Safe Haskell | None |
---|---|
Language | Haskell2010 |
Type
Contents
- 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
Description
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
- mkOpenTCvSubst :: TvSubstEnv -> CvSubstEnv -> TCvSubst
- zipOpenTCvSubst :: [TyVar] -> [Type] -> TCvSubst
- zipTopTCvSubst :: [TyVar] -> [Type] -> TCvSubst
- mkTopTCvSubst :: [(TyCoVar, 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
- extendTCvSubst :: TCvSubst -> Var -> Type -> TCvSubst
- extendTCvSubstList :: TCvSubst -> [Var] -> [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 :: TCvSubst -> Type -> Type
- substTys :: TCvSubst -> [Type] -> [Type]
- substTyWith :: [TyVar] -> [Type] -> Type -> Type
- substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type]
- substTheta :: TCvSubst -> ThetaType -> ThetaType
- 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 TyThing
A global typecheckable-thing, essentially anything that has a name.
Not to be confused with a TcTyThing
, which is also a typecheckable
thing but in the *local* context. See TcEnv
for how to retrieve
a TyThing
given a Name
.
Instances
data VisibilityFlag
type KindOrType = Type
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"
data Var
data TyBinder
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]
Instances
Constructing and deconstructing types
mkTyVarTys :: [TyVar] -> [Type]
getTyVar :: String -> 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, Coercion)
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)
Attempts to take a type application apart, as in splitAppTy_maybe
,
and panics if this is not possible
splitAppTys :: 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.
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!
repSplitAppTy_maybe :: Type -> Maybe (Type, Type)
Does the AppTy split as in splitAppTy_maybe
, but assumes that
any Core view stuff is already done
tcRepSplitAppTy_maybe :: Type -> Maybe (Type, Type)
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)
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)
Attempts to extract the argument and result types from a type
splitFunTys :: Type -> ([Type], Type)
splitFunTysN :: Int -> Type -> ([Type], Type)
Split off exactly the given number argument types, and panics if that is not possible
funResultTy :: Type -> Type
Extract the function result type and panic if that is not possible
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.
Create the plain type constructor type which has been applied to no type arguments at all.
tyConAppTyCon_maybe :: Type -> Maybe TyCon
The same as fst . splitTyConApp
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 :: Type -> TyCon
tyConAppArgs :: Type -> [Type]
splitTyConApp_maybe :: 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
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
tyConAppArgN :: Int -> Type -> Type
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
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])
Like splitTyConApp_maybe
, but doesn't look through synonyms. This
assumes the synonyms have already been dealt with.
mkForAllTy :: TyBinder -> Type -> Type
mkForAllTys :: [TyBinder] -> Type -> Type
Wraps foralls over the type using the provided TyVar
s from left to right
mkInvForAllTys :: [TyVar] -> Type -> Type
Like mkForAllTys, but assumes all variables are dependent and invisible, 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
mkNamedForAllTy :: TyVar -> VisibilityFlag -> Type -> Type
Make a dependent forall.
splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
Attempts to take a forall type apart, but only if it's a proper forall, with a named binder
splitForAllTys :: Type -> ([TyVar], Type)
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)
Take a forall type apart, or panics if that is not possible.
splitPiTy_maybe :: Type -> Maybe (TyBinder, Type)
Attempts to take a forall type apart; works with proper foralls and functions
splitPiTys :: Type -> ([TyBinder], Type)
Split off all TyBinders to a type, splitting both proper foralls and functions
splitNamedPiTys :: Type -> ([TyBinder], Type)
Like splitPiTys
but split off only named binders.
mkPiType :: Var -> Type -> Type
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
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
Essentially funResultTy
on kinds handling pi-types too
piResultTys :: Type -> [Type] -> Type
Fold piResultTy
over many types
applyTys :: Type -> [KindOrType] -> Type
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
Drops all non-anonymous ForAllTys
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.
mkCastTy :: Type -> Coercion -> Type
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
splitCastTy_maybe :: Type -> Maybe (Type, Coercion)
userTypeError_maybe :: Type -> Maybe Type
Is this type a custom user error? If so, give us the kind and the error message.
pprUserTypeErrorTy :: Type -> SDoc
Render a type corresponding to a user type error into a SDoc.
coAxNthLHS :: CoAxiom br -> Int -> Type
Get the type on the LHS of a coercion induced by a type/data family instance.
stripCoercionTy :: Type -> Coercion
splitCoercionType_maybe :: Type -> Maybe (Type, Type)
Try to split up a coercion type into the types that it coerces
splitPiTysInvisible :: Type -> ([TyBinder], Type)
filterOutInvisibleTypes :: TyCon -> [Type] -> [Type]
Given a tycon and its arguments, filters out any invisible arguments
filterOutInvisibleTyVars :: TyCon -> [TyVar] -> [TyVar]
Like filterOutInvisibles
, but works on TyVar
s
partitionInvisibles :: TyCon -> (a -> Type) -> [a] -> ([a], [a])
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
tyConBinders :: TyCon -> [TyBinder]
data TyCoMapper env m
This describes how a "map" operation over a type/coercion should behave
Constructors
TyCoMapper | |
Fields
|
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
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
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
mkPrimEqPred :: Type -> Type -> Type
Creates a primitive type equality predicate. Invariant: the types are not Coercions
mkReprPrimEqPred :: Type -> Type -> Type
mkPrimEqPredRole :: Role -> Type -> Type -> PredType
Makes a lifted equality predicate at the given role
equalityTyCon :: Role -> TyCon
mkHeteroPrimEqPred :: Kind -> Kind -> Type -> Type -> Type
Creates a primite type equality predicate with explicit kinds
mkHeteroReprPrimEqPred :: Kind -> Kind -> Type -> Type -> Type
Creates a primitive representational type equality predicate with explicit kinds
mkClassPred :: Class -> [Type] -> PredType
isClassPred :: PredType -> Bool
isNomEqPred :: PredType -> Bool
isIPPred_maybe :: Type -> Maybe (FastString, Type)
isCTupleClass :: Class -> Bool
data EqRel
classifyPredType :: PredType -> PredTree
getClassPredTys :: PredType -> (Class, [Type])
getClassPredTys_maybe :: PredType -> Maybe (Class, [Type])
getEqPredTys :: PredType -> (Type, Type)
getEqPredRole :: PredType -> Role
predTypeEqRel :: PredType -> EqRel
Get the equality relation relevant for a pred type.
Binders
sameVis :: VisibilityFlag -> VisibilityFlag -> Bool
mkNamedBinder :: Var -> VisibilityFlag -> TyBinder
Make a named binder
mkAnonBinder :: Type -> TyBinder
Make an anonymous binder
isNamedBinder :: TyBinder -> Bool
isAnonBinder :: TyBinder -> Bool
isIdLikeBinder :: TyBinder -> Bool
Does this binder bind a variable that is not erased? Returns
True
for anonymous binders.
binderVar_maybe :: TyBinder -> Maybe Var
Extract a bound variable in a binder, if any
Extract a bound variable in a binder, or panics
binderRelevantType_maybe :: TyBinder -> Maybe Type
Extract a relevant type, if there is one.
Like maybe
, but for binders.
partitionBinders :: [TyBinder] -> ([TyVar], [Type])
Break apart a list of binders into tyvars and anonymous types.
partitionBindersIntoBinders :: [TyBinder] -> ([TyBinder], [Type])
Break apart a list of binders into a list of named binders and a list of anonymous types.
binderType :: TyBinder -> Type
isVisibleBinder :: TyBinder -> Bool
Does this binder bind a visible argument?
isInvisibleBinder :: TyBinder -> Bool
Does this binder bind an invisible argument?
Common type constructors
Predicates on types
allDistinctTyVars :: [KindOrType] -> Bool
isCoercionTy :: Type -> Bool
isCoercionTy_maybe :: Type -> Maybe Coercion
isCoercionType :: Type -> Bool
Does this type classify a core Coercion?
isForAllTy :: Type -> Bool
Checks whether this is a proper forall (with a named binder)
isUnLiftedType :: Type -> Bool
See Type for what an unlifted type is
isUnboxedTupleType :: 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
isClosedAlgType :: 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. Closed type constructors are those with a fixed right hand side, as opposed to e.g. associated types
isPrimitiveType :: Type -> Bool
Returns true of types that are opaque to Haskell.
isStrictType :: 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
.
isLevityTy :: Type -> Bool
Is this the type Levity
?
isLevityVar :: TyVar -> Bool
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
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
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
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
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
coVarsOfTypes :: [Type] -> TyCoVarSet
closeOverKinds :: TyVarSet -> TyVarSet
Add the kind variables free in the kinds of the tyvars in the given set. Returns a non-deterministic set.
splitDepVarsOfType :: Type -> Pair TyCoVarSet
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
Like splitDepVarsOfType
, but over a list of types
splitVisVarsOfType :: Type -> Pair TyCoVarSet
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
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.
Well-scoped lists of variables
varSetElemsWellScoped :: VarSet -> [Var]
Extract a well-scoped list of variables from a set of variables.
toposortTyVars :: [TyVar] -> [TyVar]
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]
Get the free vars of a type in scoped order
Type comparison
eqType :: Type -> Type -> Bool
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
Compare types with respect to a (presumably) non-empty RnEnv2
.
eqTypes :: [Type] -> [Type] -> Bool
Type equality on lists of types, looking through type synonyms but not newtypes.
cmpTc :: TyCon -> TyCon -> Ordering
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
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
Like coreView
, but it also "expands" Constraint
to become
TYPE Lifted
.
flattenRepType :: RepType -> [UnaryType]
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
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
Discovers the primitive representation of a more abstract UnaryType
typeRepArity :: Arity -> Type -> RepArity
Main type substitution data types
data TCvSubst
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.
Constructors
TCvSubst InScopeSet TvSubstEnv CvSubstEnv |
Instances
Manipulating type substitutions
mkTCvSubst :: InScopeSet -> (TvSubstEnv, CvSubstEnv) -> TCvSubst
mkOpenTCvSubst :: TvSubstEnv -> CvSubstEnv -> TCvSubst
Generates the in-scope set for the TCvSubst
from the types in the incoming
environment, hence "open"
zipOpenTCvSubst :: [TyVar] -> [Type] -> TCvSubst
Generates the in-scope set for the TCvSubst
from the types in the incoming
environment, hence "open". No CoVars, please!
zipTopTCvSubst :: [TyVar] -> [Type] -> TCvSubst
Makes a subst with an empty in-scope-set. No CoVars, please!
mkTopTCvSubst :: [(TyCoVar, Type)] -> TCvSubst
Called when doing top-level substitutions. Here we expect that the free vars of the range of the substitution will be empty.
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
extendTCvSubst :: TCvSubst -> Var -> Type -> TCvSubst
extendTCvSubstList :: TCvSubst -> [Var] -> [Type] -> TCvSubst
composeTCvSubstEnv :: InScopeSet -> (TvSubstEnv, CvSubstEnv) -> (TvSubstEnv, CvSubstEnv) -> (TvSubstEnv, CvSubstEnv)
(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
Composes two substitutions, applying the second one provided first, like in function composition.
zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
zipCoEnv :: [CoVar] -> [Coercion] -> CvSubstEnv
isEmptyTCvSubst :: TCvSubst -> Bool
unionTCvSubst :: TCvSubst -> TCvSubst -> TCvSubst
Performing substitution on types and kinds
substTyWith :: [TyVar] -> [Type] -> Type -> Type
Type substitution making use of an TCvSubst
that
is assumed to be open, see zipOpenTCvSubst
substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type]
Type substitution making use of an TCvSubst
that
is assumed to be open, see zipOpenTCvSubst
substTheta :: TCvSubst -> ThetaType -> ThetaType
Substitute within a ThetaType
substTyVarBndr :: TCvSubst -> TyVar -> (TCvSubst, TyVar)
substTyVar :: TCvSubst -> TyVar -> Type
substTyVars :: TCvSubst -> [TyVar] -> [Type]
cloneTyVarBndrs :: TCvSubst -> [TyVar] -> UniqSupply -> (TCvSubst, [TyVar])
lookupTyVar :: TCvSubst -> TyVar -> Maybe Type
substTelescope :: [TyCoVar] -> [Type] -> ([Type], TCvSubst)
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
pprTypeApp :: TyCon -> [Type] -> SDoc
pprTyThingCategory :: TyThing -> SDoc
pprTyThing :: TyThing -> SDoc
pprTvBndrs :: [TyVar] -> SDoc
pprForAll :: [TyBinder] -> SDoc
Render the "forall ... ." or "forall ... ->" bit of a type. Do not pass in anonymous binders!
pprForAllImplicit :: [TyVar] -> SDoc
pprUserForAll :: [TyBinder] -> SDoc
pprSigmaType :: Type -> SDoc
pprThetaArrowTy :: ThetaType -> SDoc
pprClassPred :: Class -> [Type] -> SDoc
pprParendKind :: Kind -> SDoc
pprSourceTyCon :: TyCon -> SDoc
maybeParen :: TyPrec -> TyPrec -> SDoc -> SDoc
pprPrefixApp :: TyPrec -> SDoc -> [SDoc] -> SDoc
pprArrowChain :: TyPrec -> [SDoc] -> SDoc
Tidying type related things up for printing
tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
Grabs the free type variables, tidies them
and then uses tidyType
to work over the type itself
tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
tidyOpenKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
tidyTyCoVarBndr :: TidyEnv -> TyCoVar -> (TidyEnv, TyCoVar)
tidyTyCoVarBndrs :: TidyEnv -> [TyCoVar] -> (TidyEnv, [TyCoVar])
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
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)
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
tidyOpenTyCoVars :: TidyEnv -> [TyCoVar] -> (TidyEnv, [TyCoVar])
tidyTyVarOcc :: TidyEnv -> TyVar -> TyVar
tidyTopType :: Type -> Type
Calls tidyType
on a top-level type (i.e. with an empty tidying environment)