Safe Haskell | None |
---|---|
Language | Haskell2010 |
Module for (a) type kinds and (b) type coercions,
as used in System FC. See Expr
for
more on System FC and how coercions fit into it.
- data Coercion
- type CoercionN = Coercion
- type CoercionR = Coercion
- type CoercionP = Coercion
- data UnivCoProvenance
- data CoercionHole
- data LeftOrRight
- data Var
- type CoVar = Id
- type TyCoVar = Id
- data Role
- ltRole :: Role -> Role -> Bool
- coVarTypes :: CoVar -> (Type, Type)
- coVarKind :: CoVar -> Type
- coVarKindsTypesRole :: CoVar -> (Kind, Kind, Type, Type, Role)
- coVarRole :: CoVar -> Role
- coercionType :: Coercion -> Type
- coercionKind :: Coercion -> Pair Type
- coercionKinds :: [Coercion] -> Pair [Type]
- mkCoercionType :: Role -> Type -> Type -> Type
- coercionRole :: Coercion -> Role
- coercionKindRole :: Coercion -> (Pair Type, Role)
- mkReflCo :: Role -> Type -> Coercion
- mkRepReflCo :: Type -> Coercion
- mkNomReflCo :: Type -> Coercion
- mkCoVarCo :: CoVar -> Coercion
- mkCoVarCos :: [CoVar] -> [Coercion]
- mkAxInstCo :: Role -> CoAxiom br -> BranchIndex -> [Type] -> [Coercion] -> Coercion
- mkUnbranchedAxInstCo :: Role -> CoAxiom Unbranched -> [Type] -> [Coercion] -> Coercion
- mkAxInstRHS :: CoAxiom br -> BranchIndex -> [Type] -> [Coercion] -> Type
- mkUnbranchedAxInstRHS :: CoAxiom Unbranched -> [Type] -> [Coercion] -> Type
- mkAxInstLHS :: CoAxiom br -> BranchIndex -> [Type] -> [Coercion] -> Type
- mkUnbranchedAxInstLHS :: CoAxiom Unbranched -> [Type] -> [Coercion] -> Type
- mkPiCo :: Role -> Var -> Coercion -> Coercion
- mkPiCos :: Role -> [Var] -> Coercion -> Coercion
- mkCoCast :: Coercion -> Coercion -> Coercion
- mkSymCo :: Coercion -> Coercion
- mkTransCo :: Coercion -> Coercion -> Coercion
- mkTransAppCo :: Role -> Coercion -> Type -> Type -> Role -> Coercion -> Type -> Type -> Role -> Coercion
- mkNthCo :: Int -> Coercion -> Coercion
- mkNthCoRole :: Role -> Int -> Coercion -> Coercion
- mkLRCo :: LeftOrRight -> Coercion -> Coercion
- mkInstCo :: Coercion -> Coercion -> Coercion
- mkAppCo :: Coercion -> Coercion -> Coercion
- mkAppCos :: Coercion -> [Coercion] -> Coercion
- mkTyConAppCo :: Role -> TyCon -> [Coercion] -> Coercion
- mkFunCo :: Role -> Coercion -> Coercion -> Coercion
- mkFunCos :: Role -> [Coercion] -> Coercion -> Coercion
- mkForAllCo :: TyVar -> Coercion -> Coercion -> Coercion
- mkForAllCos :: [(TyVar, Coercion)] -> Coercion -> Coercion
- mkHomoForAllCos :: [TyVar] -> Coercion -> Coercion
- mkHomoForAllCos_NoRefl :: [TyVar] -> Coercion -> Coercion
- mkPhantomCo :: Coercion -> Type -> Type -> Coercion
- mkHomoPhantomCo :: Type -> Type -> Coercion
- toPhantomCo :: Coercion -> Coercion
- mkUnsafeCo :: Role -> Type -> Type -> Coercion
- mkHoleCo :: CoercionHole -> Role -> Type -> Type -> Coercion
- mkUnivCo :: UnivCoProvenance -> Role -> Type -> Type -> Coercion
- mkSubCo :: Coercion -> Coercion
- mkAxiomInstCo :: CoAxiom Branched -> BranchIndex -> [Coercion] -> Coercion
- mkProofIrrelCo :: Role -> Coercion -> Coercion -> Coercion -> Coercion
- downgradeRole :: Role -> Role -> Coercion -> Coercion
- maybeSubCo :: EqRel -> Coercion -> Coercion
- mkAxiomRuleCo :: CoAxiomRule -> [Coercion] -> Coercion
- mkCoherenceCo :: Coercion -> Coercion -> Coercion
- mkCoherenceRightCo :: Coercion -> Coercion -> Coercion
- mkCoherenceLeftCo :: Coercion -> Coercion -> Coercion
- mkKindCo :: Coercion -> Coercion
- castCoercionKind :: Coercion -> Coercion -> Coercion -> Coercion
- mkHeteroCoercionType :: Role -> Kind -> Kind -> Type -> Type -> Type
- instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, Coercion)
- type NormaliseStepper = RecTcChecker -> TyCon -> [Type] -> NormaliseStepResult
- data NormaliseStepResult
- composeSteppers :: NormaliseStepper -> NormaliseStepper -> NormaliseStepper
- modifyStepResultCo :: (Coercion -> Coercion) -> NormaliseStepResult -> NormaliseStepResult
- unwrapNewTypeStepper :: NormaliseStepper
- topNormaliseNewType_maybe :: Type -> Maybe (Coercion, Type)
- topNormaliseTypeX_maybe :: NormaliseStepper -> Type -> Maybe (Coercion, Type)
- decomposeCo :: Arity -> Coercion -> [Coercion]
- getCoVar_maybe :: Coercion -> Maybe CoVar
- splitTyConAppCo_maybe :: Coercion -> Maybe (TyCon, [Coercion])
- splitAppCo_maybe :: Coercion -> Maybe (Coercion, Coercion)
- splitForAllCo_maybe :: Coercion -> Maybe (TyVar, Coercion, Coercion)
- nthRole :: Role -> TyCon -> Int -> Role
- tyConRolesX :: Role -> TyCon -> [Role]
- setNominalRole_maybe :: Coercion -> Maybe Coercion
- pickLR :: LeftOrRight -> (a, a) -> a
- isReflCo :: Coercion -> Bool
- isReflCo_maybe :: Coercion -> Maybe (Type, Role)
- isReflexiveCo :: Coercion -> Bool
- isReflexiveCo_maybe :: Coercion -> Maybe (Type, Role)
- mkCoVar :: Name -> Type -> CoVar
- isCoVar :: Var -> Bool
- coVarName :: CoVar -> Name
- setCoVarName :: CoVar -> Name -> CoVar
- setCoVarUnique :: CoVar -> Unique -> CoVar
- isCoVar_maybe :: Coercion -> Maybe CoVar
- tyCoVarsOfCo :: Coercion -> TyCoVarSet
- tyCoVarsOfCos :: [Coercion] -> TyCoVarSet
- coVarsOfCo :: Coercion -> CoVarSet
- tyCoVarsOfCoAcc :: Coercion -> FV
- tyCoVarsOfCosAcc :: [Coercion] -> FV
- tyCoVarsOfCoDSet :: Coercion -> DTyCoVarSet
- coercionSize :: Coercion -> Int
- type CvSubstEnv = CoVarEnv Coercion
- emptyCvSubstEnv :: CvSubstEnv
- lookupCoVar :: TCvSubst -> Var -> Maybe Coercion
- substCo :: TCvSubst -> Coercion -> Coercion
- substCos :: TCvSubst -> [Coercion] -> [Coercion]
- substCoVar :: TCvSubst -> CoVar -> Coercion
- substCoVars :: TCvSubst -> [CoVar] -> [Coercion]
- substCoWith :: [TyVar] -> [Type] -> Coercion -> Coercion
- substCoVarBndr :: TCvSubst -> CoVar -> (TCvSubst, CoVar)
- extendTCvSubstAndInScope :: TCvSubst -> TyCoVar -> Type -> TCvSubst
- getCvSubstEnv :: TCvSubst -> CvSubstEnv
- liftCoSubst :: Role -> LiftingContext -> Type -> Coercion
- liftCoSubstTyVar :: LiftingContext -> Role -> TyVar -> Maybe Coercion
- liftCoSubstWith :: Role -> [TyCoVar] -> [Coercion] -> Type -> Coercion
- liftCoSubstWithEx :: Role -> [TyVar] -> [Coercion] -> [TyVar] -> [Type] -> (Type -> Coercion, [Type])
- emptyLiftingContext :: InScopeSet -> LiftingContext
- extendLiftingContext :: LiftingContext -> TyVar -> Coercion -> LiftingContext
- liftCoSubstVarBndrCallback :: (LiftingContext -> Type -> (Coercion, a)) -> LiftingContext -> TyVar -> (LiftingContext, TyVar, Coercion, a)
- isMappedByLC :: TyCoVar -> LiftingContext -> Bool
- mkSubstLiftingContext :: TCvSubst -> LiftingContext
- zapLiftingContext :: LiftingContext -> LiftingContext
- substForAllCoBndrCallbackLC :: Bool -> (Coercion -> Coercion) -> LiftingContext -> TyVar -> Coercion -> (LiftingContext, TyVar, Coercion)
- lcTCvSubst :: LiftingContext -> TCvSubst
- lcInScopeSet :: LiftingContext -> InScopeSet
- type LiftCoEnv = VarEnv Coercion
- data LiftingContext = LC TCvSubst LiftCoEnv
- liftEnvSubstLeft :: TCvSubst -> LiftCoEnv -> TCvSubst
- liftEnvSubstRight :: TCvSubst -> LiftCoEnv -> TCvSubst
- substRightCo :: LiftingContext -> Coercion -> Coercion
- substLeftCo :: LiftingContext -> Coercion -> Coercion
- swapLiftCoEnv :: LiftCoEnv -> LiftCoEnv
- lcSubstLeft :: LiftingContext -> TCvSubst
- lcSubstRight :: LiftingContext -> TCvSubst
- eqCoercion :: Coercion -> Coercion -> Bool
- eqCoercionX :: RnEnv2 -> Coercion -> Coercion -> Bool
- seqCo :: Coercion -> ()
- pprCo :: Coercion -> SDoc
- pprParendCo :: Coercion -> SDoc
- pprCoBndr :: Name -> Coercion -> SDoc
- pprCoAxiom :: CoAxiom br -> SDoc
- pprCoAxBranch :: CoAxiom br -> CoAxBranch -> SDoc
- pprCoAxBranchHdr :: CoAxiom br -> BranchIndex -> SDoc
- tidyCo :: TidyEnv -> Coercion -> Coercion
- tidyCos :: TidyEnv -> [Coercion] -> [Coercion]
- promoteCoercion :: Coercion -> Coercion
Main data type
A Coercion
is concrete evidence of the equality/convertibility
of two types.
data UnivCoProvenance Source
For simplicity, we have just one UnivCo that represents a coercion from
some type to some other type, with (in general) no restrictions on the
type. The UnivCoProvenance specifies more exactly what the coercion really
is and why a program should (or shouldn't!) trust the coercion.
It is reasonable to consider each constructor of UnivCoProvenance
as a totally independent coercion form; their only commonality is
that they don't tell you what types they coercion between. (That info
is in the UnivCo
constructor of Coercion
.
data CoercionHole Source
A coercion to be filled in by the type-checker. See Note [Coercion holes]
data LeftOrRight Source
Functions over coercions
coVarTypes :: CoVar -> (Type, Type) Source
coercionType :: Coercion -> Type Source
coercionKind :: Coercion -> Pair Type Source
If it is the case that
c :: (t1 ~ t2)
i.e. the kind of c
relates t1
and t2
, then coercionKind c = Pair t1 t2
.
coercionKinds :: [Coercion] -> Pair [Type] Source
Apply coercionKind
to multiple Coercion
s
mkCoercionType :: Role -> Type -> Type -> Type Source
Makes a coercion type from two types: the types whose equality
is proven by the relevant Coercion
coercionRole :: Coercion -> Role Source
Retrieve the role from a coercion.
coercionKindRole :: Coercion -> (Pair Type, Role) Source
Get a coercion's kind and role. Why both at once? See Note [Computing a coercion kind and role]
Constructing coercions
mkRepReflCo :: Type -> Coercion Source
Make a representational reflexive coercion
mkNomReflCo :: Type -> Coercion Source
Make a nominal reflexive coercion
mkCoVarCos :: [CoVar] -> [Coercion] Source
mkAxInstCo :: Role -> CoAxiom br -> BranchIndex -> [Type] -> [Coercion] -> Coercion Source
mkUnbranchedAxInstCo :: Role -> CoAxiom Unbranched -> [Type] -> [Coercion] -> Coercion Source
mkAxInstRHS :: CoAxiom br -> BranchIndex -> [Type] -> [Coercion] -> Type Source
mkUnbranchedAxInstRHS :: CoAxiom Unbranched -> [Type] -> [Coercion] -> Type Source
mkAxInstLHS :: CoAxiom br -> BranchIndex -> [Type] -> [Coercion] -> Type Source
Return the left-hand type of the axiom, when the axiom is instantiated at the types given.
mkUnbranchedAxInstLHS :: CoAxiom Unbranched -> [Type] -> [Coercion] -> Type Source
Instantiate the left-hand side of an unbranched axiom
mkSymCo :: Coercion -> Coercion Source
Create a symmetric version of the given Coercion
that asserts
equality between the same types but in the other "direction", so
a kind of t1 ~ t2
becomes the kind t2 ~ t1
.
:: Role | r1 |
-> Coercion | co1 :: ty1a ~r1 ty1b |
-> Type | ty1a |
-> Type | ty1b |
-> Role | r2 |
-> Coercion | co2 :: ty2a ~r2 ty2b |
-> Type | ty2a |
-> Type | ty2b |
-> Role | r3 |
-> Coercion | :: ty1a ty2a ~r3 ty1b ty2b |
Like mkAppCo
, but allows the second coercion to be other than
nominal. See Note [mkTransAppCo]. Role r3 cannot be more stringent
than either r1 or r2.
mkLRCo :: LeftOrRight -> Coercion -> Coercion Source
mkTyConAppCo :: Role -> TyCon -> [Coercion] -> Coercion Source
Apply a type constructor to a list of coercions. It is the caller's responsibility to get the roles correct on argument coercions.
mkForAllCo :: TyVar -> Coercion -> Coercion -> Coercion Source
Make a Coercion from a tyvar, a kind coercion, and a body coercion. The kind of the tyvar should be the left-hand kind of the kind coercion.
mkHomoForAllCos :: [TyVar] -> Coercion -> Coercion Source
Make a Coercion quantified over a type variable; the variable has the same type in both sides of the coercion
mkHomoForAllCos_NoRefl :: [TyVar] -> Coercion -> Coercion Source
Like mkHomoForAllCos
, but doesn't check if the inner coercion
is reflexive.
mkPhantomCo :: Coercion -> Type -> Type -> Coercion Source
Make a phantom coercion between two types. The coercion passed in must be a nominal coercion between the kinds of the types.
mkHomoPhantomCo :: Type -> Type -> Coercion Source
Make a phantom coercion between two types of the same kind.
toPhantomCo :: Coercion -> Coercion Source
mkUnsafeCo :: Role -> Type -> Type -> Coercion Source
Manufacture an unsafe coercion from thin air.
Currently (May 14) this is used only to implement the
unsafeCoerce#
primitive. Optimise by pushing
down through type constructors.
mkHoleCo :: CoercionHole -> Role -> Type -> Type -> Coercion Source
Make a coercion from a coercion hole
:: UnivCoProvenance | |
-> Role | role of the built coercion, "r" |
-> Type | t1 :: k1 |
-> Type | t2 :: k2 |
-> Coercion | :: t1 ~r t2 |
Make a universal coercion between two arbitrary types.
mkAxiomInstCo :: CoAxiom Branched -> BranchIndex -> [Coercion] -> Coercion Source
:: Role | role of the created coercion, "r" |
-> Coercion | :: phi1 ~N phi2 |
-> Coercion | g1 :: phi1 |
-> Coercion | g2 :: phi2 |
-> Coercion | :: g1 ~r g2 |
Make a "coercion between coercions".
downgradeRole :: Role -> Role -> Coercion -> Coercion Source
Like downgradeRole_maybe
, but panics if the change isn't a downgrade.
See Note [Role twiddling functions]
maybeSubCo :: EqRel -> Coercion -> Coercion Source
If the EqRel is ReprEq, makes a SubCo; otherwise, does nothing. Note that the input coercion should always be nominal.
mkAxiomRuleCo :: CoAxiomRule -> [Coercion] -> Coercion Source
mkCoherenceCo :: Coercion -> Coercion -> Coercion infixl 5 Source
mkCoherenceRightCo :: Coercion -> Coercion -> Coercion infixl 5 Source
A CoherenceCo c1 c2 applies the coercion c2 to the left-hand type in the kind of c1. This function uses sym to get the coercion on the right-hand type of c1. Thus, if c1 :: s ~ t, then mkCoherenceRightCo c1 c2 has the kind (s ~ (t |> c2)) down through type constructors. The second coercion must be representational.
mkCoherenceLeftCo :: Coercion -> Coercion -> Coercion infixl 5 Source
An explictly directed synonym of mkCoherenceCo. The second coercion must be representational.
castCoercionKind :: Coercion -> Coercion -> Coercion -> Coercion Source
Creates a new coercion with both of its types casted by different casts castCoercionKind g h1 h2, where g :: t1 ~ t2, has type (t1 |> h1) ~ (t2 |> h2) The second and third coercions must be nominal.
Decomposition
instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, Coercion) Source
If co :: T ts ~ rep_ty
then:
instNewTyCon_maybe T ts = Just (rep_ty, co)
Checks for a newtype, and for being saturated
type NormaliseStepper = RecTcChecker -> TyCon -> [Type] -> NormaliseStepResult Source
A function to check if we can reduce a type by one step. Used
with topNormaliseTypeX_maybe
.
data NormaliseStepResult Source
The result of stepping in a normalisation function.
See topNormaliseTypeX_maybe
.
composeSteppers :: NormaliseStepper -> NormaliseStepper -> NormaliseStepper Source
Try one stepper and then try the next, if the first doesn't make progress. So if it returns NS_Done, it means that both steppers are satisfied
unwrapNewTypeStepper :: NormaliseStepper Source
A NormaliseStepper
that unwraps newtypes, careful not to fall into
a loop. If it would fall into a loop, it produces NS_Abort
.
topNormaliseNewType_maybe :: Type -> Maybe (Coercion, Type) Source
Sometimes we want to look through a newtype
and get its associated coercion.
This function strips off newtype
layers enough to reveal something that isn't
a newtype
. Specifically, here's the invariant:
topNormaliseNewType_maybe rec_nts ty = Just (co, ty')
then (a) co : ty0 ~ ty'
.
(b) ty' is not a newtype.
The function returns Nothing
for non-newtypes
,
or unsaturated applications
This function does *not* look through type families, because it has no access to the type family environment. If you do have that at hand, consider to use topNormaliseType_maybe, which should be a drop-in replacement for topNormaliseNewType_maybe
topNormaliseTypeX_maybe :: NormaliseStepper -> Type -> Maybe (Coercion, Type) Source
A general function for normalising the top-level of a type. It continues
to use the provided NormaliseStepper
until that function fails, and then
this function returns. The roles of the coercions produced by the
NormaliseStepper
must all be the same, which is the role returned from
the call to topNormaliseTypeX_maybe
.
decomposeCo :: Arity -> Coercion -> [Coercion] Source
getCoVar_maybe :: Coercion -> Maybe CoVar Source
Attempts to obtain the type variable underlying a Coercion
splitTyConAppCo_maybe :: Coercion -> Maybe (TyCon, [Coercion]) Source
Attempts to tease a coercion apart into a type constructor and the application of a number of coercion arguments to that constructor
splitAppCo_maybe :: Coercion -> Maybe (Coercion, Coercion) Source
Attempt to take a coercion application apart.
tyConRolesX :: Role -> TyCon -> [Role] Source
setNominalRole_maybe :: Coercion -> Maybe Coercion Source
Converts a coercion to be nominal, if possible. See Note [Role twiddling functions]
pickLR :: LeftOrRight -> (a, a) -> a Source
isReflCo :: Coercion -> Bool Source
Tests if this coercion is obviously reflexive. Guaranteed to work
very quickly. Sometimes a coercion can be reflexive, but not obviously
so. c.f. isReflexiveCo
isReflCo_maybe :: Coercion -> Maybe (Type, Role) Source
Returns the type coerced if this coercion is reflexive. Guaranteed
to work very quickly. Sometimes a coercion can be reflexive, but not
obviously so. c.f. isReflexiveCo_maybe
isReflexiveCo :: Coercion -> Bool Source
Slowly checks if the coercion is reflexive. Don't call this in a loop, as it walks over the entire coercion.
isReflexiveCo_maybe :: Coercion -> Maybe (Type, Role) Source
Extracts the coerced type from a reflexive coercion. This potentially walks over the entire coercion, so avoid doing this in a loop.
Coercion variables
setCoVarName :: CoVar -> Name -> CoVar Source
setCoVarUnique :: CoVar -> Unique -> CoVar Source
isCoVar_maybe :: Coercion -> Maybe CoVar Source
Extract a covar, if possible. This check is dirty. Be ashamed of yourself. (It's dirty because it cares about the structure of a coercion, which is morally reprehensible.)
Free variables
tyCoVarsOfCo :: Coercion -> TyCoVarSet Source
tyCoVarsOfCos :: [Coercion] -> TyCoVarSet Source
coVarsOfCo :: Coercion -> CoVarSet Source
tyCoVarsOfCoAcc :: Coercion -> FV Source
tyCoVarsOfCosAcc :: [Coercion] -> FV Source
tyCoVarsOfCoDSet :: Coercion -> DTyCoVarSet Source
Get a deterministic set of the vars free in a coercion
coercionSize :: Coercion -> Int Source
Substitution
substCoVar :: TCvSubst -> CoVar -> Coercion Source
substCoVars :: TCvSubst -> [CoVar] -> [Coercion] Source
substCoWith :: [TyVar] -> [Type] -> Coercion -> Coercion Source
Coercion substitution, see zipTvSubst
Lifting
liftCoSubst :: Role -> LiftingContext -> Type -> Coercion Source
liftCoSubst role lc ty
produces a coercion (at role role
)
that coerces between lc_left(ty)
and lc_right(ty)
, where
lc_left
is a substitution mapping type variables to the left-hand
types of the mapped coercions in lc
, and similar for lc_right
.
liftCoSubstTyVar :: LiftingContext -> Role -> TyVar -> Maybe Coercion Source
liftCoSubstWithEx :: Role -> [TyVar] -> [Coercion] -> [TyVar] -> [Type] -> (Type -> Coercion, [Type]) Source
:: LiftingContext | original LC |
-> TyVar | new variable to map... |
-> Coercion | ...to this lifted version |
-> LiftingContext |
Extend a lifting context with a new type mapping.
liftCoSubstVarBndrCallback :: (LiftingContext -> Type -> (Coercion, a)) -> LiftingContext -> TyVar -> (LiftingContext, TyVar, Coercion, a) Source
isMappedByLC :: TyCoVar -> LiftingContext -> Bool Source
Is a var in the domain of a lifting context?
zapLiftingContext :: LiftingContext -> LiftingContext Source
Erase the environments in a lifting context
substForAllCoBndrCallbackLC :: Bool -> (Coercion -> Coercion) -> LiftingContext -> TyVar -> Coercion -> (LiftingContext, TyVar, Coercion) Source
Like substForAllCoBndr
, but works on a lifting context
lcTCvSubst :: LiftingContext -> TCvSubst Source
Extract the underlying substitution from the LiftingContext
lcInScopeSet :: LiftingContext -> InScopeSet Source
Get the InScopeSet
from a LiftingContext
liftEnvSubstLeft :: TCvSubst -> LiftCoEnv -> TCvSubst Source
liftEnvSubstRight :: TCvSubst -> LiftCoEnv -> TCvSubst Source
substRightCo :: LiftingContext -> Coercion -> Coercion Source
substLeftCo :: LiftingContext -> Coercion -> Coercion Source
swapLiftCoEnv :: LiftCoEnv -> LiftCoEnv Source
Apply "sym" to all coercions in a LiftCoEnv
Comparison
eqCoercion :: Coercion -> Coercion -> Bool Source
Syntactic equality of coercions
eqCoercionX :: RnEnv2 -> Coercion -> Coercion -> Bool Source
Compare two Coercion
s, with respect to an RnEnv2
Forcing evaluation of coercions
Pretty-printing
pprParendCo :: Coercion -> SDoc Source
pprCoAxiom :: CoAxiom br -> SDoc Source
pprCoAxBranch :: CoAxiom br -> CoAxBranch -> SDoc Source
pprCoAxBranchHdr :: CoAxiom br -> BranchIndex -> SDoc Source
Tidying
Other
promoteCoercion :: Coercion -> Coercion Source
like mkKindCo, but aggressively & recursively optimizes to avoid using a KindCo constructor. The output role is nominal.