Safe Haskell | None |
---|---|
Language | Haskell2010 |
- Main data types representing Types
- Main data types representing Kinds
- Type free variables
- Well-scoped lists of variables
- Type comparison
- Forcing evaluation of types
- Other views onto Types
- Type representation for the code generator
- Main type substitution data types
- Pretty-printing
- Tidying type related things up for printing
Main functions for manipulating types and type-related things
- data TyThing
- data Type
- data VisibilityFlag
- type KindOrType = Type
- type PredType = Type
- type ThetaType = [PredType]
- data Var
- type TyVar = Var
- isTyVar :: Var -> Bool
- type TyCoVar = Id
- data TyBinder
- mkTyVarTy :: TyVar -> Type
- mkTyVarTys :: [TyVar] -> [Type]
- getTyVar :: String -> Type -> TyVar
- getTyVar_maybe :: Type -> Maybe TyVar
- repGetTyVar_maybe :: Type -> Maybe TyVar
- getCastedTyVar_maybe :: Type -> Maybe (TyVar, Coercion)
- tyVarKind :: TyVar -> Kind
- mkAppTy :: Type -> Type -> Type
- mkAppTys :: Type -> [Type] -> Type
- splitAppTy :: Type -> (Type, Type)
- splitAppTys :: Type -> (Type, [Type])
- splitAppTy_maybe :: Type -> Maybe (Type, Type)
- repSplitAppTy_maybe :: Type -> Maybe (Type, Type)
- tcRepSplitAppTy_maybe :: Type -> Maybe (Type, Type)
- mkFunTy :: Type -> Type -> Type
- mkFunTys :: [Type] -> Type -> Type
- splitFunTy :: Type -> (Type, Type)
- splitFunTy_maybe :: Type -> Maybe (Type, Type)
- splitFunTys :: Type -> ([Type], Type)
- splitFunTysN :: Int -> Type -> ([Type], Type)
- funResultTy :: Type -> Type
- funArgTy :: Type -> Type
- mkTyConApp :: TyCon -> [Type] -> Type
- mkTyConTy :: TyCon -> Type
- tyConAppTyCon_maybe :: Type -> Maybe TyCon
- tyConAppTyConPicky_maybe :: Type -> Maybe TyCon
- tyConAppArgs_maybe :: Type -> Maybe [Type]
- tyConAppTyCon :: Type -> TyCon
- tyConAppArgs :: Type -> [Type]
- splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
- splitTyConApp :: Type -> (TyCon, [Type])
- tyConAppArgN :: Int -> Type -> Type
- nextRole :: Type -> Role
- splitListTyConApp_maybe :: Type -> Maybe Type
- repSplitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
- mkForAllTy :: TyBinder -> Type -> Type
- mkForAllTys :: [TyBinder] -> Type -> Type
- mkInvForAllTys :: [TyVar] -> Type -> Type
- mkSpecForAllTys :: [TyVar] -> Type -> Type
- mkVisForAllTys :: [TyVar] -> Type -> Type
- mkNamedForAllTy :: TyVar -> VisibilityFlag -> Type -> Type
- splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
- splitForAllTys :: Type -> ([TyVar], Type)
- splitForAllTy :: Type -> (TyVar, Type)
- splitPiTy_maybe :: Type -> Maybe (TyBinder, Type)
- splitPiTys :: Type -> ([TyBinder], Type)
- splitPiTy :: Type -> (TyBinder, Type)
- splitNamedPiTys :: Type -> ([TyBinder], Type)
- mkPiType :: Var -> Type -> Type
- mkPiTypes :: [Var] -> Type -> Type
- mkPiTypesPreferFunTy :: [TyVar] -> Type -> Type
- piResultTy :: Type -> Type -> Type
- piResultTys :: Type -> [Type] -> Type
- applyTys :: Type -> [KindOrType] -> Type
- applyTysD :: SDoc -> Type -> [Type] -> Type
- applyTysX :: [TyVar] -> Type -> [Type] -> Type
- dropForAlls :: Type -> Type
- mkNumLitTy :: Integer -> Type
- isNumLitTy :: Type -> Maybe Integer
- mkStrLitTy :: FastString -> Type
- isStrLitTy :: Type -> Maybe FastString
- mkCastTy :: Type -> Coercion -> Type
- mkCoercionTy :: Coercion -> Type
- splitCastTy_maybe :: Type -> Maybe (Type, Coercion)
- userTypeError_maybe :: Type -> Maybe Type
- pprUserTypeErrorTy :: Type -> SDoc
- coAxNthLHS :: CoAxiom br -> Int -> Type
- stripCoercionTy :: Type -> Coercion
- splitCoercionType_maybe :: Type -> Maybe (Type, Type)
- splitPiTysInvisible :: Type -> ([TyBinder], Type)
- filterOutInvisibleTypes :: TyCon -> [Type] -> [Type]
- filterOutInvisibleTyVars :: TyCon -> [TyVar] -> [TyVar]
- partitionInvisibles :: TyCon -> (a -> Type) -> [a] -> ([a], [a])
- synTyConResKind :: TyCon -> Kind
- tyConBinders :: TyCon -> [TyBinder]
- data TyCoMapper env m = TyCoMapper {}
- mapType :: (Applicative m, Monad m) => TyCoMapper env m -> env -> Type -> m Type
- mapCoercion :: (Applicative m, Monad m) => TyCoMapper env m -> env -> Coercion -> m Coercion
- newTyConInstRhs :: TyCon -> [Type] -> Type
- mkFamilyTyConApp :: TyCon -> [Type] -> Type
- isDictLikeTy :: Type -> Bool
- mkPrimEqPred :: Type -> Type -> Type
- mkReprPrimEqPred :: Type -> Type -> Type
- mkPrimEqPredRole :: Role -> Type -> Type -> PredType
- equalityTyCon :: Role -> TyCon
- mkHeteroPrimEqPred :: Kind -> Kind -> Type -> Type -> Type
- mkHeteroReprPrimEqPred :: Kind -> Kind -> Type -> Type -> Type
- mkClassPred :: Class -> [Type] -> PredType
- isClassPred :: PredType -> Bool
- isEqPred :: PredType -> Bool
- isNomEqPred :: PredType -> Bool
- isIPPred :: PredType -> Bool
- isIPPred_maybe :: Type -> Maybe (FastString, Type)
- isIPTyCon :: TyCon -> Bool
- isIPClass :: Class -> Bool
- isCTupleClass :: Class -> Bool
- data PredTree
- data EqRel
- eqRelRole :: EqRel -> Role
- classifyPredType :: PredType -> PredTree
- getClassPredTys :: PredType -> (Class, [Type])
- getClassPredTys_maybe :: PredType -> Maybe (Class, [Type])
- getEqPredTys :: PredType -> (Type, Type)
- getEqPredTys_maybe :: PredType -> Maybe (Role, Type, Type)
- getEqPredRole :: PredType -> Role
- predTypeEqRel :: PredType -> EqRel
- sameVis :: VisibilityFlag -> VisibilityFlag -> Bool
- mkNamedBinder :: Var -> VisibilityFlag -> TyBinder
- mkAnonBinder :: Type -> TyBinder
- isNamedBinder :: TyBinder -> Bool
- isAnonBinder :: TyBinder -> Bool
- isIdLikeBinder :: TyBinder -> Bool
- binderVisibility :: TyBinder -> VisibilityFlag
- binderVar_maybe :: TyBinder -> Maybe Var
- binderVar :: String -> TyBinder -> Var
- binderRelevantType_maybe :: TyBinder -> Maybe Type
- caseBinder :: TyBinder -> (TyVar -> a) -> (Type -> a) -> a
- partitionBinders :: [TyBinder] -> ([TyVar], [Type])
- partitionBindersIntoBinders :: [TyBinder] -> ([TyBinder], [Type])
- binderType :: TyBinder -> Type
- isVisibleBinder :: TyBinder -> Bool
- isInvisibleBinder :: TyBinder -> Bool
- funTyCon :: TyCon
- allDistinctTyVars :: [KindOrType] -> Bool
- isTyVarTy :: Type -> Bool
- isFunTy :: Type -> Bool
- isDictTy :: Type -> Bool
- isPredTy :: Type -> Bool
- isVoidTy :: Type -> Bool
- isCoercionTy :: Type -> Bool
- isCoercionTy_maybe :: Type -> Maybe Coercion
- isCoercionType :: Type -> Bool
- isForAllTy :: Type -> Bool
- isPiTy :: Type -> Bool
- isUnLiftedType :: Type -> Bool
- isUnboxedTupleType :: Type -> Bool
- isAlgType :: Type -> Bool
- isClosedAlgType :: Type -> Bool
- isPrimitiveType :: Type -> Bool
- isStrictType :: Type -> Bool
- isLevityTy :: Type -> Bool
- isLevityVar :: TyVar -> Bool
- getLevity :: String -> Type -> Type
- getLevityFromKind :: String -> Type -> Type
- type Kind = Type
- typeKind :: Type -> Kind
- liftedTypeKind :: Kind
- unliftedTypeKind :: Kind
- tyCoVarsOfType :: Type -> TyCoVarSet
- tyCoVarsOfTypes :: [Type] -> TyCoVarSet
- tyCoVarsOfTypeAcc :: Type -> FV
- tyCoVarsOfTypeDSet :: Type -> DTyCoVarSet
- coVarsOfType :: Type -> CoVarSet
- coVarsOfTypes :: [Type] -> TyCoVarSet
- closeOverKinds :: TyVarSet -> TyVarSet
- splitDepVarsOfType :: Type -> Pair TyCoVarSet
- splitDepVarsOfTypes :: [Type] -> Pair TyCoVarSet
- splitVisVarsOfType :: Type -> Pair TyCoVarSet
- splitVisVarsOfTypes :: [Type] -> Pair TyCoVarSet
- expandTypeSynonyms :: Type -> Type
- typeSize :: Type -> Int
- varSetElemsWellScoped :: VarSet -> [Var]
- toposortTyVars :: [TyVar] -> [TyVar]
- tyCoVarsOfTypeWellScoped :: Type -> [TyVar]
- eqType :: Type -> Type -> Bool
- eqTypeX :: RnEnv2 -> Type -> Type -> Bool
- eqTypes :: [Type] -> [Type] -> Bool
- cmpType :: Type -> Type -> Ordering
- cmpTypes :: [Type] -> [Type] -> Ordering
- cmpTypeX :: RnEnv2 -> Type -> Type -> Ordering
- cmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
- cmpTc :: TyCon -> TyCon -> Ordering
- eqVarBndrs :: RnEnv2 -> [Var] -> [Var] -> Maybe RnEnv2
- seqType :: Type -> ()
- seqTypes :: [Type] -> ()
- coreView :: Type -> Maybe Type
- coreViewOneStarKind :: Type -> Maybe Type
- type UnaryType = Type
- data RepType
- flattenRepType :: RepType -> [UnaryType]
- repType :: Type -> RepType
- tyConsOfType :: Type -> NameEnv TyCon
- typePrimRep :: UnaryType -> PrimRep
- typeRepArity :: Arity -> Type -> RepArity
- type TvSubstEnv = TyVarEnv Type
- data TCvSubst = TCvSubst InScopeSet TvSubstEnv CvSubstEnv
- emptyTvSubstEnv :: TvSubstEnv
- emptyTCvSubst :: TCvSubst
- mkEmptyTCvSubst :: InScopeSet -> TCvSubst
- mkTCvSubst :: InScopeSet -> (TvSubstEnv, CvSubstEnv) -> TCvSubst
- zipTvSubst :: [TyVar] -> [Type] -> TCvSubst
- mkTvSubstPrs :: [(TyVar, Type)] -> TCvSubst
- notElemTCvSubst :: Var -> TCvSubst -> Bool
- getTvSubstEnv :: TCvSubst -> TvSubstEnv
- setTvSubstEnv :: TCvSubst -> TvSubstEnv -> TCvSubst
- zapTCvSubst :: TCvSubst -> TCvSubst
- getTCvInScope :: TCvSubst -> InScopeSet
- extendTCvInScope :: TCvSubst -> Var -> TCvSubst
- extendTCvInScopeList :: TCvSubst -> [Var] -> TCvSubst
- extendTCvInScopeSet :: TCvSubst -> VarSet -> TCvSubst
- extendTCvSubst :: TCvSubst -> Var -> Type -> TCvSubst
- extendTCvSubstList :: TCvSubst -> [Var] -> [Type] -> TCvSubst
- extendTCvSubstAndInScope :: TCvSubst -> TyCoVar -> Type -> TCvSubst
- isInScope :: Var -> TCvSubst -> Bool
- composeTCvSubstEnv :: InScopeSet -> (TvSubstEnv, CvSubstEnv) -> (TvSubstEnv, CvSubstEnv) -> (TvSubstEnv, CvSubstEnv)
- composeTCvSubst :: TCvSubst -> TCvSubst -> TCvSubst
- zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
- zipCoEnv :: [CoVar] -> [Coercion] -> CvSubstEnv
- isEmptyTCvSubst :: TCvSubst -> Bool
- unionTCvSubst :: TCvSubst -> TCvSubst -> TCvSubst
- substTy :: (?callStack :: CallStack) => TCvSubst -> Type -> Type
- substTys :: TCvSubst -> [Type] -> [Type]
- substTyWith :: [TyVar] -> [Type] -> Type -> Type
- substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type]
- substTheta :: TCvSubst -> ThetaType -> ThetaType
- substTyAddInScope :: TCvSubst -> Type -> Type
- substTyUnchecked :: TCvSubst -> Type -> Type
- substTyVarBndr :: TCvSubst -> TyVar -> (TCvSubst, TyVar)
- substTyVar :: TCvSubst -> TyVar -> Type
- substTyVars :: TCvSubst -> [TyVar] -> [Type]
- cloneTyVarBndr :: TCvSubst -> TyVar -> Unique -> (TCvSubst, TyVar)
- cloneTyVarBndrs :: TCvSubst -> [TyVar] -> UniqSupply -> (TCvSubst, [TyVar])
- lookupTyVar :: TCvSubst -> TyVar -> Maybe Type
- substTelescope :: [TyCoVar] -> [Type] -> ([Type], TCvSubst)
- pprType :: Type -> SDoc
- pprParendType :: Type -> SDoc
- pprTypeApp :: TyCon -> [Type] -> SDoc
- pprTyThingCategory :: TyThing -> SDoc
- pprTyThing :: TyThing -> SDoc
- pprTvBndr :: TyVar -> SDoc
- pprTvBndrs :: [TyVar] -> SDoc
- pprForAll :: [TyBinder] -> SDoc
- pprForAllImplicit :: [TyVar] -> SDoc
- pprUserForAll :: [TyBinder] -> SDoc
- pprSigmaType :: Type -> SDoc
- pprTheta :: ThetaType -> SDoc
- pprThetaArrowTy :: ThetaType -> SDoc
- pprClassPred :: Class -> [Type] -> SDoc
- pprKind :: Kind -> SDoc
- pprParendKind :: Kind -> SDoc
- pprSourceTyCon :: TyCon -> SDoc
- data TyPrec
- maybeParen :: TyPrec -> TyPrec -> SDoc -> SDoc
- pprTyVar :: TyVar -> SDoc
- pprTcAppTy :: TyPrec -> (TyPrec -> Type -> SDoc) -> TyCon -> [Type] -> SDoc
- pprPrefixApp :: TyPrec -> SDoc -> [SDoc] -> SDoc
- pprArrowChain :: TyPrec -> [SDoc] -> SDoc
- tidyType :: TidyEnv -> Type -> Type
- tidyTypes :: TidyEnv -> [Type] -> [Type]
- tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
- tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
- tidyOpenKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
- tidyTyCoVarBndr :: TidyEnv -> TyCoVar -> (TidyEnv, TyCoVar)
- tidyTyCoVarBndrs :: TidyEnv -> [TyCoVar] -> (TidyEnv, [TyCoVar])
- tidyFreeTyCoVars :: TidyEnv -> TyCoVarSet -> TidyEnv
- tidyOpenTyCoVar :: TidyEnv -> TyCoVar -> (TidyEnv, TyCoVar)
- tidyOpenTyCoVars :: TidyEnv -> [TyCoVar] -> (TidyEnv, [TyCoVar])
- tidyTyVarOcc :: TidyEnv -> TyVar -> TyVar
- tidyTopType :: Type -> Type
- tidyKind :: TidyEnv -> Kind -> Kind
Main data types representing Types
data VisibilityFlag Source
type KindOrType = Type Source
A type of the form p
of kind Constraint
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"
A TyBinder
represents an argument to a function. TyBinders can be dependent
(Named
) or nondependent (Anon
). They may also be visible or not.
See also Note [TyBinder]
Constructing and deconstructing types
mkTyVarTys :: [TyVar] -> [Type] Source
getTyVar :: String -> Type -> TyVar Source
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
repGetTyVar_maybe :: Type -> Maybe TyVar Source
Attempts to obtain the type variable underlying a Type
, without
any expansion
getCastedTyVar_maybe :: Type -> Maybe (TyVar, Coercion) Source
If the type is a tyvar, possibly under a cast, returns it, along with the coercion. Thus, the co is :: kind tv ~R kind type
splitAppTy :: Type -> (Type, Type) Source
Attempts to take a type application apart, as in splitAppTy_maybe
,
and panics if this is not possible
splitAppTys :: Type -> (Type, [Type]) Source
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.
splitAppTy_maybe :: Type -> Maybe (Type, Type) Source
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!
repSplitAppTy_maybe :: Type -> Maybe (Type, Type) Source
Does the AppTy split as in splitAppTy_maybe
, but assumes that
any Core view stuff is already done
tcRepSplitAppTy_maybe :: Type -> Maybe (Type, Type) Source
Does the AppTy split as in tcSplitAppTy_maybe
, but assumes that
any coreView stuff is already done. Refuses to look through (c => t)
splitFunTy :: Type -> (Type, Type) Source
Attempts to extract the argument and result types from a type, and
panics if that is not possible. See also splitFunTy_maybe
splitFunTy_maybe :: Type -> Maybe (Type, Type) Source
Attempts to extract the argument and result types from a type
splitFunTys :: Type -> ([Type], Type) Source
splitFunTysN :: Int -> Type -> ([Type], Type) Source
Split off exactly the given number argument types, and panics if that is not possible
funResultTy :: Type -> Type Source
Extract the function result type and panic if that is not possible
mkTyConApp :: TyCon -> [Type] -> Type Source
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 Source
Create the plain type constructor type which has been applied to no type arguments at all.
tyConAppTyCon_maybe :: Type -> Maybe TyCon Source
The same as fst . splitTyConApp
tyConAppTyConPicky_maybe :: Type -> Maybe TyCon Source
Retrieve the tycon heading this type, if there is one. Does not look through synonyms.
tyConAppArgs_maybe :: Type -> Maybe [Type] Source
The same as snd . splitTyConApp
tyConAppTyCon :: Type -> TyCon Source
tyConAppArgs :: Type -> [Type] Source
splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type]) Source
Attempts to tease a type apart into a type constructor and the application of a number of arguments to that constructor
splitTyConApp :: Type -> (TyCon, [Type]) Source
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
tyConAppArgN :: Int -> Type -> Type Source
nextRole :: Type -> Role Source
What is the role assigned to the next parameter of this type? Usually,
this will be Nominal
, but if the type is a TyConApp
, we may be able to
do better. The type does *not* have to be well-kinded when applied for this
to work!
splitListTyConApp_maybe :: Type -> Maybe Type Source
Attempts to tease a list type apart and gives the type of the elements if successful (looks through type synonyms)
repSplitTyConApp_maybe :: Type -> Maybe (TyCon, [Type]) Source
Like splitTyConApp_maybe
, but doesn't look through synonyms. This
assumes the synonyms have already been dealt with.
mkForAllTy :: TyBinder -> Type -> Type Source
mkForAllTys :: [TyBinder] -> Type -> Type Source
Wraps foralls over the type using the provided TyVar
s from left to right
mkInvForAllTys :: [TyVar] -> Type -> Type Source
Like mkForAllTys, but assumes all variables are dependent and invisible, a common case
mkSpecForAllTys :: [TyVar] -> Type -> Type Source
Like mkForAllTys, but assumes all variables are dependent and specified, a common case
mkVisForAllTys :: [TyVar] -> Type -> Type Source
Like mkForAllTys, but assumes all variables are dependent and visible
mkNamedForAllTy :: TyVar -> VisibilityFlag -> Type -> Type Source
Make a dependent forall.
splitForAllTy_maybe :: Type -> Maybe (TyVar, Type) Source
Attempts to take a forall type apart, but only if it's a proper forall, with a named binder
splitForAllTys :: Type -> ([TyVar], Type) Source
Take a ForAllTy apart, returning the list of tyvars 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.
splitForAllTy :: Type -> (TyVar, Type) Source
Take a forall type apart, or panics if that is not possible.
splitPiTy_maybe :: Type -> Maybe (TyBinder, Type) Source
Attempts to take a forall type apart; works with proper foralls and functions
splitPiTys :: Type -> ([TyBinder], Type) Source
Split off all TyBinders to a type, splitting both proper foralls and functions
splitNamedPiTys :: Type -> ([TyBinder], Type) Source
Like splitPiTys
but split off only named binders.
mkPiType :: Var -> Type -> Type Source
Makes a (->)
type or an implicit forall type, depending
on whether it is given a type variable or a term variable.
This is used, for example, when producing the type of a lambda.
Always uses Invisible binders.
mkPiTypesPreferFunTy :: [TyVar] -> Type -> Type Source
Given a list of type-level vars, makes ForAllTys, preferring anonymous binders if the variable is, in fact, not dependent. All binders are visible.
piResultTy :: Type -> Type -> Type Source
Essentially funResultTy
on kinds handling pi-types too
piResultTys :: Type -> [Type] -> Type Source
Fold piResultTy
over many types
applyTys :: Type -> [KindOrType] -> Type Source
This function is interesting because:
- The function may have more for-alls than there are args
- Less obviously, it may have fewer for-alls
For case 2. think of:
applyTys (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.
dropForAlls :: Type -> Type Source
Drops all non-anonymous ForAllTys
mkNumLitTy :: Integer -> Type Source
isNumLitTy :: Type -> Maybe Integer Source
Is this a numeric literal. We also look through type synonyms.
mkStrLitTy :: FastString -> Type Source
isStrLitTy :: Type -> Maybe FastString Source
Is this a symbol literal. We also look through type synonyms.
mkCastTy :: Type -> Coercion -> Type Source
Make a CastTy
. The Coercion must be nominal. This function looks
at the entire structure of the type and coercion in an attempt to
maintain representation invariance (that is, any two types that are eqType
look the same). Be very wary of calling this in a loop.
mkCoercionTy :: Coercion -> Type Source
userTypeError_maybe :: Type -> Maybe Type Source
Is this type a custom user error? If so, give us the kind and the error message.
pprUserTypeErrorTy :: Type -> SDoc Source
Render a type corresponding to a user type error into a SDoc.
coAxNthLHS :: CoAxiom br -> Int -> Type Source
Get the type on the LHS of a coercion induced by a type/data family instance.
stripCoercionTy :: Type -> Coercion Source
splitCoercionType_maybe :: Type -> Maybe (Type, Type) Source
Try to split up a coercion type into the types that it coerces
splitPiTysInvisible :: Type -> ([TyBinder], Type) Source
filterOutInvisibleTypes :: TyCon -> [Type] -> [Type] Source
Given a tycon and its arguments, filters out any invisible arguments
filterOutInvisibleTyVars :: TyCon -> [TyVar] -> [TyVar] Source
Like filterOutInvisibles
, but works on TyVar
s
partitionInvisibles :: TyCon -> (a -> Type) -> [a] -> ([a], [a]) Source
Given a tycon and a list of things (which correspond to arguments), partitions the things into the invisible ones and the visible ones. The callback function is necessary for this scenario:
T :: forall k. k -> k partitionInvisibles 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.
If you're absolutely sure that your tycon's kind doesn't end in a variable, it's OK if the callback function panics, as that's the only time it's consulted.
synTyConResKind :: TyCon -> Kind Source
tyConBinders :: TyCon -> [TyBinder] Source
data TyCoMapper env m Source
This describes how a "map" operation over a type/coercion should behave
TyCoMapper | |
|
mapType :: (Applicative m, Monad m) => TyCoMapper env m -> env -> Type -> m Type Source
mapCoercion :: (Applicative m, Monad m) => TyCoMapper env m -> env -> Coercion -> m Coercion Source
newTyConInstRhs :: TyCon -> [Type] -> Type Source
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.
mkFamilyTyConApp :: TyCon -> [Type] -> Type Source
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)
isDictLikeTy :: Type -> Bool Source
mkPrimEqPred :: Type -> Type -> Type Source
Creates a primitive type equality predicate. Invariant: the types are not Coercions
mkReprPrimEqPred :: Type -> Type -> Type Source
mkPrimEqPredRole :: Role -> Type -> Type -> PredType Source
Makes a lifted equality predicate at the given role
equalityTyCon :: Role -> TyCon Source
mkHeteroPrimEqPred :: Kind -> Kind -> Type -> Type -> Type Source
Creates a primite type equality predicate with explicit kinds
mkHeteroReprPrimEqPred :: Kind -> Kind -> Type -> Type -> Type Source
Creates a primitive representational type equality predicate with explicit kinds
mkClassPred :: Class -> [Type] -> PredType Source
isClassPred :: PredType -> Bool Source
isNomEqPred :: PredType -> Bool Source
isIPPred_maybe :: Type -> Maybe (FastString, Type) Source
isCTupleClass :: Class -> Bool Source
getClassPredTys :: PredType -> (Class, [Type]) Source
getEqPredTys :: PredType -> (Type, Type) Source
getEqPredRole :: PredType -> Role Source
predTypeEqRel :: PredType -> EqRel Source
Get the equality relation relevant for a pred type.
Binders
sameVis :: VisibilityFlag -> VisibilityFlag -> Bool Source
mkNamedBinder :: Var -> VisibilityFlag -> TyBinder Source
Make a named binder
mkAnonBinder :: Type -> TyBinder Source
Make an anonymous binder
isNamedBinder :: TyBinder -> Bool Source
isAnonBinder :: TyBinder -> Bool Source
isIdLikeBinder :: TyBinder -> Bool Source
Does this binder bind a variable that is not erased? Returns
True
for anonymous binders.
binderVar_maybe :: TyBinder -> Maybe Var Source
Extract a bound variable in a binder, if any
Extract a bound variable in a binder, or panics
binderRelevantType_maybe :: TyBinder -> Maybe Type Source
Extract a relevant type, if there is one.
Like maybe
, but for binders.
partitionBinders :: [TyBinder] -> ([TyVar], [Type]) Source
Break apart a list of binders into tyvars and anonymous types.
partitionBindersIntoBinders :: [TyBinder] -> ([TyBinder], [Type]) Source
Break apart a list of binders into a list of named binders and a list of anonymous types.
binderType :: TyBinder -> Type Source
isVisibleBinder :: TyBinder -> Bool Source
Does this binder bind a visible argument?
isInvisibleBinder :: TyBinder -> Bool Source
Does this binder bind an invisible argument?
Common type constructors
Predicates on types
allDistinctTyVars :: [KindOrType] -> Bool Source
isCoercionTy :: Type -> Bool Source
isCoercionType :: Type -> Bool Source
Does this type classify a core Coercion?
isForAllTy :: Type -> Bool Source
Checks whether this is a proper forall (with a named binder)
isUnLiftedType :: Type -> Bool Source
See Type for what an unlifted type is
isUnboxedTupleType :: Type -> Bool Source
isAlgType :: Type -> Bool Source
See Type for what an algebraic type is. Should only be applied to types, as opposed to e.g. partially saturated type constructors
isClosedAlgType :: Type -> Bool Source
See Type for what an algebraic type is. Should only be applied to types, as opposed to e.g. partially saturated type constructors. Closed type constructors are those with a fixed right hand side, as opposed to e.g. associated types
isPrimitiveType :: Type -> Bool Source
Returns true of types that are opaque to Haskell.
isStrictType :: Type -> Bool Source
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
.
isLevityTy :: Type -> Bool Source
Is this the type Levity
?
isLevityVar :: TyVar -> Bool Source
Is a tyvar of type Levity
?
Extract the levity classifier of a type. Panics if this is not possible.
Extract the levity classifier of a type from its kind. For example, getLevityFromKind * = Lifted; getLevityFromKind # = Unlifted. Panics if this is not possible.
Main data types representing Kinds
Finding the kind of a type
Common Kind
Type free variables
tyCoVarsOfType :: Type -> TyCoVarSet Source
Returns free variables of a type, including kind variables as a non-deterministic set. For type synonyms it does not expand the synonym.
tyCoVarsOfTypes :: [Type] -> TyCoVarSet Source
Returns free variables of types, including kind variables as a non-deterministic set. For type synonyms it does not expand the synonym.
tyCoVarsOfTypeAcc :: Type -> FV Source
The worker for tyVarsOfType
and tyVarsOfTypeList
.
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 FV.
Eta-expanded because that makes it run faster (apparently)
tyCoVarsOfTypeDSet :: Type -> DTyCoVarSet Source
tyVarsOfType
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 FV.
coVarsOfType :: Type -> CoVarSet Source
coVarsOfTypes :: [Type] -> TyCoVarSet Source
closeOverKinds :: TyVarSet -> TyVarSet Source
Add the kind variables free in the kinds of the tyvars in the given set. Returns a non-deterministic set.
splitDepVarsOfType :: Type -> Pair TyCoVarSet Source
Retrieve the free variables in this type, splitting them based on whether the variable was used in a dependent context. It's possible for a variable to be reported twice, if it's used both dependently and non-dependently. (This isn't the most precise analysis, because it's used in the typechecking knot. It might list some dependent variables as also non-dependent.)
splitDepVarsOfTypes :: [Type] -> Pair TyCoVarSet Source
Like splitDepVarsOfType
, but over a list of types
splitVisVarsOfType :: Type -> Pair TyCoVarSet Source
Retrieve the free variables in this type, splitting them based on whether they are used visibly or invisibly. Invisible ones come first.
splitVisVarsOfTypes :: [Type] -> Pair TyCoVarSet Source
expandTypeSynonyms :: Type -> Type Source
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.
Well-scoped lists of variables
varSetElemsWellScoped :: VarSet -> [Var] Source
Extract a well-scoped list of variables from a set of variables.
toposortTyVars :: [TyVar] -> [TyVar] Source
Do a topological sort on a list of tyvars. This is a deterministic sorting operation (that is, doesn't depend on Uniques).
tyCoVarsOfTypeWellScoped :: Type -> [TyVar] Source
Get the free vars of a type in scoped order
Type comparison
eqType :: Type -> Type -> Bool Source
Type equality on source types. Does not look through newtypes
or
PredType
s, but it does look through type synonyms.
This first checks that the kinds of the types are equal and then
checks whether the types are equal, ignoring casts and coercions.
(The kind check is a recursive call, but since all kinds have type
Type
, there is no need to check the types of kinds.)
See also Note [Non-trivial definitional equality] in TyCoRep.
eqTypeX :: RnEnv2 -> Type -> Type -> Bool Source
Compare types with respect to a (presumably) non-empty RnEnv2
.
eqTypes :: [Type] -> [Type] -> Bool Source
Type equality on lists of types, looking through type synonyms but not newtypes.
cmpTc :: TyCon -> TyCon -> Ordering Source
Compare two TyCon
s. NB: This should never see the "star synonyms",
as recognized by Kind.isStarKindSynonymTyCon. See Note
[Kind Constraint and kind *] in Kind.
Forcing evaluation of types
Other views onto Types
coreView :: Type -> Maybe Type Source
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.
By being non-recursive and inlined, this case analysis gets efficiently joined onto the case analysis that the caller is already doing
coreViewOneStarKind :: Type -> Maybe Type Source
Like coreView
, but it also "expands" Constraint
to become
TYPE Lifted
.
flattenRepType :: RepType -> [UnaryType] Source
repType :: Type -> RepType Source
Looks through:
- For-alls
- Synonyms
- Predicates
- All newtypes, including recursive ones, but not newtype families
- Casts
It's useful in the back end of the compiler.
tyConsOfType :: Type -> NameEnv TyCon Source
All type constructors occurring in the type; looking through type synonyms, but not newtypes. When it finds a Class, it returns the class TyCon.
Type representation for the code generator
typePrimRep :: UnaryType -> PrimRep Source
Discovers the primitive representation of a more abstract UnaryType
typeRepArity :: Arity -> Type -> RepArity Source
Main type substitution data types
Type & coercion substitution
The following invariants must hold of a TCvSubst
:
- The in-scope set is needed only to guide the generation of fresh uniques
- In particular, the kind of the type variables in the in-scope set is not relevant
- The substitution is only applied ONCE! This is because in general such application will not reach a fixed point.
Manipulating type substitutions
mkTCvSubst :: InScopeSet -> (TvSubstEnv, CvSubstEnv) -> TCvSubst Source
zipTvSubst :: [TyVar] -> [Type] -> TCvSubst Source
Generates the in-scope set for the TCvSubst
from the types in the incoming
environment. No CoVars, please!
mkTvSubstPrs :: [(TyVar, Type)] -> TCvSubst Source
Generates the in-scope set for the TCvSubst
from the types in the
incoming environment. No CoVars, please!
notElemTCvSubst :: Var -> TCvSubst -> Bool Source
setTvSubstEnv :: TCvSubst -> TvSubstEnv -> TCvSubst Source
zapTCvSubst :: TCvSubst -> TCvSubst Source
extendTCvInScope :: TCvSubst -> Var -> TCvSubst Source
extendTCvInScopeList :: TCvSubst -> [Var] -> TCvSubst Source
extendTCvInScopeSet :: TCvSubst -> VarSet -> TCvSubst Source
composeTCvSubstEnv :: InScopeSet -> (TvSubstEnv, CvSubstEnv) -> (TvSubstEnv, CvSubstEnv) -> (TvSubstEnv, CvSubstEnv) Source
(compose env1 env2)(x)
is env1(env2(x))
; i.e. apply env2
then env1
.
It assumes that both are idempotent.
Typically, env1
is the refinement to a base substitution env2
composeTCvSubst :: TCvSubst -> TCvSubst -> TCvSubst Source
Composes two substitutions, applying the second one provided first, like in function composition.
zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv Source
zipCoEnv :: [CoVar] -> [Coercion] -> CvSubstEnv Source
isEmptyTCvSubst :: TCvSubst -> Bool Source
unionTCvSubst :: TCvSubst -> TCvSubst -> TCvSubst Source
Performing substitution on types and kinds
substTy :: (?callStack :: CallStack) => TCvSubst -> Type -> Type Source
Substitute within a Type
The substitution has to satisfy the invariants described in
Note [The substitution invariant].
substTyWith :: [TyVar] -> [Type] -> Type -> Type Source
Type substitution, see zipTvSubst
substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type] Source
Type substitution, see zipTvSubst
substTyAddInScope :: TCvSubst -> Type -> Type Source
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 :: TCvSubst -> Type -> Type Source
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.
substTyVar :: TCvSubst -> TyVar -> Type Source
substTyVars :: TCvSubst -> [TyVar] -> [Type] Source
cloneTyVarBndrs :: TCvSubst -> [TyVar] -> UniqSupply -> (TCvSubst, [TyVar]) Source
substTelescope :: [TyCoVar] -> [Type] -> ([Type], TCvSubst) Source
Create a substitution from tyvars to types, but later types may depend on earlier ones. Return the substed types and the built substitution.
Pretty-printing
pprParendType :: Type -> SDoc Source
pprTypeApp :: TyCon -> [Type] -> SDoc Source
pprTyThingCategory :: TyThing -> SDoc Source
pprTyThing :: TyThing -> SDoc Source
pprTvBndrs :: [TyVar] -> SDoc Source
pprForAll :: [TyBinder] -> SDoc Source
Render the "forall ... ." or "forall ... ->" bit of a type. Do not pass in anonymous binders!
pprForAllImplicit :: [TyVar] -> SDoc Source
pprUserForAll :: [TyBinder] -> SDoc Source
pprSigmaType :: Type -> SDoc Source
pprThetaArrowTy :: ThetaType -> SDoc Source
pprClassPred :: Class -> [Type] -> SDoc Source
pprParendKind :: Kind -> SDoc Source
pprSourceTyCon :: TyCon -> SDoc Source
pprArrowChain :: TyPrec -> [SDoc] -> SDoc Source
Tidying type related things up for printing
tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type) Source
Grabs the free type variables, tidies them
and then uses tidyType
to work over the type itself
tidyTyCoVarBndrs :: TidyEnv -> [TyCoVar] -> (TidyEnv, [TyCoVar]) Source
This tidies up a type for printing in an error message, or in an interface file.
It doesn't change the uniques at all, just the print names.
tidyFreeTyCoVars :: TidyEnv -> TyCoVarSet -> TidyEnv Source
Add the free TyVar
s to the env in tidy form,
so that we can tidy the type they are free in
tidyOpenTyCoVar :: TidyEnv -> TyCoVar -> (TidyEnv, TyCoVar) Source
Treat a new TyCoVar
as a binder, and give it a fresh tidy name
using the environment if one has not already been allocated. See
also tidyTyCoVarBndr
tidyTyVarOcc :: TidyEnv -> TyVar -> TyVar Source
tidyTopType :: Type -> Type Source
Calls tidyType
on a top-level type (i.e. with an empty tidying environment)