GHC.Core.Type

ghc-lib-parser-9.14.1.20251220: The GHC API, decoupled from GHC versions

Safe Haskell | Ignore
Language | GHC2021

GHC.Core.Type

Contents

- Main data types representing Types
  - Constructing and deconstructing types
  - Analyzing types
  - Binders
  - Predicates on types
- Space-saving construction
  - Levity and boxity
- Multiplicity
- Main data types representing Kinds
  - Finding the kind of a type
  - Common Kind
- Type free variables
  - Closing over kinds
- Forcing evaluation of types
- Other views onto Types
- Main type substitution data types
  - Manipulating type substitutions
  - Performing substitution on types and kinds
- Kinds

Description

Main functions for manipulating types and type-related things

Synopsis

- data Type
- data ForAllTyFlag where
  - Invisible !Specificity
  - Required
  - pattern Specified :: ForAllTyFlag
  - pattern Inferred :: ForAllTyFlag
- data FunTyFlag
  - = FTF_T_T
  - | FTF_T_C
  - | FTF_C_T
  - | FTF_C_C
- data Specificity
  - = InferredSpec
  - | SpecifiedSpec
- type KindOrType = Type
- type PredType = Type
- type ThetaType = [PredType]
- type FRRType = Type
- data Var
- type TyVar = Var
- isTyVar :: Var -> Bool
- type TyCoVar = Id
- data PiTyBinder
- type ForAllTyBinder = VarBndr TyCoVar ForAllTyFlag
- type TyVarBinder = VarBndr TyVar ForAllTyFlag
- type Mult = Type
- data Scaled a
- type KnotTied (ty :: k) = ty
- type RuntimeRepType = Type
- mkTyVarTy :: TyVar -> Type
- mkTyVarTys :: [TyVar] -> [Type]
- getTyVar :: HasDebugCallStack => Type -> TyVar
- getTyVar_maybe :: Type -> Maybe TyVar
- repGetTyVar_maybe :: Type -> Maybe TyVar
- getCastedTyVar_maybe :: Type -> Maybe (TyVar, CoercionN)
- tyVarKind :: TyVar -> Kind
- varType :: Var -> Kind
- mkAppTy :: Type -> Type -> Type
- mkAppTys :: Type -> [Type] -> Type
- splitAppTy :: Type -> (Type, Type)
- splitAppTys :: HasDebugCallStack => Type -> (Type, [Type])
- splitAppTysNoView :: HasDebugCallStack => Type -> (Type, [Type])
- splitAppTy_maybe :: Type -> Maybe (Type, Type)
- splitAppTyNoView_maybe :: HasDebugCallStack => Type -> Maybe (Type, Type)
- tcSplitAppTyNoView_maybe :: Type -> Maybe (Type, Type)
- mkFunTy :: HasDebugCallStack => FunTyFlag -> Mult -> Type -> Type -> Type
- mkVisFunTy :: HasDebugCallStack => Mult -> Type -> Type -> Type
- mkVisFunTyMany :: HasDebugCallStack => Type -> Type -> Type
- mkVisFunTysMany :: [Type] -> Type -> Type
- mkScaledFunTys :: HasDebugCallStack => [Scaled Type] -> Type -> Type
- mkInvisFunTy :: HasDebugCallStack => Type -> Type -> Type
- mkInvisFunTys :: HasDebugCallStack => [Type] -> Type -> Type
- tcMkVisFunTy :: Mult -> Type -> Type -> Type
- tcMkScaledFunTys :: [Scaled Type] -> Type -> Type
- tcMkInvisFunTy :: TypeOrConstraint -> Type -> Type -> Type
- splitFunTy :: Type -> (Mult, Type, Type)
- splitFunTy_maybe :: Type -> Maybe (FunTyFlag, Mult, Type, Type)
- splitVisibleFunTy_maybe :: Type -> Maybe (Type, Type)
- splitFunTys :: Type -> ([Scaled Type], Type)
- funResultTy :: HasDebugCallStack => Type -> Type
- funArgTy :: HasDebugCallStack => Type -> Type
- funTyConAppTy_maybe :: FunTyFlag -> Type -> Type -> Type -> Maybe (TyCon, [Type])
- funTyFlagTyCon :: FunTyFlag -> TyCon
- tyConAppFunTy_maybe :: HasDebugCallStack => TyCon -> [Type] -> Maybe Type
- tyConAppFunCo_maybe :: HasDebugCallStack => Role -> TyCon -> [Coercion] -> Maybe Coercion
- mkFunctionType :: HasDebugCallStack => Mult -> Type -> Type -> Type
- mkScaledFunctionTys :: [Scaled Type] -> Type -> Type
- chooseFunTyFlag :: HasDebugCallStack => Type -> Type -> FunTyFlag
- mkTyConApp :: TyCon -> [Type] -> Type
- mkTyConTy :: TyCon -> Type
- tyConAppTyCon_maybe :: Type -> Maybe TyCon
- tyConAppTyConPicky_maybe :: Type -> Maybe TyCon
- tyConAppArgs_maybe :: Type -> Maybe [Type]
- tyConAppTyCon :: HasDebugCallStack => Type -> TyCon
- tyConAppArgs :: HasDebugCallStack => Type -> [Type]
- splitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
- splitTyConAppNoView_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
- splitTyConApp :: Type -> (TyCon, [Type])
- tcSplitTyConApp :: Type -> (TyCon, [Type])
- tcSplitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
- mkForAllTy :: ForAllTyBinder -> Type -> Type
- mkForAllTys :: [ForAllTyBinder] -> Type -> Type
- mkInvisForAllTys :: [InvisTVBinder] -> Type -> Type
- mkTyCoInvForAllTys :: [TyCoVar] -> Type -> Type
- mkSpecForAllTy :: TyVar -> Type -> Type
- mkSpecForAllTys :: [TyVar] -> Type -> Type
- mkVisForAllTys :: [TyVar] -> Type -> Type
- mkTyCoForAllTy :: TyCoVar -> ForAllTyFlag -> Type -> Type
- mkTyCoForAllTys :: [ForAllTyBinder] -> Type -> Type
- mkTyCoInvForAllTy :: TyCoVar -> Type -> Type
- mkInfForAllTy :: TyVar -> Type -> Type
- mkInfForAllTys :: [TyVar] -> Type -> Type
- splitForAllTyCoVars :: Type -> ([TyCoVar], Type)
- splitForAllTyVars :: Type -> ([TyVar], Type)
- splitForAllReqTyBinders :: Type -> ([ReqTyBinder], Type)
- splitForAllInvisTyBinders :: Type -> ([InvisTyBinder], Type)
- splitForAllForAllTyBinders :: Type -> ([ForAllTyBinder], Type)
- splitForAllForAllTyBinder_maybe :: Type -> Maybe (ForAllTyBinder, Type)
- splitForAllTyCoVar_maybe :: Type -> Maybe (TyCoVar, Type)
- splitForAllTyCoVar :: Type -> (TyCoVar, Type)
- splitForAllTyVar_maybe :: Type -> Maybe (TyVar, Type)
- splitForAllCoVar_maybe :: Type -> Maybe (CoVar, Type)
- splitPiTy_maybe :: Type -> Maybe (PiTyBinder, Type)
- splitPiTy :: Type -> (PiTyBinder, Type)
- splitPiTys :: Type -> ([PiTyBinder], Type)
- collectPiTyBinders :: Type -> [PiTyBinder]
- getRuntimeArgTys :: Type -> [(Scaled Type, FunTyFlag)]
- mkTyConBindersPreferAnon :: [TyVar] -> TyCoVarSet -> [TyConBinder]
- mkPiTy :: HasDebugCallStack => PiTyBinder -> Type -> Type
- mkPiTys :: HasDebugCallStack => [PiTyBinder] -> Type -> Type
- piResultTy :: HasDebugCallStack => Type -> Type -> Type
- piResultTys :: HasDebugCallStack => Type -> [Type] -> Type
- applyTysX :: HasDebugCallStack => [TyVar] -> Type -> [Type] -> Type
- dropForAlls :: Type -> Type
- mkFamilyTyConApp :: TyCon -> [Type] -> Type
- buildSynTyCon :: Name -> [KnotTied TyConBinder] -> Kind -> [Role] -> KnotTied Type -> TyCon
- mkNumLitTy :: Integer -> Type
- isNumLitTy :: Type -> Maybe Integer
- mkStrLitTy :: FastString -> Type
- isStrLitTy :: Type -> Maybe FastString
- mkCharLitTy :: Char -> Type
- isCharLitTy :: Type -> Maybe Char
- isLitTy :: Type -> Maybe TyLit
- getRuntimeRep :: HasDebugCallStack => Type -> RuntimeRepType
- splitRuntimeRep_maybe :: RuntimeRepType -> Maybe (TyCon, [Type])
- kindRep_maybe :: HasDebugCallStack => Kind -> Maybe RuntimeRepType
- kindRep :: HasDebugCallStack => Kind -> RuntimeRepType
- getLevity :: HasDebugCallStack => Type -> Type
- levityType_maybe :: LevityType -> Maybe Levity
- mkCastTy :: Type -> Coercion -> Type
- mkCoercionTy :: Coercion -> Type
- splitCastTy_maybe :: Type -> Maybe (Type, Coercion)
- type ErrorMsgType = Type
- userTypeError_maybe :: Type -> Maybe ErrorMsgType
- deepUserTypeError_maybe :: Type -> Maybe ErrorMsgType
- pprUserTypeErrorTy :: ErrorMsgType -> SDoc
- coAxNthLHS :: forall (br :: BranchFlag). CoAxiom br -> Int -> Type
- stripCoercionTy :: Type -> Coercion
- splitInvisPiTys :: Type -> ([PiTyBinder], Type)
- splitInvisPiTysN :: Int -> Type -> ([PiTyBinder], Type)
- invisibleBndrCount :: Type -> Int
- filterOutInvisibleTypes :: TyCon -> [Type] -> [Type]
- filterOutInferredTypes :: TyCon -> [Type] -> [Type]
- partitionInvisibleTypes :: TyCon -> [Type] -> ([Type], [Type])
- partitionInvisibles :: [(a, ForAllTyFlag)] -> ([a], [a])
- tyConForAllTyFlags :: TyCon -> [Type] -> [ForAllTyFlag]
- appTyForAllTyFlags :: Type -> [Type] -> [ForAllTyFlag]
- data TyCoMapper env (m :: Type -> Type) = TyCoMapper {
  - tcm_tyvar :: env -> TyVar -> m Type
  - tcm_covar :: env -> CoVar -> m Coercion
  - tcm_hole :: env -> CoercionHole -> m Coercion
  - tcm_tycobinder :: forall r. env -> TyCoVar -> ForAllTyFlag -> (env -> TyCoVar -> m r) -> m r
  - tcm_tycon :: TyCon -> m TyCon
  }
- mapTyCo :: Monad m => TyCoMapper () m -> (Type -> m Type, [Type] -> m [Type], Coercion -> m Coercion, [Coercion] -> m [Coercion])
- mapTyCoX :: Monad m => TyCoMapper env m -> (env -> Type -> m Type, env -> [Type] -> m [Type], env -> Coercion -> m Coercion, env -> [Coercion] -> m [Coercion])
- data TyCoFolder env a = TyCoFolder {
  - tcf_view :: Type -> Maybe Type
  - tcf_tyvar :: env -> TyVar -> a
  - tcf_covar :: env -> CoVar -> a
  - tcf_hole :: env -> CoercionHole -> a
  - tcf_tycobinder :: env -> TyCoVar -> ForAllTyFlag -> env
  }
- foldTyCo :: Monoid a => TyCoFolder env a -> env -> (Type -> a, [Type] -> a, Coercion -> a, [Coercion] -> a)
- noView :: Type -> Maybe Type
- newTyConInstRhs :: TyCon -> [Type] -> Type
- mkForAllTyBinder :: vis -> TyCoVar -> VarBndr TyCoVar vis
- mkForAllTyBinders :: vis -> [TyCoVar] -> [VarBndr TyCoVar vis]
- mkTyVarBinder :: vis -> TyVar -> VarBndr TyVar vis
- mkTyVarBinders :: vis -> [TyVar] -> [VarBndr TyVar vis]
- tyVarSpecToBinders :: [VarBndr a Specificity] -> [VarBndr a ForAllTyFlag]
- isAnonPiTyBinder :: PiTyBinder -> Bool
- binderVar :: VarBndr tv argf -> tv
- binderVars :: [VarBndr tv argf] -> [tv]
- binderType :: VarBndr TyCoVar argf -> Type
- binderFlag :: VarBndr tv argf -> argf
- binderFlags :: [VarBndr tv argf] -> [argf]
- piTyBinderType :: PiTyBinder -> Type
- namedPiTyBinder_maybe :: PiTyBinder -> Maybe TyCoVar
- anonPiTyBinderType_maybe :: PiTyBinder -> Maybe Type
- isVisibleForAllTyFlag :: ForAllTyFlag -> Bool
- isInvisibleForAllTyFlag :: ForAllTyFlag -> Bool
- isVisiblePiTyBinder :: PiTyBinder -> Bool
- isInvisiblePiTyBinder :: PiTyBinder -> Bool
- isNamedPiTyBinder :: PiTyBinder -> Bool
- tyConBindersPiTyBinders :: [TyConBinder] -> [PiTyBinder]
- isTyVarTy :: Type -> Bool
- isFunTy :: Type -> Bool
- isCoercionTy :: Type -> Bool
- isCoercionTy_maybe :: Type -> Maybe Coercion
- isForAllTy :: Type -> Bool
- isForAllTy_ty :: Type -> Bool
- isForAllTy_co :: Type -> Bool
- isForAllTy_invis_ty :: Type -> Bool
- isPiTy :: Type -> Bool
- isTauTy :: Type -> Bool
- isFamFreeTy :: Type -> Bool
- isAtomicTy :: Type -> Bool
- isValidJoinPointType :: JoinArity -> Type -> Bool
- tyConAppNeedsKindSig :: Bool -> TyCon -> Int -> Bool
- mkTYPEapp :: RuntimeRepType -> Type
- mkTYPEapp_maybe :: RuntimeRepType -> Maybe Type
- mkCONSTRAINTapp :: RuntimeRepType -> Type
- mkCONSTRAINTapp_maybe :: RuntimeRepType -> Maybe Type
- mkBoxedRepApp_maybe :: LevityType -> Maybe Type
- mkTupleRepApp_maybe :: Type -> Maybe Type
- typeOrConstraintKind :: TypeOrConstraint -> RuntimeRepType -> Kind
- liftedTypeOrConstraintKind :: TypeOrConstraint -> Kind
- sORTKind_maybe :: Kind -> Maybe (TypeOrConstraint, Type)
- typeTypeOrConstraint :: HasDebugCallStack => Type -> TypeOrConstraint
- typeLevity :: HasDebugCallStack => Type -> Levity
- typeLevity_maybe :: HasDebugCallStack => Type -> Maybe Levity
- tyConIsTYPEorCONSTRAINT :: TyCon -> Bool
- isLiftedTypeKind :: Kind -> Bool
- isUnliftedTypeKind :: Kind -> Bool
- pickyIsLiftedTypeKind :: Kind -> Bool
- isLiftedRuntimeRep :: RuntimeRepType -> Bool
- isUnliftedRuntimeRep :: RuntimeRepType -> Bool
- runtimeRepLevity_maybe :: RuntimeRepType -> Maybe Levity
- isBoxedRuntimeRep :: RuntimeRepType -> Bool
- isLiftedLevity :: Type -> Bool
- isUnliftedLevity :: Type -> Bool
- isUnliftedType :: HasDebugCallStack => Type -> Bool
- isBoxedType :: Type -> Bool
- isUnboxedTupleType :: Type -> Bool
- isUnboxedSumType :: Type -> Bool
- kindBoxedRepLevity_maybe :: Type -> Maybe Levity
- mightBeLiftedType :: Type -> Bool
- mightBeUnliftedType :: Type -> Bool
- definitelyLiftedType :: Type -> Bool
- definitelyUnliftedType :: Type -> Bool
- isAlgType :: Type -> Bool
- isDataFamilyApp :: Type -> Bool
- isSatTyFamApp :: Type -> Maybe (TyCon, [Type])
- isPrimitiveType :: Type -> Bool
- isStrictType :: HasDebugCallStack => Type -> Bool
- isTerminatingType :: HasDebugCallStack => Type -> Bool
- isLevityTy :: Type -> Bool
- isLevityVar :: TyVar -> Bool
- isRuntimeRepTy :: Type -> Bool
- isRuntimeRepVar :: TyVar -> Bool
- isRuntimeRepKindedTy :: Type -> Bool
- dropRuntimeRepArgs :: [Type] -> [Type]
- isMultiplicityTy :: Type -> Bool
- isMultiplicityVar :: TyVar -> Bool
- unrestricted :: a -> Scaled a
- linear :: a -> Scaled a
- tymult :: a -> Scaled a
- mkScaled :: Mult -> a -> Scaled a
- irrelevantMult :: Scaled a -> a
- scaledSet :: Scaled a -> b -> Scaled b
- pattern OneTy :: Mult
- pattern ManyTy :: Mult
- isOneTy :: Mult -> Bool
- isManyTy :: Mult -> Bool
- isLinearType :: Type -> Bool
- type Kind = Type
- typeKind :: HasDebugCallStack => Type -> Kind
- typeHasFixedRuntimeRep :: HasDebugCallStack => Type -> Bool
- tcIsLiftedTypeKind :: Kind -> Bool
- isConstraintKind :: Kind -> Bool
- isConstraintLikeKind :: Kind -> Bool
- returnsConstraintKind :: Kind -> Bool
- tcIsBoxedTypeKind :: Kind -> Bool
- isTypeLikeKind :: Kind -> Bool
- liftedTypeKind :: Type
- unliftedTypeKind :: Type
- tyCoFVsOfType :: Type -> FV
- tyCoFVsBndr :: ForAllTyBinder -> FV -> FV
- tyCoFVsVarBndr :: Var -> FV -> FV
- tyCoFVsVarBndrs :: [Var] -> FV -> FV
- tyCoVarsOfType :: Type -> TyCoVarSet
- tyCoVarsOfTypes :: [Type] -> TyCoVarSet
- tyCoVarsOfTypeDSet :: Type -> DTyCoVarSet
- coVarsOfType :: Type -> CoVarSet
- coVarsOfTypes :: [Type] -> CoVarSet
- anyFreeVarsOfType :: (TyCoVar -> Bool) -> Type -> Bool
- anyFreeVarsOfTypes :: (TyCoVar -> Bool) -> [Type] -> Bool
- noFreeVarsOfType :: Type -> Bool
- expandTypeSynonyms :: Type -> Type
- expandSynTyConApp_maybe :: TyCon -> [Type] -> Maybe Type
- typeSize :: Type -> Int
- occCheckExpand :: [Var] -> Type -> Maybe Type
- closeOverKindsDSet :: DTyVarSet -> DTyVarSet
- closeOverKindsList :: [TyVar] -> [TyVar]
- closeOverKinds :: TyCoVarSet -> TyCoVarSet
- seqType :: Type -> ()
- seqTypes :: [Type] -> ()
- coreView :: Type -> Maybe Type
- coreFullView :: Type -> Type
- rewriterView :: Type -> Maybe Type
- tyConsOfType :: Type -> UniqSet TyCon
- type TvSubstEnv = TyVarEnv Type
- type IdSubstEnv = IdEnv CoreExpr
- data Subst = Subst InScopeSet IdSubstEnv TvSubstEnv CvSubstEnv
- emptyTvSubstEnv :: TvSubstEnv
- emptySubst :: Subst
- mkEmptySubst :: InScopeSet -> Subst
- mkTCvSubst :: InScopeSet -> TvSubstEnv -> CvSubstEnv -> Subst
- zipTvSubst :: HasDebugCallStack => [TyVar] -> [Type] -> Subst
- mkTvSubstPrs :: [(TyVar, Type)] -> Subst
- zipTCvSubst :: HasDebugCallStack => [TyCoVar] -> [Type] -> Subst
- notElemSubst :: Var -> Subst -> Bool
- getTvSubstEnv :: Subst -> TvSubstEnv
- zapSubst :: Subst -> Subst
- substInScopeSet :: Subst -> InScopeSet
- setInScope :: Subst -> InScopeSet -> Subst
- getSubstRangeTyCoFVs :: Subst -> VarSet
- extendSubstInScope :: Subst -> Var -> Subst
- extendSubstInScopeList :: Subst -> [Var] -> Subst
- extendSubstInScopeSet :: Subst -> VarSet -> Subst
- extendTCvSubst :: Subst -> TyCoVar -> Type -> Subst
- extendCvSubst :: Subst -> CoVar -> Coercion -> Subst
- extendTvSubst :: Subst -> TyVar -> Type -> Subst
- extendTvSubstList :: Subst -> [(TyVar, Type)] -> Subst
- extendTvSubstAndInScope :: Subst -> TyVar -> Type -> Subst
- extendTCvSubstList :: Subst -> [Var] -> [Type] -> Subst
- extendTvSubstWithClone :: Subst -> TyVar -> TyVar -> Subst
- extendTCvSubstWithClone :: Subst -> TyCoVar -> TyCoVar -> Subst
- isInScope :: Var -> Subst -> Bool
- composeTCvSubst :: Subst -> Subst -> Subst
- zipTyEnv :: HasDebugCallStack => [TyVar] -> [Type] -> TvSubstEnv
- zipCoEnv :: HasDebugCallStack => [CoVar] -> [Coercion] -> CvSubstEnv
- isEmptySubst :: Subst -> Bool
- unionSubst :: Subst -> Subst -> Subst
- isEmptyTCvSubst :: Subst -> Bool
- substTy :: HasDebugCallStack => Subst -> Type -> Type
- substTys :: HasDebugCallStack => Subst -> [Type] -> [Type]
- substScaledTy :: HasDebugCallStack => Subst -> Scaled Type -> Scaled Type
- substScaledTys :: HasDebugCallStack => Subst -> [Scaled Type] -> [Scaled Type]
- substTyWith :: HasDebugCallStack => [TyVar] -> [Type] -> Type -> Type
- substTysWith :: HasDebugCallStack => [TyVar] -> [Type] -> [Type] -> [Type]
- substTheta :: HasDebugCallStack => Subst -> ThetaType -> ThetaType
- substTyAddInScope :: HasDebugCallStack => Subst -> Type -> Type
- substTyUnchecked :: Subst -> Type -> Type
- substTysUnchecked :: Subst -> [Type] -> [Type]
- substScaledTyUnchecked :: HasDebugCallStack => Subst -> Scaled Type -> Scaled Type
- substScaledTysUnchecked :: Subst -> [Scaled Type] -> [Scaled Type]
- substThetaUnchecked :: Subst -> ThetaType -> ThetaType
- substTyWithUnchecked :: [TyVar] -> [Type] -> Type -> Type
- substCo :: HasDebugCallStack => Subst -> Coercion -> Coercion
- substCoUnchecked :: Subst -> Coercion -> Coercion
- substCoWithUnchecked :: [TyVar] -> [Type] -> Coercion -> Coercion
- substTyVarBndr :: HasDebugCallStack => Subst -> TyVar -> (Subst, TyVar)
- substTyVarBndrs :: HasDebugCallStack => Subst -> [TyVar] -> (Subst, [TyVar])
- substTyVar :: Subst -> TyVar -> Type
- substTyVars :: Subst -> [TyVar] -> [Type]
- substVarBndr :: HasDebugCallStack => Subst -> TyCoVar -> (Subst, TyCoVar)
- substVarBndrs :: HasDebugCallStack => Subst -> [TyCoVar] -> (Subst, [TyCoVar])
- substTyCoBndr :: Subst -> PiTyBinder -> (Subst, PiTyBinder)
- substTyVarToTyVar :: HasDebugCallStack => Subst -> TyVar -> TyVar
- cloneTyVarBndr :: Subst -> TyVar -> Unique -> (Subst, TyVar)
- cloneTyVarBndrs :: Subst -> [TyVar] -> UniqSupply -> (Subst, [TyVar])
- lookupTyVar :: Subst -> TyVar -> Maybe Type
- isTYPEorCONSTRAINT :: Kind -> Bool
- isConcreteType :: Type -> Bool
- isFixedRuntimeRepKind :: HasDebugCallStack => Kind -> Bool

# Main data types representing Types

Types are any, but at least one, of:

Boxed
  Iff its representation is a pointer to an object on the GC'd heap. Operationally, heap objects can be entered as a means of evaluation.
Lifted
  Iff it has bottom as an element: An instance of a lifted type might diverge when evaluated. GHC Haskell's unboxed types are unlifted. An unboxed, but lifted type is not very useful. (Example: A byte-represented type, where evaluating 0xff computes the 12345678th collatz number modulo 0xff.) Only lifted types may be unified with a type variable.
Algebraic
  Iff it is a type with one or more constructors, whether declared with `data` or `newtype`. An algebraic type is one that can be deconstructed with a case expression. There are algebraic types that are not lifted types, like unlifted data types or unboxed tuples.
Data
  Iff it is a type declared with `data`, or a boxed tuple. There are also unlifted data types.
Primitive
  Iff it is a built-in type that can't be expressed in Haskell.
Unlifted
  Anything that isn't lifted is considered unlifted.

Currently, all primitive types are unlifted, but that's not necessarily the case: for example, `Int` could be primitive.

Some primitive types are unboxed, such as `Int#`, whereas some are boxed but unlifted (such as `ByteArray#`). The only primitive types that we classify as algebraic are the unboxed tuples.

Some examples of type classifications that may make this a bit clearer are:

    Type          primitive       boxed           lifted          algebraic
    -----------------------------------------------------------------------------
    Int#          Yes             No              No              No
    ByteArray#    Yes             Yes             No              No
    (# a, b #)  Yes             No              No              Yes
    (# a | b #) Yes             No              No              Yes
    (  a, b  )    No              Yes             Yes             Yes
    [a]           No              Yes             Yes             Yes

A source type is a type that is a separate type as far as the type checker is concerned, but which has a more low-level representation as far as Core-to-Core passes and the rest of the back end is concerned.

You don't normally have to worry about this, as the utility functions in this module will automatically convert a source into a representation type if they are spotted, to the best of its abilities. If you don't want this to happen, use the equivalent functions from the TcType module.

data Type #

#### Instances

Instances details

Data Type # |
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) -> Type -> c Type # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Type # toConstr :: Type -> Constr # dataTypeOf :: Type -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Type) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Type) # gmapT :: (forall b. Data b => b -> b) -> Type -> Type # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Type -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Type -> r # gmapQ :: (forall d. Data d => d -> u) -> Type -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Type -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Type -> m Type # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Type -> m Type # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Type -> m Type #
Outputable Type # |
Instance details Defined in GHC.Core.TyCo.Rep Methods ppr :: Type -> SDoc #
Eq (DeBruijn Type) # |
Instance details Defined in GHC.Core.Map.Type Methods (==) :: DeBruijn Type -> DeBruijn Type -> Bool # (/=) :: DeBruijn Type -> DeBruijn Type -> Bool #

data ForAllTyFlag #

ForAllTyFlag

Is something required to appear in source Haskell (`Required`), permitted by request (`Specified`) (visible type application), or prohibited entirely from appearing in source Haskell (`Inferred`)? See Note [VarBndrs, ForAllTyBinders, TyConBinders, and visibility] in GHC.Core.TyCo.Rep

Constructors

Invisible !Specificity |
Required |

Bundled Patterns

pattern Specified :: ForAllTyFlag |
pattern Inferred :: ForAllTyFlag |

#### Instances

Instances details

NFData ForAllTyFlag # |
Instance details Defined in GHC.Hs.Specificity Methods rnf :: ForAllTyFlag -> () #
Data ForAllTyFlag # |
Instance details Defined in Language.Haskell.Syntax.Specificity Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> ForAllTyFlag -> c ForAllTyFlag # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c ForAllTyFlag # toConstr :: ForAllTyFlag -> Constr # dataTypeOf :: ForAllTyFlag -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c ForAllTyFlag) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c ForAllTyFlag) # gmapT :: (forall b. Data b => b -> b) -> ForAllTyFlag -> ForAllTyFlag # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ForAllTyFlag -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ForAllTyFlag -> r # gmapQ :: (forall d. Data d => d -> u) -> ForAllTyFlag -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> ForAllTyFlag -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> ForAllTyFlag -> m ForAllTyFlag # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ForAllTyFlag -> m ForAllTyFlag # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ForAllTyFlag -> m ForAllTyFlag #
Binary ForAllTyFlag # |
Instance details Defined in GHC.Hs.Specificity Methods put_ :: WriteBinHandle -> ForAllTyFlag -> IO () # put :: WriteBinHandle -> ForAllTyFlag -> IO (Bin ForAllTyFlag) # get :: ReadBinHandle -> IO ForAllTyFlag #
Outputable ForAllTyFlag # |
Instance details Defined in GHC.Hs.Specificity Methods ppr :: ForAllTyFlag -> SDoc #
Eq ForAllTyFlag # |
Instance details Defined in Language.Haskell.Syntax.Specificity Methods (==) :: ForAllTyFlag -> ForAllTyFlag -> Bool # (/=) :: ForAllTyFlag -> ForAllTyFlag -> Bool #
Ord ForAllTyFlag # |
Instance details Defined in Language.Haskell.Syntax.Specificity Methods compare :: ForAllTyFlag -> ForAllTyFlag -> Ordering # (<) :: ForAllTyFlag -> ForAllTyFlag -> Bool # (<=) :: ForAllTyFlag -> ForAllTyFlag -> Bool # (>) :: ForAllTyFlag -> ForAllTyFlag -> Bool # (>=) :: ForAllTyFlag -> ForAllTyFlag -> Bool # max :: ForAllTyFlag -> ForAllTyFlag -> ForAllTyFlag # min :: ForAllTyFlag -> ForAllTyFlag -> ForAllTyFlag #
OutputableBndrFlag ForAllTyFlag p # |
Instance details Defined in GHC.Hs.Type Methods pprTyVarBndr :: HsTyVarBndr ForAllTyFlag (GhcPass p) -> SDoc
Outputable tv => Outputable (VarBndr tv ForAllTyFlag) # |
Instance details Defined in GHC.Types.Var Methods ppr :: VarBndr tv ForAllTyFlag -> SDoc #

data FunTyFlag #

The non-dependent version of `ForAllTyFlag`. See Note [FunTyFlag] Appears here partly so that it's together with its friends ForAllTyFlag and ForallVisFlag, but also because it is used in IfaceType, rather early in the compilation chain

Constructors

FTF_T_T |
FTF_T_C |
FTF_C_T |
FTF_C_C |

#### Instances

Instances details

NFData FunTyFlag # |
Instance details Defined in GHC.Types.Var Methods rnf :: FunTyFlag -> () #
Data FunTyFlag # |
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) -> FunTyFlag -> c FunTyFlag # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c FunTyFlag # toConstr :: FunTyFlag -> Constr # dataTypeOf :: FunTyFlag -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c FunTyFlag) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c FunTyFlag) # gmapT :: (forall b. Data b => b -> b) -> FunTyFlag -> FunTyFlag # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> FunTyFlag -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> FunTyFlag -> r # gmapQ :: (forall d. Data d => d -> u) -> FunTyFlag -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> FunTyFlag -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> FunTyFlag -> m FunTyFlag # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> FunTyFlag -> m FunTyFlag # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> FunTyFlag -> m FunTyFlag #
Binary FunTyFlag # |
Instance details Defined in GHC.Types.Var Methods put_ :: WriteBinHandle -> FunTyFlag -> IO () # put :: WriteBinHandle -> FunTyFlag -> IO (Bin FunTyFlag) # get :: ReadBinHandle -> IO FunTyFlag #
Outputable FunTyFlag # |
Instance details Defined in GHC.Types.Var Methods ppr :: FunTyFlag -> SDoc #
Eq FunTyFlag # |
Instance details Defined in GHC.Types.Var Methods (==) :: FunTyFlag -> FunTyFlag -> Bool # (/=) :: FunTyFlag -> FunTyFlag -> Bool #
Ord FunTyFlag # |
Instance details Defined in GHC.Types.Var Methods compare :: FunTyFlag -> FunTyFlag -> Ordering # (<) :: FunTyFlag -> FunTyFlag -> Bool # (<=) :: FunTyFlag -> FunTyFlag -> Bool # (>) :: FunTyFlag -> FunTyFlag -> Bool # (>=) :: FunTyFlag -> FunTyFlag -> Bool # max :: FunTyFlag -> FunTyFlag -> FunTyFlag # min :: FunTyFlag -> FunTyFlag -> FunTyFlag #

data Specificity #

Whether an `Invisible` argument may appear in source Haskell.

Constructors

InferredSpec | the argument may not appear in source Haskell, it is only inferred.
SpecifiedSpec | the argument may appear in source Haskell, but isn't required.

#### Instances

Instances details

NFData Specificity # |
Instance details Defined in GHC.Hs.Specificity Methods rnf :: Specificity -> () #
Data Specificity # |
Instance details Defined in Language.Haskell.Syntax.Specificity Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Specificity -> c Specificity # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Specificity # toConstr :: Specificity -> Constr # dataTypeOf :: Specificity -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Specificity) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Specificity) # gmapT :: (forall b. Data b => b -> b) -> Specificity -> Specificity # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Specificity -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Specificity -> r # gmapQ :: (forall d. Data d => d -> u) -> Specificity -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Specificity -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Specificity -> m Specificity # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Specificity -> m Specificity # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Specificity -> m Specificity #
Binary Specificity # |
Instance details Defined in GHC.Hs.Specificity Methods put_ :: WriteBinHandle -> Specificity -> IO () # put :: WriteBinHandle -> Specificity -> IO (Bin Specificity) # get :: ReadBinHandle -> IO Specificity #
Eq Specificity # |
Instance details Defined in Language.Haskell.Syntax.Specificity Methods (==) :: Specificity -> Specificity -> Bool # (/=) :: Specificity -> Specificity -> Bool #
Ord Specificity # |
Instance details Defined in Language.Haskell.Syntax.Specificity Methods compare :: Specificity -> Specificity -> Ordering # (<) :: Specificity -> Specificity -> Bool # (<=) :: Specificity -> Specificity -> Bool # (>) :: Specificity -> Specificity -> Bool # (>=) :: Specificity -> Specificity -> Bool # max :: Specificity -> Specificity -> Specificity # min :: Specificity -> Specificity -> Specificity #
OutputableBndrFlag Specificity p # |
Instance details Defined in GHC.Hs.Type Methods pprTyVarBndr :: HsTyVarBndr Specificity (GhcPass p) -> SDoc
Outputable tv => Outputable (VarBndr tv Specificity) # |
Instance details Defined in GHC.Types.Var Methods ppr :: VarBndr tv Specificity -> SDoc #

type KindOrType = Type #

The key representation of types within the compiler

type PredType = Type #

A type of the form `p` of constraint kind represents a value whose type is the Haskell predicate `p`, where a predicate is what occurs before the `=>` in a Haskell type.

We use `PredType` as documentation to mark those types that we guarantee to have this kind.

It can be expanded into its representation, but:

- The type checker must treat it as opaque
- The rest of the compiler treats it as transparent

Consider these examples:

    f :: (Eq a) => a -> Int
    g :: (?x :: Int -> Int) => a -> Int
    h :: (r\l) => {r} => {l::Int | r}

Here the `Eq a` and `?x :: Int -> Int` and `rl` are all called "predicates"

type ThetaType = [PredType] #

A collection of `PredType`s

type FRRType = Type #

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 # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Var # toConstr :: Var -> Constr # dataTypeOf :: Var -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Var) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Var) # gmapT :: (forall b. Data b => b -> b) -> Var -> Var # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Var -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Var -> r # gmapQ :: (forall d. Data d => d -> u) -> Var -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Var -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Var -> m Var # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Var -> m Var # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Var -> m Var #
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 #
OutputableBndr Var # |
Instance details Defined in GHC.Core.Ppr Methods pprBndr :: BindingSite -> Var -> SDoc # pprPrefixOcc :: Var -> SDoc # pprInfixOcc :: Var -> SDoc # bndrIsJoin_maybe :: Var -> JoinPointHood #
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 #
Eq (DeBruijn CoreAlt) # |
Instance details Defined in GHC.Core.Map.Expr Methods (==) :: DeBruijn CoreAlt -> DeBruijn CoreAlt -> Bool # (/=) :: DeBruijn CoreAlt -> DeBruijn CoreAlt -> Bool #
Eq (DeBruijn CoreExpr) # |
Instance details Defined in GHC.Core.Map.Expr Methods (==) :: DeBruijn CoreExpr -> DeBruijn CoreExpr -> Bool # (/=) :: DeBruijn CoreExpr -> DeBruijn CoreExpr -> Bool #
Eq (DeBruijn Var) # |
Instance details Defined in GHC.Core.Map.Type Methods (==) :: DeBruijn Var -> DeBruijn Var -> Bool # (/=) :: DeBruijn Var -> DeBruijn Var -> Bool #
OutputableBndr (Id, TagSig) # |
Instance details Defined in GHC.Stg.EnforceEpt.TagSig Methods pprBndr :: BindingSite -> (Id, TagSig) -> SDoc # pprPrefixOcc :: (Id, TagSig) -> SDoc # pprInfixOcc :: (Id, TagSig) -> SDoc # bndrIsJoin_maybe :: (Id, TagSig) -> JoinPointHood #
type Anno Id # |
Instance details Defined in GHC.Hs.Extension type Anno Id = SrcSpanAnnN

type TyVar = Var #

Type or kind Variable

isTyVar :: Var -> Bool #

Is this a type-level (i.e., computationally irrelevant, thus erasable) variable? Satisfies `isTyVar = not . isId`.

type TyCoVar = Id #

Type or Coercion Variable

data PiTyBinder #

A `PiTyBinder` represents an argument to a function. PiTyBinders can be dependent (`Named`) or nondependent (`Anon`). They may also be visible or not. See Note [PiTyBinders]

#### Instances

Instances details

Data PiTyBinder # |
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) -> PiTyBinder -> c PiTyBinder # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c PiTyBinder # toConstr :: PiTyBinder -> Constr # dataTypeOf :: PiTyBinder -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c PiTyBinder) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c PiTyBinder) # gmapT :: (forall b. Data b => b -> b) -> PiTyBinder -> PiTyBinder # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> PiTyBinder -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> PiTyBinder -> r # gmapQ :: (forall d. Data d => d -> u) -> PiTyBinder -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> PiTyBinder -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> PiTyBinder -> m PiTyBinder # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> PiTyBinder -> m PiTyBinder # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> PiTyBinder -> m PiTyBinder #
Outputable PiTyBinder # |
Instance details Defined in GHC.Types.Var Methods ppr :: PiTyBinder -> SDoc #

type ForAllTyBinder = VarBndr TyCoVar ForAllTyFlag #

Variable Binder

A `ForAllTyBinder` is the binder of a ForAllTy It's convenient to define this synonym here rather its natural home in GHC.Core.TyCo.Rep, because it's used in GHC.Core.DataCon.hs-boot See Note [VarBndrs, ForAllTyBinders, TyConBinders, and visibility]

A `TyVarBinder` is a binder with only TyVar

type TyVarBinder = VarBndr TyVar ForAllTyFlag #

type Mult = Type #

Mult is a type alias for Type.

Mult must contain Type because multiplicity variables are mere type variables (of kind Multiplicity) in Haskell. So the simplest implementation is to make Mult be Type.

Multiplicities can be formed with: - One: GHC.Types.One (= oneDataCon) - Many: GHC.Types.Many (= manyDataCon) - Multiplication: GHC.Types.MultMul (= multMulTyCon)

So that Mult feels a bit more structured, we provide pattern synonyms and smart constructors for these.

data Scaled a #

A shorthand for data with an attached `Mult` element (the multiplicity).

#### Instances

Instances details

Data a => Data (Scaled a) # |
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) -> Scaled a -> c (Scaled a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Scaled a) # toConstr :: Scaled a -> Constr # dataTypeOf :: Scaled a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Scaled a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a)) # gmapT :: (forall b. Data b => b -> b) -> Scaled a -> Scaled a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r # gmapQ :: (forall d. Data d => d -> u) -> Scaled a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Scaled a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) #
Outputable a => Outputable (Scaled a) # |
Instance details Defined in GHC.Core.TyCo.Rep Methods ppr :: Scaled a -> SDoc #

type KnotTied (ty :: k) = ty #

A type labeled `KnotTied` might have knot-tied tycons in it. See Note [Type checking recursive type and class declarations] in GHC.Tc.TyCl

type RuntimeRepType = Type #

Type synonym used for types of kind RuntimeRep.

## Constructing and deconstructing types

mkTyVarTy :: TyVar -> Type #

mkTyVarTys :: [TyVar] -> [Type] #

getTyVar :: HasDebugCallStack => Type -> TyVar #

Attempts to obtain the type variable underlying a `Type`, and panics with the given message if this is not a type variable type. See also `getTyVar_maybe`

getTyVar_maybe :: Type -> Maybe TyVar #

Attempts to obtain the type variable underlying a `Type`

repGetTyVar_maybe :: Type -> Maybe TyVar #

Attempts to obtain the type variable underlying a `Type`, without any expansion

getCastedTyVar_maybe :: Type -> Maybe (TyVar, CoercionN) #

If the type is a tyvar, possibly under a cast, returns it, along with the coercion. Thus, the co is :: kind tv ~N kind ty

tyVarKind :: TyVar -> Kind #

varType :: Var -> Kind #

The type or kind of the `Var` in question

mkAppTy :: Type -> Type -> Type #

Applies a type to another, as in e.g. `k a`

mkAppTys :: Type -> [Type] -> Type #

splitAppTy :: Type -> (Type, Type) #

Attempts to take a type application apart, as in `splitAppTy_maybe`, and panics if this is not possible

splitAppTys :: HasDebugCallStack => Type -> (Type, [Type]) #

Recursively splits a type as far as is possible, leaving a residual type being applied to and the type arguments applied to it. Never fails, even if that means returning an empty list of type applications.

splitAppTysNoView :: HasDebugCallStack => Type -> (Type, [Type]) #

Like `splitAppTys`, but doesn't look through type synonyms

splitAppTy_maybe :: Type -> Maybe (Type, Type) #

Attempt to take a type application apart, whether it is a function, type constructor, or plain type application. Note that type family applications are NEVER unsaturated by this!

splitAppTyNoView_maybe :: HasDebugCallStack => Type -> Maybe (Type, Type) #

Does the AppTy split as in `splitAppTy_maybe`, but assumes that any coreView stuff is already done

tcSplitAppTyNoView_maybe :: Type -> Maybe (Type, Type) #

Just like splitAppTyNoView_maybe, but does not split (c => t) See Note [Decomposing fat arrow c=>t]

mkFunTy :: HasDebugCallStack => FunTyFlag -> Mult -> Type -> Type -> Type infixr 3 #

mkVisFunTy :: HasDebugCallStack => Mult -> Type -> Type -> Type #

mkVisFunTyMany :: HasDebugCallStack => Type -> Type -> Type infixr 3 #

Make nested arrow types | Special, common, case: Arrow type with mult Many

mkVisFunTysMany :: [Type] -> Type -> Type #

mkScaledFunTys :: HasDebugCallStack => [Scaled Type] -> Type -> Type #

mkInvisFunTy :: HasDebugCallStack => Type -> Type -> Type infixr 3 #

mkInvisFunTys :: HasDebugCallStack => [Type] -> Type -> Type #

tcMkVisFunTy :: Mult -> Type -> Type -> Type #

tcMkScaledFunTys :: [Scaled Type] -> Type -> Type #

tcMkInvisFunTy :: TypeOrConstraint -> Type -> Type -> Type #

splitFunTy :: Type -> (Mult, Type, Type) #

Attempts to extract the multiplicity, argument and result types from a type, and panics if that is not possible. See also `splitFunTy_maybe`

splitFunTy_maybe :: Type -> Maybe (FunTyFlag, Mult, Type, Type) #

Attempts to extract the multiplicity, argument and result types from a type

splitVisibleFunTy_maybe :: Type -> Maybe (Type, Type) #

Works on visible function types only (t1 -> t2), and returns t1 and t2, but not the multiplicity

splitFunTys :: Type -> ([Scaled Type], Type) #

funResultTy :: HasDebugCallStack => Type -> Type #

Extract the function result type and panic if that is not possible

funArgTy :: HasDebugCallStack => Type -> Type #

Extract the function argument type and panic if that is not possible

Just like `piResultTys` but for a single argument Try not to iterate `piResultTy`, because it's inefficient to substitute one variable at a time; instead use 'piResultTys"

funTyConAppTy_maybe :: FunTyFlag -> Type -> Type -> Type -> Maybe (TyCon, [Type]) #

Given the components of a FunTy figure out the corresponding TyConApp.

funTyFlagTyCon :: FunTyFlag -> TyCon #

tyConAppFunTy_maybe :: HasDebugCallStack => TyCon -> [Type] -> Maybe Type #

Return Just if this TyConApp should be represented as a FunTy

tyConAppFunCo_maybe :: HasDebugCallStack => Role -> TyCon -> [Coercion] -> Maybe Coercion #

Return Just if this TyConAppCo should be represented as a FunCo

mkFunctionType :: HasDebugCallStack => Mult -> Type -> Type -> Type #

This one works out the FunTyFlag from the argument type See GHC.Types.Var Note [FunTyFlag]

mkScaledFunctionTys :: [Scaled Type] -> Type -> Type #

Like mkFunctionType, compute the FunTyFlag from the arguments

chooseFunTyFlag :: HasDebugCallStack => Type -> Type -> FunTyFlag #

See GHC.Types.Var Note [FunTyFlag]

mkTyConApp :: TyCon -> [Type] -> Type #

A key function: builds a `TyConApp` or `FunTy` as appropriate to its arguments. Applies its arguments to the constructor from left to right.

mkTyConTy :: TyCon -> Type #

(mkTyConTy tc) returns (TyConApp tc []) but arranges to share that TyConApp among all calls See Note [Sharing nullary TyConApps] So it's just an alias for tyConNullaryTy!

tyConAppTyCon_maybe :: Type -> Maybe TyCon #

The same as `fst . splitTyConApp` We can short-cut the FunTy case

tyConAppTyConPicky_maybe :: Type -> Maybe TyCon #

Retrieve the tycon heading this type, if there is one. Does not look through synonyms.

tyConAppArgs_maybe :: Type -> Maybe [Type] #

The same as `snd . splitTyConApp`

tyConAppTyCon :: HasDebugCallStack => Type -> TyCon #

tyConAppArgs :: HasDebugCallStack => Type -> [Type] #

splitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type]) #

Attempts to tease a type apart into a type constructor and the application of a number of arguments to that constructor

splitTyConAppNoView_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type]) #

splitTyConApp :: Type -> (TyCon, [Type]) #

Attempts to tease a type apart into a type constructor and the application of a number of arguments to that constructor. Panics if that is not possible. See also `splitTyConApp_maybe`

tcSplitTyConApp :: Type -> (TyCon, [Type]) #

tcSplitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type]) #

tcSplitTyConApp_maybe splits a type constructor application into its type constructor and applied types.

Differs from splitTyConApp_maybe in that it does *not* split types headed with (=>), as that's not a TyCon in the type-checker.

Note that this may fail (in funTyConAppTy_maybe) in the case of a `FunTy` with an argument of unknown kind `FunTy` (e.g. `FunTy (a :: k) Int`, since the kind of `a` isn't of the form `TYPE rep`. This isn't usually a problem but may be temporarily the case during canonicalization: see Note [Decomposing FunTy] in GHC.Tc.Solver.Equality and Note [The Purely Kinded Type Invariant (PKTI)] in GHC.Tc.Gen.HsType, Wrinkle around FunTy

Consequently, you may need to zonk your type before using this function.

mkForAllTy :: ForAllTyBinder -> Type -> Type #

Like `mkTyCoForAllTy`, but does not check the occurrence of the binder See Note [Unused coercion variable in ForAllTy]

mkForAllTys :: [ForAllTyBinder] -> Type -> Type #

Wraps foralls over the type using the provided `TyCoVar`s from left to right

mkInvisForAllTys :: [InvisTVBinder] -> Type -> Type #

Wraps foralls over the type using the provided `InvisTVBinder`s from left to right

mkTyCoInvForAllTys :: [TyCoVar] -> Type -> Type #

Like `mkForAllTys`, but assumes all variables are dependent and `Inferred`, a common case

mkSpecForAllTy :: TyVar -> Type -> Type #

Like `mkForAllTy`, but assumes the variable is dependent and `Specified`, a common case

mkSpecForAllTys :: [TyVar] -> Type -> Type #

Like `mkForAllTys`, but assumes all variables are dependent and `Specified`, a common case

mkVisForAllTys :: [TyVar] -> Type -> Type #

Like mkForAllTys, but assumes all variables are dependent and visible

mkTyCoForAllTy :: TyCoVar -> ForAllTyFlag -> Type -> Type #

Make a dependent forall over a TyCoVar

mkTyCoForAllTys :: [ForAllTyBinder] -> Type -> Type #

Make a dependent forall over a TyCoVar

mkTyCoInvForAllTy :: TyCoVar -> Type -> Type #

Make a dependent forall over an `Inferred` variable

mkInfForAllTy :: TyVar -> Type -> Type #

Like `mkTyCoInvForAllTy`, but tv should be a tyvar

mkInfForAllTys :: [TyVar] -> Type -> Type #

Like `mkTyCoInvForAllTys`, but tvs should be a list of tyvar

splitForAllTyCoVars :: Type -> ([TyCoVar], Type) #

Take a ForAllTy apart, returning the list of tycovars and the result type. This always succeeds, even if it returns only an empty list. Note that the result type returned may have free variables that were bound by a forall.

splitForAllTyVars :: Type -> ([TyVar], Type) #

Like `splitForAllTyCoVars`, but split only for tyvars. This always succeeds, even if it returns only an empty list. Note that the result type returned may have free variables that were bound by a forall.

splitForAllReqTyBinders :: Type -> ([ReqTyBinder], Type) #

Like `splitForAllTyCoVars`, but only splits `ForAllTy`s with `Required` type variable binders. Furthermore, each returned tyvar is annotated with `()`.

splitForAllInvisTyBinders :: Type -> ([InvisTyBinder], Type) #

Like `splitForAllTyCoVars`, but only splits `ForAllTy`s with `Invisible` type variable binders. Furthermore, each returned tyvar is annotated with its `Specificity`.

splitForAllForAllTyBinders :: Type -> ([ForAllTyBinder], Type) #

Take a ForAllTy apart, returning the binders and result type

splitForAllForAllTyBinder_maybe :: Type -> Maybe (ForAllTyBinder, Type) #

Attempts to take a ForAllTy apart, returning the full ForAllTyBinder

splitForAllTyCoVar_maybe :: Type -> Maybe (TyCoVar, Type) #

Attempts to take a ForAllTy apart, returning the Var

splitForAllTyCoVar :: Type -> (TyCoVar, Type) #

Take a forall type apart, or panics if that is not possible.

splitForAllTyVar_maybe :: Type -> Maybe (TyVar, Type) #

Attempts to take a ForAllTy apart, but only if the binder is a TyVar

splitForAllCoVar_maybe :: Type -> Maybe (CoVar, Type) #

Like `splitForAllTyCoVar_maybe`, but only returns Just if it is a covar binder.

splitPiTy_maybe :: Type -> Maybe (PiTyBinder, Type) #

Attempts to take a forall type apart; works with proper foralls and functions

splitPiTy :: Type -> (PiTyBinder, Type) #

Takes a forall type apart, or panics

splitPiTys :: Type -> ([PiTyBinder], Type) #

Split off all PiTyBinders to a type, splitting both proper foralls and functions

collectPiTyBinders :: Type -> [PiTyBinder] #

getRuntimeArgTys :: Type -> [(Scaled Type, FunTyFlag)] #

Extracts a list of run-time arguments from a function type, looking through newtypes to the right of arrows.

Examples:

       newtype Identity a = I a

       getRuntimeArgTys (Int -> Bool -> Double) == [(Int, FTF_T_T), (Bool, FTF_T_T)]
       getRuntimeArgTys (Identity Int -> Bool -> Double) == [(Identity Int, FTF_T_T), (Bool, FTF_T_T)]
       getRuntimeArgTys (Int -> Identity (Bool -> Identity Double)) == [(Int, FTF_T_T), (Bool, FTF_T_T)]
       getRuntimeArgTys (forall a. Show a => Identity a -> a -> Int -> Bool)
                == [(Show a, FTF_C_T), (Identity a, FTF_T_T),(a, FTF_T_T),(Int, FTF_T_T)]

Note that, in the last case, the returned types might mention an out-of-scope type variable. This function is used only when we really care about the kinds of the returned types, so this is OK.

- *Warning**: this function can return an infinite list. For example:

      newtype N a = MkN (a -> N a)
      getRuntimeArgTys (N a) == repeat (a, FTF_T_T)

mkTyConBindersPreferAnon #

Arguments

:: [TyVar] | binders
-> TyCoVarSet | free variables of result
-> [TyConBinder] |

Given a list of type-level vars and the free vars of a result kind, makes PiTyBinders, preferring anonymous binders if the variable is, in fact, not dependent. e.g. mkTyConBindersPreferAnon (k:*),(b:k),(c:k) We want (k:*) Named, (b:k) Anon, (c:k) Anon

All non-coercion binders are visible.

mkPiTy :: HasDebugCallStack => PiTyBinder -> Type -> Type #

mkPiTys :: HasDebugCallStack => [PiTyBinder] -> Type -> Type #

piResultTy :: HasDebugCallStack => Type -> Type -> Type #

piResultTys :: HasDebugCallStack => Type -> [Type] -> Type #

(piResultTys f_ty [ty1, .., tyn]) gives the type of (f ty1 .. tyn) where f :: f_ty `piResultTys` is interesting because: 1. `f_ty` may have more for-alls than there are args 2. Less obviously, it may have fewer for-alls For case 2. think of: piResultTys (forall a.a) [forall b.b, Int] This really can happen, but only (I think) in situations involving undefined. For example: undefined :: forall a. a Term: undefined `(forall b. b->b)` Int This term should have type (Int -> Int), but notice that there are more type args than foralls in `undefined`s type.

applyTysX :: HasDebugCallStack => [TyVar] -> Type -> [Type] -> Type #

dropForAlls :: Type -> Type #

Drops all ForAllTys

mkFamilyTyConApp :: TyCon -> [Type] -> Type #

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

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

Where the instance tycon is :RTL, so:

    mkFamilyTyConApp :RTL Int  =  T (Maybe Int)

buildSynTyCon #

Arguments

:: Name |
-> [KnotTied TyConBinder] |
-> Kind | result kind
-> [Role] |
-> KnotTied Type |
-> TyCon |

mkNumLitTy :: Integer -> Type #

isNumLitTy :: Type -> Maybe Integer #

Is this a numeric literal. We also look through type synonyms.

mkStrLitTy :: FastString -> Type #

isStrLitTy :: Type -> Maybe FastString #

Is this a symbol literal. We also look through type synonyms.

mkCharLitTy :: Char -> Type #

isCharLitTy :: Type -> Maybe Char #

Is this a char literal? We also look through type synonyms.

isLitTy :: Type -> Maybe TyLit #

Is this a type literal (symbol, numeric, or char)?

getRuntimeRep :: HasDebugCallStack => Type -> RuntimeRepType #

Extract the RuntimeRep classifier of a type. For instance, `getRuntimeRep_maybe Int = LiftedRep`. Panics if this is not possible.

splitRuntimeRep_maybe :: RuntimeRepType -> Maybe (TyCon, [Type]) #

(splitRuntimeRep_maybe rr) takes a Type rr :: RuntimeRep, and returns the (TyCon,[Type]) for the RuntimeRep, if possible, where the TyCon is one of the promoted DataCons of RuntimeRep. Remember: the unique on TyCon that is a a promoted DataCon is the same as the unique on the DataCon See Note [Promoted data constructors] in GHC.Core.TyCon May not be possible if `rr` is a type variable or type family application

kindRep_maybe :: HasDebugCallStack => Kind -> Maybe RuntimeRepType #

Given a kind (TYPE rr) or (CONSTRAINT rr), extract its RuntimeRep classifier rr. For example, `kindRep_maybe * = Just LiftedRep` Returns `Nothing` if the kind is not of form (TYPE rr)

kindRep :: HasDebugCallStack => Kind -> RuntimeRepType #

Extract the RuntimeRep classifier of a type from its kind. For example, `kindRep * = LiftedRep`; Panics if this is not possible. Treats * and Constraint as the same

getLevity :: HasDebugCallStack => Type -> Type #

Extract the `Levity` of a type. For example, `getLevity Int = Lifted`, or `getLevity (Array# Int) = Unlifted`.

Panics if this is not possible. Does not look through type family applications.

levityType_maybe :: LevityType -> Maybe Levity #

`levityType_maybe` takes a Type of kind Levity, and returns its levity May not be possible for a type variable or type family application

mkCastTy :: Type -> Coercion -> Type #

Make a `CastTy`. The Coercion must be nominal. Checks the Coercion for reflexivity, dropping it if it's reflexive. See `Note [Respecting definitional equality]` in GHC.Core.TyCo.Rep

mkCoercionTy :: Coercion -> Type #

splitCastTy_maybe :: Type -> Maybe (Type, Coercion) #

type ErrorMsgType = Type #

A type of kind `ErrorMessage` (from the `TypeError` module).

userTypeError_maybe :: Type -> Maybe ErrorMsgType #

Is this type a custom user error? If so, give us the error message.

deepUserTypeError_maybe :: Type -> Maybe ErrorMsgType #

pprUserTypeErrorTy :: ErrorMsgType -> SDoc #

Render a type corresponding to a user type error into a SDoc.

coAxNthLHS :: forall (br :: BranchFlag). CoAxiom br -> Int -> Type #

Get the type on the LHS of a coercion induced by a type/data family instance.

stripCoercionTy :: Type -> Coercion #

splitInvisPiTys :: Type -> ([PiTyBinder], Type) #

Like `splitPiTys`, but returns only *invisible* binders, including constraints. Stops at the first visible binder.

splitInvisPiTysN :: Int -> Type -> ([PiTyBinder], Type) #

Same as `splitInvisPiTys`, but stop when - you have found `n` `PiTyBinder`s, - or you run out of invisible binders

invisibleBndrCount :: Type -> Int #

filterOutInvisibleTypes :: TyCon -> [Type] -> [Type] #

Given a `TyCon` and a list of argument types, filter out any invisible (i.e., `Inferred` or `Specified`) arguments.

filterOutInferredTypes :: TyCon -> [Type] -> [Type] #

Given a `TyCon` and a list of argument types, filter out any `Inferred` arguments.

partitionInvisibleTypes :: TyCon -> [Type] -> ([Type], [Type]) #

Given a `TyCon` and a list of argument types, partition the arguments into:

1. `Inferred` or `Specified` (i.e., invisible) arguments and
2. `Required` (i.e., visible) arguments

partitionInvisibles :: [(a, ForAllTyFlag)] -> ([a], [a]) #

Given a list of things paired with their visibilities, partition the things into (invisible things, visible things).

tyConForAllTyFlags :: TyCon -> [Type] -> [ForAllTyFlag] #

Given a `TyCon` and a list of argument types to which the `TyCon` is applied, determine each argument's visibility (`Inferred`, `Specified`, or `Required`).

Wrinkle: consider the following scenario:

    T :: forall k. k -> k
    tyConForAllTyFlags T [forall m. m -> m -> m, S, R, Q]

After substituting, we get

    T (forall m. m -> m -> m) :: (forall m. m -> m -> m) -> forall n. n -> n -> n

Thus, the first argument is invisible, `S` is visible, `R` is invisible again, and `Q` is visible.

appTyForAllTyFlags :: Type -> [Type] -> [ForAllTyFlag] #

Given a `Type` and a list of argument types to which the `Type` is applied, determine each argument's visibility (`Inferred`, `Specified`, or `Required`).

Most of the time, the arguments will be `Required`, but not always. Consider `f :: forall a. a -> Type`. In `f Type Bool`, the first argument (`Type`) is `Specified` and the second argument (`Bool`) is `Required`. It is precisely this sort of higher-rank situation in which `appTyForAllTyFlags` comes in handy, since `f Type Bool` would be represented in Core using `AppTy`s. (See also #15792).

## Analyzing types

data TyCoMapper env (m :: Type -> Type) #

This describes how a "map" operation over a type/coercion should behave

Constructors

TyCoMapper |
Fields tcm_tyvar :: env -> TyVar -> m Type tcm_covar :: env -> CoVar -> m Coercion tcm_hole :: env -> CoercionHole -> m Coercion What to do with coercion holes. See Note [Coercion holes] in GHC.Core.TyCo.Rep. tcm_tycobinder :: forall r. env -> TyCoVar -> ForAllTyFlag -> (env -> TyCoVar -> m r) -> m r The returned env is used in the extended scope tcm_tycon :: TyCon -> m TyCon This is used only for TcTyCons a) To zonk TcTyCons b) To turn TcTyCons into TyCons. See Note [Type checking recursive type and class declarations] in GHC.Tc.TyCl

mapTyCo :: Monad m => TyCoMapper () m -> (Type -> m Type, [Type] -> m [Type], Coercion -> m Coercion, [Coercion] -> m [Coercion]) #

mapTyCoX :: Monad m => TyCoMapper env m -> (env -> Type -> m Type, env -> [Type] -> m [Type], env -> Coercion -> m Coercion, env -> [Coercion] -> m [Coercion]) #

data TyCoFolder env a #

Constructors

TyCoFolder |
Fields tcf_view :: Type -> Maybe Type tcf_tyvar :: env -> TyVar -> a tcf_covar :: env -> CoVar -> a tcf_hole :: env -> CoercionHole -> a What to do with coercion holes. See Note [Coercion holes] in GHC.Core.TyCo.Rep. tcf_tycobinder :: env -> TyCoVar -> ForAllTyFlag -> env The returned env is used in the extended scope

foldTyCo :: Monoid a => TyCoFolder env a -> env -> (Type -> a, [Type] -> a, Coercion -> a, [Coercion] -> a) #

noView :: Type -> Maybe Type #

A view function that looks through nothing.

newTyConInstRhs :: TyCon -> [Type] -> Type #

Unwrap one `layer` of newtype on a type constructor and its arguments, using an eta-reduced version of the `newtype` if possible. This requires tys to have at least `newTyConInstArity tycon` elements.

## Binders

mkForAllTyBinder :: vis -> TyCoVar -> VarBndr TyCoVar vis #

Make a named binder

mkForAllTyBinders :: vis -> [TyCoVar] -> [VarBndr TyCoVar vis] #

Make many named binders

mkTyVarBinder :: vis -> TyVar -> VarBndr TyVar vis #

Make a named binder `var` should be a type variable

mkTyVarBinders :: vis -> [TyVar] -> [VarBndr TyVar vis] #

Make many named binders Input vars should be type variables

tyVarSpecToBinders :: [VarBndr a Specificity] -> [VarBndr a ForAllTyFlag] #

isAnonPiTyBinder :: PiTyBinder -> Bool #

Does this binder bind a variable that is not erased? Returns `True` for anonymous binders.

binderVar :: VarBndr tv argf -> tv #

binderVars :: [VarBndr tv argf] -> [tv] #

binderType :: VarBndr TyCoVar argf -> Type #

binderFlag :: VarBndr tv argf -> argf #

binderFlags :: [VarBndr tv argf] -> [argf] #

piTyBinderType :: PiTyBinder -> Type #

namedPiTyBinder_maybe :: PiTyBinder -> Maybe TyCoVar #

anonPiTyBinderType_maybe :: PiTyBinder -> Maybe Type #

Extract a relevant type, if there is one.

isVisibleForAllTyFlag :: ForAllTyFlag -> Bool #

Does this `ForAllTyFlag` classify an argument that is written in Haskell?

isInvisibleForAllTyFlag :: ForAllTyFlag -> Bool #

Does this `ForAllTyFlag` classify an argument that is not written in Haskell?

isVisiblePiTyBinder :: PiTyBinder -> Bool #

Does this binder bind a visible argument?

isInvisiblePiTyBinder :: PiTyBinder -> Bool #

Does this binder bind an invisible argument?

isNamedPiTyBinder :: PiTyBinder -> Bool #

tyConBindersPiTyBinders :: [TyConBinder] -> [PiTyBinder] #

## Predicates on types

isTyVarTy :: Type -> Bool #

isFunTy :: Type -> Bool #

Is this a function? Note: `forall {b}. Show b => b -> IO b` will not be considered a function by this function. It would merely be a forall wrapping a function type.

isCoercionTy :: Type -> Bool #

isCoercionTy_maybe :: Type -> Maybe Coercion #

isForAllTy :: Type -> Bool #

Checks whether this is a proper forall (with a named binder)

isForAllTy_ty :: Type -> Bool #

Like `isForAllTy`, but returns True only if it is a tyvar binder

isForAllTy_co :: Type -> Bool #

Like `isForAllTy`, but returns True only if it is a covar binder

isForAllTy_invis_ty :: Type -> Bool #

Like `isForAllTy`, but returns True only if it is an inferred tyvar binder

isPiTy :: Type -> Bool #

Is this a function or forall?

isTauTy :: Type -> Bool #

isFamFreeTy :: Type -> Bool #

isAtomicTy :: Type -> Bool #

isValidJoinPointType :: JoinArity -> Type -> Bool #

Determine whether a type could be the type of a join point of given total arity, according to the polymorphism rule. A join point cannot be polymorphic in its return type, since given join j `a` b x y z = e1 in e2, the types of e1 and e2 must be the same, and a and b are not in scope for e2. (See Note [The polymorphism rule of join points] in GHC.Core.) Returns False also if the type simply doesn't have enough arguments.

Note that we need to know how many arguments (type *and* value) the putative join point takes; for instance, if j :: forall a. a -> Int then j could be a binary join point returning an Int, but it could *not* be a unary join point returning a -> Int.

TODO: See Note [Excess polymorphism and join points]

tyConAppNeedsKindSig #

Arguments

:: Bool | Should specified binders count towards injective positions in the kind of the TyCon? (If you're using visible kind applications, then you want True here.
-> TyCon |
-> Int | The number of args the `TyCon` is applied to.
-> Bool | Does `T t_1 ... t_n` need a kind signature? (Where `n` is the number of arguments)

Does a `TyCon` (that is applied to some number of arguments) need to be ascribed with an explicit kind signature to resolve ambiguity if rendered as a source-syntax type? (See `Note [When does a tycon application need an explicit kind signature?]` for a full explanation of what this function checks for.)

# Space-saving construction

mkTYPEapp :: RuntimeRepType -> Type #

mkTYPEapp_maybe :: RuntimeRepType -> Maybe Type #

Given a `RuntimeRep`, applies `TYPE` to it. On the fly it rewrites TYPE LiftedRep --> liftedTypeKind (a synonym) TYPE UnliftedRep --> unliftedTypeKind (ditto) TYPE ZeroBitRep --> zeroBitTypeKind (ditto) NB: no need to check for TYPE (BoxedRep Lifted), TYPE (BoxedRep Unlifted) because those inner types should already have been rewritten to LiftedRep and UnliftedRep respectively, by mkTyConApp

see Note [TYPE and CONSTRAINT] in GHC.Builtin.Types.Prim. See Note [Using synonyms to compress types] in GHC.Core.Type

mkCONSTRAINTapp :: RuntimeRepType -> Type #

Just like mkTYPEapp

mkCONSTRAINTapp_maybe :: RuntimeRepType -> Maybe Type #

Just like mkTYPEapp_maybe

mkBoxedRepApp_maybe :: LevityType -> Maybe Type #

Given a `Levity`, apply `BoxedRep` to it On the fly, rewrite BoxedRep Lifted --> liftedRepTy (a synonym) BoxedRep Unlifted --> unliftedRepTy (ditto) See Note [TYPE and CONSTRAINT] in GHC.Builtin.Types.Prim. See Note [Using synonyms to compress types] in GHC.Core.Type

mkTupleRepApp_maybe :: Type -> Maybe Type #

Given a `[RuntimeRep]`, apply `TupleRep` to it On the fly, rewrite TupleRep [] -> zeroBitRepTy (a synonym) See Note [TYPE and CONSTRAINT] in GHC.Builtin.Types.Prim. See Note [Using synonyms to compress types] in GHC.Core.Type

typeOrConstraintKind :: TypeOrConstraint -> RuntimeRepType -> Kind #

liftedTypeOrConstraintKind :: TypeOrConstraint -> Kind #

### Levity and boxity

sORTKind_maybe :: Kind -> Maybe (TypeOrConstraint, Type) #

typeTypeOrConstraint :: HasDebugCallStack => Type -> TypeOrConstraint #

typeLevity :: HasDebugCallStack => Type -> Levity #

typeLevity_maybe :: HasDebugCallStack => Type -> Maybe Levity #

Tries to compute the `Levity` of the given type. Returns either a definite `Levity`, or `Nothing` if we aren't sure (e.g. the type is representation-polymorphic).

Panics if the kind does not have the shape `TYPE r`.

tyConIsTYPEorCONSTRAINT :: TyCon -> Bool #

isLiftedTypeKind :: Kind -> Bool #

Returns True if the argument is (lifted) Type or Constraint See Note [TYPE and CONSTRAINT] in GHC.Builtin.Types.Prim

isUnliftedTypeKind :: Kind -> Bool #

Returns True if the kind classifies unlifted types (like 'Int#') and False otherwise. Note that this returns False for representation-polymorphic kinds, which may be specialized to a kind that classifies unlifted types.

pickyIsLiftedTypeKind :: Kind -> Bool #

isLiftedRuntimeRep :: RuntimeRepType -> Bool #

Check whether a type of kind `RuntimeRep` is lifted.

`isLiftedRuntimeRep` is:

- True of `LiftedRep :: RuntimeRep`
- False of type variables, type family applications, and of other reps such as `IntRep :: RuntimeRep`.

isUnliftedRuntimeRep :: RuntimeRepType -> Bool #

Check whether a type of kind `RuntimeRep` is unlifted.

- True of definitely unlifted `RuntimeRep`s such as `UnliftedRep`, `IntRep`, `FloatRep`, ...
- False of `LiftedRep`,
- False for type variables and type family applications.

runtimeRepLevity_maybe :: RuntimeRepType -> Maybe Levity #

Check whether a type (usually of kind `RuntimeRep`) is lifted, unlifted, or unknown. Returns Nothing if the type isn't of kind `RuntimeRep`.

`runtimeRepLevity_maybe rr` returns:

- `Just Lifted` if `rr` is `LiftedRep :: RuntimeRep`
- `Just Unlifted` if `rr` is definitely unlifted, e.g. `IntRep`
- `Nothing` if not known (e.g. it's a type variable or a type family application).

isBoxedRuntimeRep :: RuntimeRepType -> Bool #

See `isBoxedRuntimeRep_maybe`.

isLiftedLevity :: Type -> Bool #

isUnliftedLevity :: Type -> Bool #

isUnliftedType :: HasDebugCallStack => Type -> Bool #

Is the given type definitely unlifted? See Type for what an unlifted type is.

Panics on representation-polymorphic types; See `mightBeUnliftedType` for a more approximate predicate that behaves better in the presence of representation polymorphism.

isBoxedType :: Type -> Bool #

See Type for what a boxed type is. Panics on representation-polymorphic types; See `mightBeUnliftedType` for a more approximate predicate that behaves better in the presence of representation polymorphism.

isUnboxedTupleType :: Type -> Bool #

isUnboxedSumType :: Type -> Bool #

kindBoxedRepLevity_maybe :: Type -> Maybe Levity #

Check whether a kind is of the form `TYPE (BoxedRep Lifted)` or `TYPE (BoxedRep Unlifted)`.

Returns:

- `Just Lifted` for `TYPE (BoxedRep Lifted)` and `Type`,
- `Just Unlifted` for `TYPE (BoxedRep Unlifted)` and `UnliftedType`,
- `Nothing` for anything else, e.g. `TYPE IntRep`, `TYPE (BoxedRep l)`, etc.

mightBeLiftedType :: Type -> Bool #

Returns:

- `False` if the type is guaranteed unlifted or
- `True` if it lifted, OR we aren't sure (e.g. in a representation-polymorphic case)

mightBeUnliftedType :: Type -> Bool #

Returns:

- `False` if the type is guaranteed lifted or
- `True` if it is unlifted, OR we aren't sure (e.g. in a representation-polymorphic case)

definitelyLiftedType :: Type -> Bool #

definitelyUnliftedType :: Type -> Bool #

isAlgType :: Type -> Bool #

See Type for what an algebraic type is. Should only be applied to types, as opposed to e.g. partially saturated type constructors

isDataFamilyApp :: Type -> Bool #

Check whether a type is a data family type

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

isPrimitiveType :: Type -> Bool #

Returns true of types that are opaque to Haskell.

isStrictType :: HasDebugCallStack => Type -> Bool #

Computes whether an argument (or let right hand side) should be computed strictly or lazily, based only on its type. Currently, it's just `isUnliftedType`. Panics on representation-polymorphic types.

isTerminatingType :: HasDebugCallStack => Type -> Bool #

True = a term of this type cannot be bottom This identifies the types described by Note [NON-BOTTOM-DICTS invariant] in GHC.Core NB: unlifted types are not terminating types! e.g. you can write a term (loop 1)::Int# that diverges.

isLevityTy :: Type -> Bool #

Is this the type `Levity`?

isLevityVar :: TyVar -> Bool #

Is a tyvar of type `Levity`?

isRuntimeRepTy :: Type -> Bool #

Is this the type `RuntimeRep`?

isRuntimeRepVar :: TyVar -> Bool #

Is a tyvar of type `RuntimeRep`?

isRuntimeRepKindedTy :: Type -> Bool #

Is this a type of kind RuntimeRep? (e.g. LiftedRep)

dropRuntimeRepArgs :: [Type] -> [Type] #

Drops prefix of RuntimeRep constructors in `TyConApp`s. Useful for e.g. dropping 'LiftedRep arguments of unboxed tuple TyCon applications:

dropRuntimeRepArgs [ 'LiftedRep, 'IntRep , String, Int# ] == [String, Int#]

# Multiplicity

isMultiplicityTy :: Type -> Bool #

Is this the type `Multiplicity`?

isMultiplicityVar :: TyVar -> Bool #

Is a tyvar of type `Multiplicity`?

unrestricted :: a -> Scaled a #

Scale a payload by Many

linear :: a -> Scaled a #

Scale a payload by One

tymult :: a -> Scaled a #

Scale a payload by Many; used for type arguments in core

mkScaled :: Mult -> a -> Scaled a #

irrelevantMult :: Scaled a -> a #

scaledSet :: Scaled a -> b -> Scaled b #

pattern OneTy :: Mult #

pattern ManyTy :: Mult #

isOneTy :: Mult -> Bool #

isManyTy :: Mult -> Bool #

isLinearType :: Type -> Bool #

`isLinear t` returns `True` of a if `t` is a type of (curried) function where at least one argument is linear (or otherwise non-unrestricted). We use this function to check whether it is safe to eta reduce an Id in CorePrep. It is always safe to return `True`, because `True` deactivates the optimisation.

# Main data types representing Kinds

type Kind = Type #

The key type representing kinds in the compiler.

## Finding the kind of a type

typeKind :: HasDebugCallStack => Type -> Kind #

typeHasFixedRuntimeRep :: HasDebugCallStack => Type -> Bool #

Returns True if a type has a syntactically fixed runtime rep, as per Note [Fixed RuntimeRep] in GHC.Tc.Utils.Concrete.

This function is equivalent to `isFixedRuntimeRepKind . typeKind` but much faster.

Precondition: The type has kind `(`TYPE` blah)`

tcIsLiftedTypeKind :: Kind -> Bool #

Is this kind equivalent to `Type` i.e. TYPE LiftedRep?

isConstraintKind :: Kind -> Bool #

isConstraintLikeKind :: Kind -> Bool #

returnsConstraintKind :: Kind -> Bool #

tcIsBoxedTypeKind :: Kind -> Bool #

Is this kind equivalent to `TYPE (BoxedRep l)` for some `l :: Levity`?

isTypeLikeKind :: Kind -> Bool #

Is this kind equivalent to `TYPE r` (for some unknown r)?

This considers `Constraint` to be distinct from `*`.

## Common Kind

liftedTypeKind :: Type #

unliftedTypeKind :: Type #

# Type free variables

tyCoFVsOfType :: Type -> FV #

The worker for `tyCoFVsOfType` and `tyCoFVsOfTypeList`. The previous implementation used `unionVarSet` which is O(n+m) and can make the function quadratic. It's exported, so that it can be composed with other functions that compute free variables. See Note [FV naming conventions] in GHC.Utils.FV.

Eta-expanded because that makes it run faster (apparently) See Note [FV eta expansion] in GHC.Utils.FV for explanation.

tyCoFVsBndr :: ForAllTyBinder -> FV -> FV #

tyCoFVsVarBndr :: Var -> FV -> FV #

tyCoFVsVarBndrs :: [Var] -> FV -> FV #

tyCoVarsOfType :: Type -> TyCoVarSet #

tyCoVarsOfTypes :: [Type] -> TyCoVarSet #

tyCoVarsOfTypeDSet :: Type -> DTyCoVarSet #

`tyCoFVsOfType` that returns free variables of a type in a deterministic set. For explanation of why using `VarSet` is not deterministic see Note [Deterministic FV] in GHC.Utils.FV.

coVarsOfType :: Type -> CoVarSet #

coVarsOfTypes :: [Type] -> CoVarSet #

anyFreeVarsOfType :: (TyCoVar -> Bool) -> Type -> Bool #

anyFreeVarsOfTypes :: (TyCoVar -> Bool) -> [Type] -> Bool #

noFreeVarsOfType :: Type -> Bool #

expandTypeSynonyms :: Type -> Type #

Expand out all type synonyms. Actually, it'd suffice to expand out just the ones that discard type variables (e.g. type Funny a = Int) But we don't know which those are currently, so we just expand all.

`expandTypeSynonyms` only expands out type synonyms mentioned in the type, not in the kinds of any TyCon or TyVar mentioned in the type.

Keep this synchronized with `synonymTyConsOfType`

expandSynTyConApp_maybe :: TyCon -> [Type] -> Maybe Type #

`expandSynTyConApp_maybe tc tys` expands the RHS of type synonym `tc` instantiated at arguments `tys`, or returns `Nothing` if `tc` is not a synonym.

typeSize :: Type -> Int #

occCheckExpand :: [Var] -> Type -> Maybe Type #

## Closing over kinds

closeOverKindsDSet :: DTyVarSet -> DTyVarSet #

Add the kind variables free in the kinds of the tyvars in the given set. Returns a deterministic set.

closeOverKindsList :: [TyVar] -> [TyVar] #

Add the kind variables free in the kinds of the tyvars in the given set. Returns a deterministically ordered list.

closeOverKinds :: TyCoVarSet -> TyCoVarSet #

# Forcing evaluation of types

seqType :: Type -> () #

seqTypes :: [Type] -> () #

# Other views onto Types

coreView :: Type -> Maybe Type #

This function strips off the top layer only of a type synonym application (if any) its underlying representation type. Returns `Nothing` if there is nothing to look through.

This function does not look through type family applications.

By being non-recursive and inlined, this case analysis gets efficiently joined onto the case analysis that the caller is already doing

coreFullView :: Type -> Type #

Iterates `coreView` until there is no more to synonym to expand. NB: coreFullView is non-recursive and can be inlined; core_full_view is the recursive one See Note [Inlining coreView].

rewriterView :: Type -> Maybe Type #

tyConsOfType :: Type -> UniqSet TyCon #

All type constructors occurring in the type; looking through type synonyms, but not newtypes. When it finds a Class, it returns the class TyCon.

# Main type substitution data types

type TvSubstEnv = TyVarEnv Type #

A substitution of `Type`s for `TyVar`s and `Kind`s for `KindVar`s

type IdSubstEnv = IdEnv CoreExpr #

A substitution of `Expr`s for non-coercion `Id`s

data Subst #

Type & coercion & id substitution

The Subst data type defined in this module contains substitution for tyvar, covar and id. However, operations on IdSubstEnv (mapping from Id to CoreExpr) that require the definition of the Expr data type are defined in GHC.Core.Subst to avoid circular module dependency.

Constructors

Subst InScopeSet IdSubstEnv TvSubstEnv CvSubstEnv |

#### Instances

Instances details

Outputable Subst # |
Instance details Defined in GHC.Core.TyCo.Subst Methods ppr :: Subst -> SDoc #

## Manipulating type substitutions

emptyTvSubstEnv :: TvSubstEnv #

emptySubst :: Subst #

mkEmptySubst :: InScopeSet -> Subst #

mkTCvSubst :: InScopeSet -> TvSubstEnv -> CvSubstEnv -> Subst #

zipTvSubst :: HasDebugCallStack => [TyVar] -> [Type] -> Subst #

Generates the in-scope set for the `Subst` from the types in the incoming environment. No CoVars or Ids, please!

mkTvSubstPrs :: [(TyVar, Type)] -> Subst #

Generates the in-scope set for the `TCvSubst` from the types in the incoming environment. No CoVars, please! The InScopeSet is just a thunk so with a bit of luck it'll never be evaluated

zipTCvSubst :: HasDebugCallStack => [TyCoVar] -> [Type] -> Subst #

notElemSubst :: Var -> Subst -> Bool #

getTvSubstEnv :: Subst -> TvSubstEnv #

zapSubst :: Subst -> Subst #

Remove all substitutions that might have been built up while preserving the in-scope set originally called zapSubstEnv

substInScopeSet :: Subst -> InScopeSet #

Find the in-scope set: see Note [The substitution invariant]

setInScope :: Subst -> InScopeSet -> Subst #

getSubstRangeTyCoFVs :: Subst -> VarSet #

Returns the free variables of the types in the range of a substitution as a non-deterministic set.

extendSubstInScope :: Subst -> Var -> Subst #

Add the `Var` to the in-scope set

extendSubstInScopeList :: Subst -> [Var] -> Subst #

Add the `Var`s to the in-scope set: see also `extendInScope`

extendSubstInScopeSet :: Subst -> VarSet -> Subst #

Add the `Var`s to the in-scope set: see also `extendInScope`

extendTCvSubst :: Subst -> TyCoVar -> Type -> Subst #

extendCvSubst :: Subst -> CoVar -> Coercion -> Subst #

Add a substitution from a `CoVar` to a `Coercion` to the `Subst`: you must ensure that the in-scope set satisfies Note [The substitution invariant] after extending the substitution like this

extendTvSubst :: Subst -> TyVar -> Type -> Subst #

Add a substitution for a `TyVar` to the `Subst` The `TyVar` *must* be a real TyVar, and not a CoVar You must ensure that the in-scope set is such that Note [The substitution invariant] holds after extending the substitution like this.

extendTvSubstList :: Subst -> [(TyVar, Type)] -> Subst #

Adds multiple `TyVar` substitutions to the `Subst`: see also `extendTvSubst`

extendTvSubstAndInScope :: Subst -> TyVar -> Type -> Subst #

extendTCvSubstList :: Subst -> [Var] -> [Type] -> Subst #

extendTvSubstWithClone :: Subst -> TyVar -> TyVar -> Subst #

extendTCvSubstWithClone :: Subst -> TyCoVar -> TyCoVar -> Subst #

isInScope :: Var -> Subst -> Bool #

composeTCvSubst :: Subst -> Subst -> Subst #

Composes two substitutions, applying the second one provided first, like in function composition. This function leaves IdSubstEnv untouched because IdSubstEnv is not used during substitution for types.

zipTyEnv :: HasDebugCallStack => [TyVar] -> [Type] -> TvSubstEnv #

The InScopeSet is just a thunk so with a bit of luck it'll never be evaluated

zipCoEnv :: HasDebugCallStack => [CoVar] -> [Coercion] -> CvSubstEnv #

isEmptySubst :: Subst -> Bool #

unionSubst :: Subst -> Subst -> Subst #

isEmptyTCvSubst :: Subst -> Bool #

Checks whether the tyvar and covar environments are empty. This function should be used over `isEmptySubst` when substituting for types, because types currently do not contain expressions; we can safely disregard the expression environment when deciding whether to skip a substitution. Using `isEmptyTCvSubst` gives us a non-trivial performance boost (up to 70% less allocation for T18223)

## Performing substitution on types and kinds

substTy :: HasDebugCallStack => Subst -> Type -> Type #

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

substTys :: HasDebugCallStack => Subst -> [Type] -> [Type] #

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

substScaledTy :: HasDebugCallStack => Subst -> Scaled Type -> Scaled Type #

substScaledTys :: HasDebugCallStack => Subst -> [Scaled Type] -> [Scaled Type] #

substTyWith :: HasDebugCallStack => [TyVar] -> [Type] -> Type -> Type #

Type substitution, see `zipTvSubst`

substTysWith :: HasDebugCallStack => [TyVar] -> [Type] -> [Type] -> [Type] #

Type substitution, see `zipTvSubst`

substTheta :: HasDebugCallStack => Subst -> ThetaType -> ThetaType #

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

substTyAddInScope :: HasDebugCallStack => Subst -> Type -> Type #

Substitute within a `Type` after adding the free variables of the type to the in-scope set. This is useful for the case when the free variables aren't already in the in-scope set or easily available. See also Note [The substitution invariant].

substTyUnchecked :: Subst -> Type -> Type #

Substitute within a `Type` disabling the sanity checks. The problems that the sanity checks in substTy catch are described in Note [The substitution invariant]. The goal of #11371 is to migrate all the calls of substTyUnchecked to substTy and remove this function. Please don't use in new code.

substTysUnchecked :: Subst -> [Type] -> [Type] #

Substitute within several `Type`s disabling the sanity checks. The problems that the sanity checks in substTys catch are described in Note [The substitution invariant]. The goal of #11371 is to migrate all the calls of substTysUnchecked to substTys and remove this function. Please don't use in new code.

substScaledTyUnchecked :: HasDebugCallStack => Subst -> Scaled Type -> Scaled Type #

substScaledTysUnchecked :: Subst -> [Scaled Type] -> [Scaled Type] #

substThetaUnchecked :: Subst -> ThetaType -> ThetaType #

Substitute within a `ThetaType` disabling the sanity checks. The problems that the sanity checks in substTys catch are described in Note [The substitution invariant]. The goal of #11371 is to migrate all the calls of substThetaUnchecked to substTheta and remove this function. Please don't use in new code.

substTyWithUnchecked :: [TyVar] -> [Type] -> Type -> Type #

Type substitution, see `zipTvSubst`. Disables sanity checks. The problems that the sanity checks in substTy catch are described in Note [The substitution invariant]. The goal of #11371 is to migrate all the calls of substTyUnchecked to substTy and remove this function. Please don't use in new code.

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

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

substCoUnchecked :: Subst -> Coercion -> Coercion #

Substitute within a `Coercion` disabling sanity checks. The problems that the sanity checks in substCo catch are described in Note [The substitution invariant]. The goal of #11371 is to migrate all the calls of substCoUnchecked to substCo and remove this function. Please don't use in new code.

substCoWithUnchecked :: [TyVar] -> [Type] -> Coercion -> Coercion #

Coercion substitution, see `zipTvSubst`. Disables sanity checks. The problems that the sanity checks in substCo catch are described in Note [The substitution invariant]. The goal of #11371 is to migrate all the calls of substCoUnchecked to substCo and remove this function. Please don't use in new code.

substTyVarBndr :: HasDebugCallStack => Subst -> TyVar -> (Subst, TyVar) #

substTyVarBndrs :: HasDebugCallStack => Subst -> [TyVar] -> (Subst, [TyVar]) #

substTyVar :: Subst -> TyVar -> Type #

substTyVars :: Subst -> [TyVar] -> [Type] #

substVarBndr :: HasDebugCallStack => Subst -> TyCoVar -> (Subst, TyCoVar) #

substVarBndrs :: HasDebugCallStack => Subst -> [TyCoVar] -> (Subst, [TyCoVar]) #

substTyCoBndr :: Subst -> PiTyBinder -> (Subst, PiTyBinder) #

substTyVarToTyVar :: HasDebugCallStack => Subst -> TyVar -> TyVar #

cloneTyVarBndr :: Subst -> TyVar -> Unique -> (Subst, TyVar) #

cloneTyVarBndrs :: Subst -> [TyVar] -> UniqSupply -> (Subst, [TyVar]) #

lookupTyVar :: Subst -> TyVar -> Maybe Type #

# Kinds

isTYPEorCONSTRAINT :: Kind -> Bool #

Does this classify a type allowed to have values? Responds True to things like *, TYPE Lifted, TYPE IntRep, TYPE v, Constraint.

True of a kind `TYPE _` or `CONSTRAINT _`

isConcreteType :: Type -> Bool #

Tests whether the given type is concrete, i.e. it whether it consists only of concrete type constructors, concrete type variables, and applications.

See Note [Concrete types] in GHC.Tc.Utils.Concrete.

isFixedRuntimeRepKind :: HasDebugCallStack => Kind -> Bool #

Checks that a kind of the form `Type`, `Constraint` or `'TYPE r` is concrete. See `isConcreteType`.

Precondition: The type has kind `TYPE blah` or `CONSTRAINT blah`