ghc-9.6.0.20230128: 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 Source #

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

Instances

Instances details
Data Coercion Source # 
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 Source # 
Instance details

Defined in GHC.Core.TyCo.Rep

Methods

ppr :: Coercion -> SDoc Source #

Eq (DeBruijn Coercion) Source # 
Instance details

Defined in GHC.Core.Map.Type

data MCoercion Source #

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 Source # 
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 Source # 
Instance details

Defined in GHC.Core.TyCo.Rep

Methods

ppr :: MCoercion -> SDoc Source #

data CoSel Source #

Instances

Instances details
Data CoSel Source # 
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) -> CoSel -> c CoSel Source #

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

toConstr :: CoSel -> Constr Source #

dataTypeOf :: CoSel -> DataType Source #

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

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

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

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

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

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

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

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

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

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

NFData CoSel Source # 
Instance details

Defined in GHC.Core.TyCo.Rep

Methods

rnf :: CoSel -> () Source #

Binary CoSel Source # 
Instance details

Defined in GHC.Core.TyCo.Rep

Outputable CoSel Source # 
Instance details

Defined in GHC.Core.TyCo.Rep

Methods

ppr :: CoSel -> SDoc Source #

Eq CoSel Source # 
Instance details

Defined in GHC.Core.TyCo.Rep

Methods

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

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

data FunSel Source #

Constructors

SelMult 
SelArg 
SelRes 

Instances

Instances details
Data FunSel Source # 
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) -> FunSel -> c FunSel Source #

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

toConstr :: FunSel -> Constr Source #

dataTypeOf :: FunSel -> DataType Source #

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

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

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

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

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

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

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

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

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

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

Outputable FunSel Source # 
Instance details

Defined in GHC.Core.TyCo.Rep

Methods

ppr :: FunSel -> SDoc Source #

Eq FunSel Source # 
Instance details

Defined in GHC.Core.TyCo.Rep

Methods

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

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

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.

Instances

Instances details
Data UnivCoProvenance Source # 
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 Source # 
Instance details

Defined in GHC.Core.TyCo.Rep

data CoercionHole Source #

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

Constructors

CoercionHole 

Instances

Instances details
Data CoercionHole Source # 
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 #

Uniquable CoercionHole Source # 
Instance details

Defined in GHC.Core.TyCo.Rep

Outputable CoercionHole Source # 
Instance details

Defined in GHC.Core.TyCo.Rep

data LeftOrRight Source #

Constructors

CLeft 
CRight 

Instances

Instances details
Data LeftOrRight Source # 
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 Source # 
Instance details

Defined in GHC.Types.Basic

Outputable LeftOrRight Source # 
Instance details

Defined in GHC.Types.Basic

Methods

ppr :: LeftOrRight -> SDoc Source #

Eq LeftOrRight Source # 
Instance details

Defined in GHC.Types.Basic

data Var Source #

Variable

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

Instances

Instances details
Data Var Source # 
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 Source # 
Instance details

Defined in GHC.Types.Var

HasOccName Var Source # 
Instance details

Defined in GHC.Types.Var

Methods

occName :: Var -> OccName Source #

Uniquable Var Source # 
Instance details

Defined in GHC.Types.Var

Methods

getUnique :: Var -> Unique Source #

Outputable Var Source # 
Instance details

Defined in GHC.Types.Var

Methods

ppr :: Var -> SDoc Source #

OutputableBndr Var Source # 
Instance details

Defined in GHC.Core.Ppr

Eq Var Source # 
Instance details

Defined in GHC.Types.Var

Methods

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

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

Ord Var Source # 
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 #

Eq (DeBruijn CoreAlt) Source # 
Instance details

Defined in GHC.Core.Map.Expr

Eq (DeBruijn CoreExpr) Source # 
Instance details

Defined in GHC.Core.Map.Expr

Eq (DeBruijn Var) Source # 
Instance details

Defined in GHC.Core.Map.Type

OutputableBndr (Id, TagSig) Source # 
Instance details

Defined in GHC.Stg.InferTags.TagSig

type Anno Id Source # 
Instance details

Defined in GHC.Hs.Extension

type Anno (LocatedN Id) Source # 
Instance details

Defined in GHC.Hs.Binds

type Anno [LocatedN Id] Source # 
Instance details

Defined in GHC.Hs.Binds

type CoVar = Id Source #

Coercion Variable

type TyCoVar = Id Source #

Type or Coercion Variable

data Role Source #

See Note [Roles] in GHC.Core.Coercion

Order of constructors matters: the Ord instance coincides with the *super*typing relation on roles.

Instances

Instances details
Data Role Source # 
Instance details

Defined in Language.Haskell.Syntax.Basic

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 Source # 
Instance details

Defined in GHC.Core.Coercion.Axiom

Outputable Role Source # 
Instance details

Defined in GHC.Core.Coercion.Axiom

Methods

ppr :: Role -> SDoc Source #

Eq Role Source # 
Instance details

Defined in Language.Haskell.Syntax.Basic

Methods

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

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

Ord Role Source # 
Instance details

Defined in Language.Haskell.Syntax.Basic

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 #

type Anno (Maybe Role) Source # 
Instance details

Defined in GHC.Hs.Decls

type Anno (Maybe Role) Source # 
Instance details

Defined in GHC.Hs.Decls

Functions over coercions

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

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

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.

coercionRole :: Coercion -> Role Source #

Retrieve the role from a coercion.

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

Get a coercion's kind and role.

Constructing coercions

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

Make a generalized reflexive coercion

mkReflCo :: Role -> Type -> Coercion Source #

Make a reflexive coercion

mkRepReflCo :: Type -> Coercion Source #

Make a representational reflexive coercion

mkNomReflCo :: Type -> Coercion Source #

Make a nominal reflexive coercion

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

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

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

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.

mkTransCo :: Coercion -> Coercion -> Coercion Source #

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

getNthFun Source #

Arguments

:: FunSel 
-> a

multiplicity

-> a

argument

-> a

result

-> a

One of the above three

Extract the nth field of a FunCo

mkAppCo Source #

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 Source #

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

mkTyConAppCo :: HasDebugCallStack => 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.

mkFunCo1 :: HasDebugCallStack => Role -> FunTyFlag -> CoercionN -> Coercion -> Coercion -> Coercion Source #

Build a function Coercion from two other Coercions. That is, given co1 :: a ~ b and co2 :: x ~ y produce co :: (a -> x) ~ (b -> y) or (a => x) ~ (b => y), depending on the kind of a/b. This (most common) version takes a single FunTyFlag, which is used for both fco_afl and ftf_afr of the FunCo

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

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 Source #

Make nested ForAllCos

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

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 Source #

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 Source #

Make a coercion from a coercion hole

mkUnivCo Source #

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 Source #

Arguments

:: Role

role of the created coercion, "r"

-> CoercionN

:: 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]

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

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

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

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

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

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 Source #

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 Source #

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

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

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 Source #

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 Source #

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.

mkPrimEqPred :: Type -> Type -> Type Source #

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

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

Makes a lifted equality predicate at the given role

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

Creates a primitive type equality predicate with explicit kinds

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

Creates a primitive representational type equality predicate with explicit kinds

Decomposition

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

If `instNewTyCon_maybe T ts = Just (rep_ty, co)` then `co :: T ts ~R# rep_ty`

Checks for a newtype, and for being saturated

type NormaliseStepper ev = RecTcChecker -> TyCon -> [Type] -> NormaliseStepResult ev Source #

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

data NormaliseStepResult ev Source #

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

Instances

Instances details
Functor NormaliseStepResult Source # 
Instance details

Defined in GHC.Core.Coercion

Outputable ev => Outputable (NormaliseStepResult ev) Source # 
Instance details

Defined in GHC.Core.Coercion

composeSteppers :: NormaliseStepper ev -> NormaliseStepper ev -> NormaliseStepper ev 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 Coercion 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 : ty ~ 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) 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.

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 -> Infinite Role -> [Coercion] Source #

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 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.)

splitAppCo_maybe :: Coercion -> Maybe (Coercion, Coercion) Source #

Attempt to take a coercion application apart.

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

Like splitForAllCo_maybe, but only returns Just for tyvar binder

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

Like splitForAllCo_maybe, but only returns Just for covar binder

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

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

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

isGReflCo :: Coercion -> Bool Source #

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

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

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

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

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.

isGReflMCo :: MCoercion -> Bool Source #

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

mkTransMCo :: MCoercion -> MCoercion -> MCoercion Source #

Compose two MCoercions via transitivity

mkCastTyMCo :: Type -> MCoercion -> Type Source #

Cast a type by an MCoercion

mkSymMCo :: MCoercion -> MCoercion Source #

Get the reverse of an MCoercion

Coercion variables

isCoVar :: Var -> Bool Source #

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

Free variables

tyCoVarsOfCoDSet :: Coercion -> DTyCoVarSet Source #

Get a deterministic set of the vars free in a coercion

Substitution

type CvSubstEnv = CoVarEnv Coercion Source #

A substitution of Coercions for CoVars

substCo :: HasDebugCallStack => Subst -> Coercion -> Coercion Source #

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

substCos :: HasDebugCallStack => Subst -> [Coercion] -> [Coercion] Source #

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

substCoWith :: HasDebugCallStack => [TyVar] -> [Type] -> Coercion -> Coercion Source #

Coercion substitution, see zipTvSubst

Lifting

liftCoSubst :: HasDebugCallStack => 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.

extendLiftingContext Source #

Arguments

:: LiftingContext

original LC

-> TyCoVar

new variable to map...

-> Coercion

...to this lifted version

-> LiftingContext 

Extend a lifting context with a new mapping.

extendLiftingContextAndInScope Source #

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

liftCoSubstVarBndrUsing Source #

Arguments

:: (r -> CoercionN)

coercion getter

-> (LiftingContext -> Type -> r)

callback

-> LiftingContext 
-> TyCoVar 
-> (LiftingContext, TyCoVar, r) 

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

lcSubst :: LiftingContext -> Subst Source #

Extract the underlying substitution from the LiftingContext

data LiftingContext Source #

Constructors

LC Subst LiftCoEnv 

Instances

Instances details
Outputable LiftingContext Source # 
Instance details

Defined in GHC.Core.Coercion

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 Coercions, with respect to an RnEnv2

Forcing evaluation of coercions

Pretty-printing

Tidying

tidyCo :: TidyEnv -> Coercion -> Coercion Source #

Tidy a Coercion

See Note [Strictness in tidyType and friends]

Other

promoteCoercion :: Coercion -> CoercionN Source #

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

buildCoercion :: Type -> Type -> CoercionN Source #

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.

mkRuntimeRepCo :: HasDebugCallStack => Coercion -> Coercion Source #

Given a coercion co1 :: (a :: TYPE r1) ~ (b :: TYPE r2), (or CONSTRAINT instead of TYPE) produce a coercion rep_co :: r1 ~ r2.

hasCoercionHoleTy :: Type -> Bool Source #

Is there a coercion hole in this type?

hasCoercionHoleCo :: Coercion -> Bool Source #

Is there a coercion hole in this coercion?