ghc-9.0.2: The GHC API
Safe HaskellSafe-Inferred
LanguageHaskell2010

GHC.Core.Coercion

Description

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.

Synopsis

Main data type

data Coercion #

A Coercion is concrete evidence of the equality/convertibility of two types.

Instances

Instances details
Data Coercion # 
Instance details

Defined in GHC.Core.TyCo.Rep

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Coercion -> c Coercion Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Coercion Source #

toConstr :: Coercion -> Constr Source #

dataTypeOf :: Coercion -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Coercion) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Coercion) Source #

gmapT :: (forall b. Data b => b -> b) -> Coercion -> Coercion Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Coercion -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Coercion -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Coercion -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Coercion -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Coercion -> m Coercion Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Coercion -> m Coercion Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Coercion -> m Coercion Source #

Outputable Coercion # 
Instance details

Defined in GHC.Core.TyCo.Rep

data MCoercion #

A semantically more meaningful type to represent what may or may not be a useful Coercion.

Constructors

MRefl 
MCo Coercion 

Instances

Instances details
Data MCoercion # 
Instance details

Defined in GHC.Core.TyCo.Rep

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MCoercion -> c MCoercion Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c MCoercion Source #

toConstr :: MCoercion -> Constr Source #

dataTypeOf :: MCoercion -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c MCoercion) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MCoercion) Source #

gmapT :: (forall b. Data b => b -> b) -> MCoercion -> MCoercion Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MCoercion -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MCoercion -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> MCoercion -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> MCoercion -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> MCoercion -> m MCoercion Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> MCoercion -> m MCoercion Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> MCoercion -> m MCoercion Source #

Outputable MCoercion # 
Instance details

Defined in GHC.Core.TyCo.Rep

data UnivCoProvenance #

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.

Instances

Instances details
Data UnivCoProvenance # 
Instance details

Defined in GHC.Core.TyCo.Rep

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> UnivCoProvenance -> c UnivCoProvenance Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c UnivCoProvenance Source #

toConstr :: UnivCoProvenance -> Constr Source #

dataTypeOf :: UnivCoProvenance -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c UnivCoProvenance) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c UnivCoProvenance) Source #

gmapT :: (forall b. Data b => b -> b) -> UnivCoProvenance -> UnivCoProvenance Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> UnivCoProvenance -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> UnivCoProvenance -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance Source #

Outputable UnivCoProvenance # 
Instance details

Defined in GHC.Core.TyCo.Rep

data CoercionHole #

A coercion to be filled in by the type-checker. See Note [Coercion holes]

Instances

Instances details
Data CoercionHole # 
Instance details

Defined in GHC.Core.TyCo.Rep

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> CoercionHole -> c CoercionHole Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c CoercionHole Source #

toConstr :: CoercionHole -> Constr Source #

dataTypeOf :: CoercionHole -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c CoercionHole) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CoercionHole) Source #

gmapT :: (forall b. Data b => b -> b) -> CoercionHole -> CoercionHole Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CoercionHole -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CoercionHole -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> CoercionHole -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> CoercionHole -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> CoercionHole -> m CoercionHole Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> CoercionHole -> m CoercionHole Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> CoercionHole -> m CoercionHole Source #

Outputable CoercionHole # 
Instance details

Defined in GHC.Core.TyCo.Rep

data BlockSubstFlag #

Instances

Instances details
Outputable BlockSubstFlag # 
Instance details

Defined in GHC.Core.TyCo.Rep

data LeftOrRight #

Constructors

CLeft 
CRight 

Instances

Instances details
Data LeftOrRight # 
Instance details

Defined in GHC.Types.Basic

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> LeftOrRight -> c LeftOrRight Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c LeftOrRight Source #

toConstr :: LeftOrRight -> Constr Source #

dataTypeOf :: LeftOrRight -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c LeftOrRight) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c LeftOrRight) Source #

gmapT :: (forall b. Data b => b -> b) -> LeftOrRight -> LeftOrRight Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> LeftOrRight -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> LeftOrRight -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> LeftOrRight -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> LeftOrRight -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> LeftOrRight -> m LeftOrRight Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> LeftOrRight -> m LeftOrRight Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> LeftOrRight -> m LeftOrRight Source #

Binary LeftOrRight # 
Instance details

Defined in GHC.Utils.Binary

Outputable LeftOrRight # 
Instance details

Defined in GHC.Types.Basic

Eq LeftOrRight # 
Instance details

Defined in GHC.Types.Basic

data Var #

Variable

Essentially a typed Name, that may also contain some additional information about the Var and its use sites.

Instances

Instances details
Data Var # 
Instance details

Defined in GHC.Types.Var

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Var -> c Var Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Var Source #

toConstr :: Var -> Constr Source #

dataTypeOf :: Var -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Var) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Var) Source #

gmapT :: (forall b. Data b => b -> b) -> Var -> Var Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Var -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Var -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Var -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Var -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Var -> m Var Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Var -> m Var Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Var -> m Var Source #

NamedThing Var # 
Instance details

Defined in GHC.Types.Var

Methods

getOccName :: Var -> OccName #

getName :: Var -> Name #

HasOccName Var # 
Instance details

Defined in GHC.Types.Var

Methods

occName :: Var -> OccName #

Uniquable Var # 
Instance details

Defined in GHC.Types.Var

Methods

getUnique :: Var -> Unique #

Outputable Var # 
Instance details

Defined in GHC.Types.Var

Methods

ppr :: Var -> SDoc #

pprPrec :: Rational -> Var -> SDoc #

OutputableBndr Var # 
Instance details

Defined in GHC.Core.Ppr

Eq Var # 
Instance details

Defined in GHC.Types.Var

Methods

(==) :: Var -> Var -> Bool #

(/=) :: Var -> Var -> Bool #

Ord Var # 
Instance details

Defined in GHC.Types.Var

Methods

compare :: Var -> Var -> Ordering #

(<) :: Var -> Var -> Bool #

(<=) :: Var -> Var -> Bool #

(>) :: Var -> Var -> Bool #

(>=) :: Var -> Var -> Bool #

max :: Var -> Var -> Var #

min :: Var -> Var -> Var #

type CoVar = Id #

Coercion Variable

type TyCoVar = Id #

Type or Coercion Variable

data Role #

Instances

Instances details
Data Role # 
Instance details

Defined in GHC.Core.Coercion.Axiom

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Role -> c Role Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Role Source #

toConstr :: Role -> Constr Source #

dataTypeOf :: Role -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Role) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Role) Source #

gmapT :: (forall b. Data b => b -> b) -> Role -> Role Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Role -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Role -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Role -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Role -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Role -> m Role Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Role -> m Role Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Role -> m Role Source #

Binary Role # 
Instance details

Defined in GHC.Core.Coercion.Axiom

Methods

put_ :: BinHandle -> Role -> IO () #

put :: BinHandle -> Role -> IO (Bin Role) #

get :: BinHandle -> IO Role #

Outputable Role # 
Instance details

Defined in GHC.Core.Coercion.Axiom

Methods

ppr :: Role -> SDoc #

pprPrec :: Rational -> Role -> SDoc #

Eq Role # 
Instance details

Defined in GHC.Core.Coercion.Axiom

Methods

(==) :: Role -> Role -> Bool #

(/=) :: Role -> Role -> Bool #

Ord Role # 
Instance details

Defined in GHC.Core.Coercion.Axiom

Methods

compare :: Role -> Role -> Ordering #

(<) :: Role -> Role -> Bool #

(<=) :: Role -> Role -> Bool #

(>) :: Role -> Role -> Bool #

(>=) :: Role -> Role -> Bool #

max :: Role -> Role -> Role #

min :: Role -> Role -> Role #

ltRole :: Role -> Role -> Bool #

Functions over coercions

mkCoercionType :: Role -> Type -> Type -> Type #

Makes a coercion type from two types: the types whose equality is proven by the relevant Coercion

coercionKind :: Coercion -> Pair Type #

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] #

Apply coercionKind to multiple Coercions

coercionRole :: Coercion -> Role #

Retrieve the role from a coercion.

coercionKindRole :: Coercion -> (Pair Type, Role) #

Get a coercion's kind and role.

Constructing coercions

mkGReflCo :: Role -> Type -> MCoercionN -> Coercion #

Make a generalized reflexive coercion

mkReflCo :: Role -> Type -> Coercion #

Make a reflexive coercion

mkRepReflCo :: Type -> Coercion #

Make a representational reflexive coercion

mkNomReflCo :: Type -> Coercion #

Make a nominal reflexive coercion

mkAxInstLHS :: CoAxiom br -> BranchIndex -> [Type] -> [Coercion] -> Type #

Return the left-hand type of the axiom, when the axiom is instantiated at the types given.

mkUnbranchedAxInstLHS :: CoAxiom Unbranched -> [Type] -> [Coercion] -> Type #

Instantiate the left-hand side of an unbranched axiom

mkPiCo :: Role -> Var -> Coercion -> Coercion #

Make a forall Coercion, where both types related by the coercion are quantified over the same variable.

mkSymCo :: Coercion -> Coercion #

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.

mkTransCo :: Coercion -> Coercion -> Coercion #

Create a new Coercion by composing the two given Coercions transitively. (co1 ; co2)

mkTransMCo :: MCoercion -> MCoercion -> MCoercion #

Compose two MCoercions via transitivity

nthCoRole :: Int -> Coercion -> Role #

If you're about to call mkNthCo r n co, then r should be whatever nthCoRole n co returns.

mkInstCo :: Coercion -> Coercion -> Coercion #

Instantiates a Coercion.

mkAppCo #

Arguments

:: Coercion

:: t1 ~r t2

-> Coercion

:: s1 ~N s2, where s1 :: k1, s2 :: k2

-> Coercion

:: t1 s1 ~r t2 s2

Apply a Coercion to another Coercion. The second coercion must be Nominal, unless the first is Phantom. If the first is Phantom, then the second can be either Phantom or Nominal.

mkAppCos :: Coercion -> [Coercion] -> Coercion #

Applies multiple Coercions to another Coercion, from left to right. See also mkAppCo.

mkTyConAppCo :: HasDebugCallStack => Role -> TyCon -> [Coercion] -> Coercion #

Apply a type constructor to a list of coercions. It is the caller's responsibility to get the roles correct on argument coercions.

mkFunCo :: Role -> CoercionN -> Coercion -> Coercion -> Coercion #

Build a function Coercion from two other Coercions. That is, given co1 :: a ~ b and co2 :: x ~ y produce co :: (a -> x) ~ (b -> y).

mkForAllCo :: TyCoVar -> CoercionN -> Coercion -> Coercion #

Make a Coercion from a tycovar, a kind coercion, and a body coercion. The kind of the tycovar should be the left-hand kind of the kind coercion. See Note [Unused coercion variable in ForAllCo]

mkForAllCos :: [(TyCoVar, CoercionN)] -> Coercion -> Coercion #

Make nested ForAllCos

mkHomoForAllCos :: [TyCoVar] -> Coercion -> Coercion #

Make a Coercion quantified over a type/coercion variable; the variable has the same type in both sides of the coercion

mkPhantomCo :: Coercion -> Type -> Type -> Coercion #

Make a phantom coercion between two types. The coercion passed in must be a nominal coercion between the kinds of the types.

mkHoleCo :: CoercionHole -> Coercion #

Make a coercion from a coercion hole

mkUnivCo #

Arguments

:: 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.

mkProofIrrelCo #

Arguments

:: 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 #

Like downgradeRole_maybe, but panics if the change isn't a downgrade. See Note [Role twiddling functions]

mkGReflRightCo :: Role -> Type -> CoercionN -> Coercion #

Given ty :: k1, co :: k1 ~ k2, produces co' :: ty ~r (ty |> co)

mkGReflLeftCo :: Role -> Type -> CoercionN -> Coercion #

Given ty :: k1, co :: k1 ~ k2, produces co' :: (ty |> co) ~r ty

mkCoherenceLeftCo :: Role -> Type -> CoercionN -> Coercion -> Coercion #

Given ty :: k1, co :: k1 ~ k2, co2:: ty ~r ty', produces @co' :: (ty |> co) ~r ty' It is not only a utility function, but it saves allocation when co is a GRefl coercion.

mkCoherenceRightCo :: Role -> Type -> CoercionN -> Coercion -> Coercion #

Given ty :: k1, co :: k1 ~ k2, co2:: ty' ~r ty, produces @co' :: ty' ~r (ty |> co) It is not only a utility function, but it saves allocation when co is a GRefl coercion.

mkKindCo :: Coercion -> Coercion #

Given co :: (a :: k) ~ (b :: k') produce co' :: k ~ k'.

castCoercionKind :: Coercion -> CoercionN -> CoercionN -> Coercion #

Creates a new coercion with both of its types casted by different casts castCoercionKind g h1 h2, where g :: t1 ~r t2, has type (t1 |> h1) ~r (t2 |> h2). h1 and h2 must be nominal. It calls coercionKindRole, so it's quite inefficient (which I stands for) Use castCoercionKind2 instead if t1, t2, and r are known beforehand.

castCoercionKind1 :: Coercion -> Role -> Type -> Type -> CoercionN -> Coercion #

castCoercionKind1 g r t1 t2 h = coercionKind g r t1 t2 h h That is, it's a specialised form of castCoercionKind, where the two kind coercions are identical castCoercionKind1 g r t1 t2 h, where g :: t1 ~r t2, has type (t1 |> h) ~r (t2 |> h). h must be nominal. See Note [castCoercionKind1]

castCoercionKind2 :: Coercion -> Role -> Type -> Type -> CoercionN -> CoercionN -> Coercion #

Creates a new coercion with both of its types casted by different casts castCoercionKind2 g r t1 t2 h1 h2, where g :: t1 ~r t2, has type (t1 |> h1) ~r (t2 |> h2). h1 and h2 must be nominal.

mkFamilyTyConAppCo :: TyCon -> [CoercionN] -> CoercionN #

Given a family instance TyCon and its arg Coercions, return the corresponding family Coercion. E.g:

data family T a
data instance T (Maybe b) = MkT b

Where the instance TyCon is :RTL, so:

mkFamilyTyConAppCo :RTL (co :: a ~# Int) = T (Maybe a) ~# T (Maybe Int)

cf. mkFamilyTyConApp

mkPrimEqPred :: Type -> Type -> Type #

Creates a primitive type equality predicate. Invariant: the types are not Coercions

mkPrimEqPredRole :: Role -> Type -> Type -> PredType #

Makes a lifted equality predicate at the given role

mkHeteroPrimEqPred :: Kind -> Kind -> Type -> Type -> Type #

Creates a primitive type equality predicate with explicit kinds

mkHeteroReprPrimEqPred :: Kind -> Kind -> Type -> Type -> Type #

Creates a primitive representational type equality predicate with explicit kinds

Decomposition

instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, Coercion) #

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 ev = RecTcChecker -> TyCon -> [Type] -> NormaliseStepResult ev #

A function to check if we can reduce a type by one step. Used with topNormaliseTypeX.

data NormaliseStepResult ev #

The result of stepping in a normalisation function. See topNormaliseTypeX.

Constructors

NS_Done

Nothing more to do

NS_Abort

Utter failure. The outer function should fail too.

NS_Step RecTcChecker Type ev

We stepped, yielding new bits; ^ ev is evidence; Usually a co :: old type ~ new type

composeSteppers :: NormaliseStepper ev -> NormaliseStepper ev -> NormaliseStepper ev #

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 Coercion #

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) #

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 If topNormliseNewType_maybe ty = Just (co, ty'), then co : ty ~R ty'

topNormaliseTypeX :: NormaliseStepper ev -> (ev -> ev -> ev) -> Type -> Maybe (ev, Type) #

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.

Typically ev is Coercion.

If topNormaliseTypeX step plus ty = Just (ev, ty') then ty ~ev1~ t1 ~ev2~ t2 ... ~evn~ ty' and ev = ev1 plus ev2 plus ... plus evn If it returns Nothing then no newtype unwrapping could happen

decomposeCo :: Arity -> Coercion -> [Role] -> [Coercion] #

This breaks a Coercion with type T A B C ~ T D E F into a list of Coercions of kinds A ~ D, B ~ E and E ~ F. Hence:

decomposeCo 3 c [r1, r2, r3] = [nth r1 0 c, nth r2 1 c, nth r3 2 c]

getCoVar_maybe :: Coercion -> Maybe CoVar #

Attempts to obtain the type variable underlying a Coercion

splitTyConAppCo_maybe :: Coercion -> Maybe (TyCon, [Coercion]) #

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) #

Attempt to take a coercion application apart.

splitForAllCo_ty_maybe :: Coercion -> Maybe (TyVar, Coercion, Coercion) #

Like splitForAllCo_maybe, but only returns Just for tyvar binder

splitForAllCo_co_maybe :: Coercion -> Maybe (CoVar, Coercion, Coercion) #

Like splitForAllCo_maybe, but only returns Just for covar binder

nthRole :: Role -> TyCon -> Int -> Role #

setNominalRole_maybe :: Role -> Coercion -> Maybe Coercion #

Converts a coercion to be nominal, if possible. See Note [Role twiddling functions]

pickLR :: LeftOrRight -> (a, a) -> a #

isGReflCo :: Coercion -> Bool #

Tests if this coercion is obviously a generalized reflexive coercion. Guaranteed to work very quickly.

isReflCo :: Coercion -> Bool #

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) #

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

isGReflCo_maybe :: Coercion -> Maybe (Type, Role) #

Returns the type coerced if this coercion is a generalized reflexive coercion. Guaranteed to work very quickly.

isReflexiveCo :: Coercion -> Bool #

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) #

Extracts the coerced type from a reflexive coercion. This potentially walks over the entire coercion, so avoid doing this in a loop.

isGReflMCo :: MCoercion -> Bool #

Tests if this MCoercion is obviously generalized reflexive Guaranteed to work very quickly.

Coercion variables

isCoVar :: Var -> Bool #

Is this a coercion variable? Satisfies isId v ==> isCoVar v == not (isNonCoVarId v).

isCoVar_maybe :: Coercion -> Maybe CoVar #

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

tyCoVarsOfCoDSet :: Coercion -> DTyCoVarSet #

Get a deterministic set of the vars free in a coercion

Substitution

type CvSubstEnv = CoVarEnv Coercion #

A substitution of Coercions for CoVars

substCo :: HasCallStack => TCvSubst -> Coercion -> Coercion #

Substitute within a Coercion The substitution has to satisfy the invariants described in Note [The substitution invariant].

substCos :: HasCallStack => TCvSubst -> [Coercion] -> [Coercion] #

Substitute within several Coercions The substitution has to satisfy the invariants described in Note [The substitution invariant].

substCoWith :: HasCallStack => [TyVar] -> [Type] -> Coercion -> Coercion #

Coercion substitution, see zipTvSubst

Lifting

liftCoSubst :: HasDebugCallStack => Role -> LiftingContext -> Type -> Coercion #

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.

liftCoSubstWithEx :: Role -> [TyVar] -> [Coercion] -> [TyCoVar] -> [Type] -> (Type -> Coercion, [Type]) #

extendLiftingContext #

Arguments

:: LiftingContext

original LC

-> TyCoVar

new variable to map...

-> Coercion

...to this lifted version

-> LiftingContext 

Extend a lifting context with a new mapping.

extendLiftingContextAndInScope #

Arguments

:: LiftingContext

Original LC

-> TyCoVar

new variable to map...

-> Coercion

to this coercion

-> LiftingContext 

Extend a lifting context with a new mapping, and extend the in-scope set

isMappedByLC :: TyCoVar -> LiftingContext -> Bool #

Is a var in the domain of a lifting context?

zapLiftingContext :: LiftingContext -> LiftingContext #

Erase the environments in a lifting context

lcTCvSubst :: LiftingContext -> TCvSubst #

Extract the underlying substitution from the LiftingContext

data LiftingContext #

Constructors

LC TCvSubst LiftCoEnv 

Instances

Instances details
Outputable LiftingContext # 
Instance details

Defined in GHC.Core.Coercion

swapLiftCoEnv :: LiftCoEnv -> LiftCoEnv #

Apply "sym" to all coercions in a LiftCoEnv

Comparison

eqCoercion :: Coercion -> Coercion -> Bool #

Syntactic equality of coercions

eqCoercionX :: RnEnv2 -> Coercion -> Coercion -> Bool #

Compare two Coercions, with respect to an RnEnv2

Forcing evaluation of coercions

seqCo :: Coercion -> () #

Pretty-printing

Tidying

Other

promoteCoercion :: Coercion -> CoercionN #

like mkKindCo, but aggressively & recursively optimizes to avoid using a KindCo constructor. The output role is nominal.

buildCoercion :: Type -> Type -> CoercionN #

Assuming that two types are the same, ignoring coercions, find a nominal coercion between the types. This is useful when optimizing transitivity over coercion applications, where splitting two AppCos might yield different kinds. See Note [EtaAppCo] in GHC.Core.Coercion.Opt.

badCoercionHole :: Type -> Bool #

Is there a blocking coercion hole in this type? See GHC.Tc.Solver.Canonical Note [Equalities with incompatible kinds]

badCoercionHoleCo :: Coercion -> Bool #

Is there a blocking coercion hole in this coercion? See GHC.Tc.Solver.Canonical Note [Equalities with incompatible kinds]