
SubCoimplements 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
maybeSubCo, which convert among the roles;
they are documented in the source.
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.
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
we don't quite need to be as careful with them.
The solution is that, when desugaring to
Coercions, we pass in a
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
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.
The type of a nominal coercion is headed by
order to support NewtypeWrappers, we must also have a way of storing
representational coercions. Their types are headed by