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])
- repSplitAppTys :: 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
- mkTyBindersPreferAnon :: [TyVar] -> Type -> [TyBinder]
- piResultTy :: Type -> Type -> Type
- piResultTys :: 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
- 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 :: VisibilityFlag -> Var -> TyBinder
- mkNamedBinders :: VisibilityFlag -> [TyVar] -> [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
- isRuntimeRepTy :: Type -> Bool
- isRuntimeRepVar :: TyVar -> Bool
- isRuntimeRepKindedTy :: Type -> Bool
- dropRuntimeRepArgs :: [Type] -> [Type]
- getRuntimeRep :: String -> Type -> Type
- getRuntimeRepFromKind :: String -> Type -> Type
- type Kind = Type
- typeKind :: Type -> Kind
- liftedTypeKind :: 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]
- tyCoVarsOfTypesWellScoped :: [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
- kindPrimRep :: Kind -> PrimRep
- tyConPrimRep :: TyCon -> PrimRep
- 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 -> TyCoVar -> Type -> TCvSubst
- extendCvSubst :: TCvSubst -> CoVar -> Coercion -> TCvSubst
- extendTvSubst :: TCvSubst -> TyVar -> Type -> TCvSubst
- extendTvSubstList :: TCvSubst -> [Var] -> [Type] -> TCvSubst
- extendTvSubstAndInScope :: TCvSubst -> TyVar -> 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 :: (?callStack :: CallStack) => TCvSubst -> [Type] -> [Type]
- substTyWith :: (?callStack :: CallStack) => [TyVar] -> [Type] -> Type -> Type
- substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type]
- substTheta :: (?callStack :: CallStack) => TCvSubst -> ThetaType -> ThetaType
- substTyAddInScope :: TCvSubst -> Type -> Type
- substTyUnchecked :: TCvSubst -> Type -> Type
- substTysUnchecked :: TCvSubst -> [Type] -> [Type]
- substThetaUnchecked :: TCvSubst -> ThetaType -> ThetaType
- substTyWithBindersUnchecked :: [TyBinder] -> [Type] -> Type -> Type
- substTyWithUnchecked :: [TyVar] -> [Type] -> Type -> Type
- substCoUnchecked :: TCvSubst -> Coercion -> Coercion
- substCoWithUnchecked :: [TyVar] -> [Type] -> Coercion -> Coercion
- substTyVarBndr :: (?callStack :: CallStack) => 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
- 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
- tidyTyBinder :: TidyEnv -> TyBinder -> (TidyEnv, TyBinder)
- tidyTyBinders :: TidyEnv -> [TyBinder] -> (TidyEnv, [TyBinder])
Main data types representing Types
Types are one of:
- Unboxed
- Iff its representation is other than a pointer Unboxed types are also unlifted.
- Lifted
- Iff it has bottom as an element. Closures always have lifted types: i.e. any let-bound identifier in Core must have a lifted type. Operationally, a lifted object is one that can be entered. 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
ornewtype
. An algebraic type is one that can be deconstructed with a case expression. This is not the same as lifted types, because we also include unboxed tuples in this classification. - Data
- Iff it is a type declared with
data
, or a boxed tuple. - Primitive
- Iff it is a built-in type that can't be expressed in Haskell.
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 ) 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 it's abilities. If you don't want this to happen, use the equivalent functions from the TcType module.
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
getTyVar_maybe :: Type -> Maybe TyVar Source #
Attempts to obtain the type variable underlying a Type
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.
repSplitAppTys :: Type -> (Type, [Type]) Source #
Like splitAppTys
, but doesn't look through type synonyms
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
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
funArgTy :: Type -> Type Source #
Extract the function argument 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.
tyConAppTyConPicky_maybe :: Type -> Maybe TyCon Source #
Retrieve the tycon heading this type, if there is one. Does not look through synonyms.
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
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.
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.
mkTyBindersPreferAnon :: [TyVar] -> Type -> [TyBinder] Source #
Given a list of type-level vars and a result type, makes TyBinders, preferring anonymous binders if the variable is, in fact, not dependent. All binders are visible.
piResultTy :: Type -> Type -> Type Source #
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"
piResultTys :: Type -> [Type] -> Type Source #
(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.
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
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 #
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
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
isClassPred :: PredType -> Bool Source #
isNomEqPred :: PredType -> Bool Source #
isIPPred_maybe :: Type -> Maybe (FastString, Type) Source #
isCTupleClass :: Class -> Bool Source #
classifyPredType :: PredType -> PredTree 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 :: VisibilityFlag -> Var -> TyBinder Source #
Make a named binder
mkNamedBinders :: VisibilityFlag -> [TyVar] -> [TyBinder] Source #
Make many named binders
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.
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 #
isPredTy :: Type -> Bool Source #
Is the type suitable to classify a given/wanted in the typechecker?
isCoercionTy :: Type -> Bool Source #
isCoercionType :: Type -> Bool Source #
isForAllTy :: Type -> Bool Source #
Checks whether this is a proper forall (with a named binder)
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
.
isRuntimeRepTy :: Type -> Bool Source #
Is this the type RuntimeRep
?
isRuntimeRepVar :: TyVar -> Bool Source #
Is a tyvar of type RuntimeRep
?
isRuntimeRepKindedTy :: Type -> Bool Source #
Is this a type of kind RuntimeRep? (e.g. PtrRep)
dropRuntimeRepArgs :: [Type] -> [Type] Source #
Extract the RuntimeRep classifier of a type. Panics if this is not possible.
getRuntimeRepFromKind Source #
Extract the RuntimeRep classifier of a type from its kind. For example, getRuntimeRepFromKind * = PtrRepLifted; getRuntimeRepFromKind # = PtrRepUnlifted. 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. (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
tyCoVarsOfTypesWellScoped :: [Type] -> [TyVar] Source #
Get the free vars of types 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 PtrRepLifted
.
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
kindPrimRep :: Kind -> PrimRep Source #
Take a kind (of shape TYPE rr
) and produce the PrimRep
of values
of types of this kind.
tyConPrimRep :: TyCon -> PrimRep Source #
Find the primitive representation of a TyCon
. Defined here to
avoid module loops. Call this only on unlifted tycons.
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
mkEmptyTCvSubst :: InScopeSet -> TCvSubst Source #
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!
getTvSubstEnv :: TCvSubst -> TvSubstEnv Source #
setTvSubstEnv :: TCvSubst -> TvSubstEnv -> TCvSubst Source #
zapTCvSubst :: TCvSubst -> TCvSubst Source #
getTCvInScope :: TCvSubst -> InScopeSet 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.
isEmptyTCvSubst :: TCvSubst -> Bool 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].
substTys :: (?callStack :: CallStack) => TCvSubst -> [Type] -> [Type] Source #
Substitute within several Type
s
The substitution has to satisfy the invariants described in
Note [The substitution invariant].
substTyWith :: (?callStack :: CallStack) => [TyVar] -> [Type] -> Type -> Type Source #
Type substitution, see zipTvSubst
substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type] Source #
Type substitution, see zipTvSubst
substTheta :: (?callStack :: CallStack) => TCvSubst -> ThetaType -> ThetaType Source #
Substitute within a ThetaType
The substitution has to satisfy the invariants described in
Note [The substitution invariant].
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.
substTysUnchecked :: TCvSubst -> [Type] -> [Type] Source #
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.
substThetaUnchecked :: TCvSubst -> ThetaType -> ThetaType Source #
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.
substTyWithBindersUnchecked :: [TyBinder] -> [Type] -> Type -> Type Source #
Type substitution using Binder
s disabling the sanity checks.
Anonymous binders simply ignore their matching type.
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.
substTyWithUnchecked :: [TyVar] -> [Type] -> Type -> Type Source #
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.
substCoUnchecked :: TCvSubst -> Coercion -> Coercion Source #
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 Source #
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.
cloneTyVarBndrs :: TCvSubst -> [TyVar] -> UniqSupply -> (TCvSubst, [TyVar]) Source #
Pretty-printing
pprParendType :: 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 #
pprParendKind :: Kind -> SDoc Source #
pprSourceTyCon :: TyCon -> SDoc Source #
Tidying type related things up for printing
tidyOpenTypes :: 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