Safe Haskell  None 

Language  Haskell2010 
 Main data types representing Types
 Main data types representing Kinds
 Type free variables
 Wellscoped lists of variables
 Type comparison
 Forcing evaluation of types
 Other views onto Types
 Type representation for the code generator
 Main type substitution data types
 Prettyprinting
 Tidying type related things up for printing
Main functions for manipulating types and typerelated 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
 tyCoFVsOfType :: Type > FV
 tyCoVarsOfTypeDSet :: Type > DTyCoVarSet
 coVarsOfType :: Type > CoVarSet
 coVarsOfTypes :: [Type] > TyCoVarSet
 closeOverKinds :: TyVarSet > TyVarSet
 closeOverKindsList :: [TyVar] > [TyVar]
 splitVisVarsOfType :: Type > Pair TyCoVarSet
 splitVisVarsOfTypes :: [Type] > Pair TyCoVarSet
 expandTypeSynonyms :: Type > Type
 typeSize :: Type > Int
 dVarSetElemsWellScoped :: DVarSet > [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
 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
 getTCvSubstRangeFVs :: TCvSubst > VarSet
 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 > [TyCoVar] > 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 letbound 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 builtin 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 lowlevel representation as far as CoretoCore 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 #
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"
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] #
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
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.
repSplitAppTys :: Type > (Type, [Type]) #
Like splitAppTys
, but doesn't look through type synonyms
splitAppTy_maybe :: Type > Maybe (Type, Type) #
Attempt to take a type application apart, whether it is a function, type constructor, or plain type application. Note that type family applications are NEVER unsaturated by this!
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 wellkinded 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.
mkTyBindersPreferAnon :: [TyVar] > Type > [TyBinder] #
Given a list of typelevel 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 #
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 #
(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 foralls than there are args
2. Less obviously, it may have fewer foralls
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 #
Drops all nonanonymous 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 #
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 #
data TyCoMapper env m #
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 #
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 etareduced 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 #
classifyPredType :: PredType > PredTree #
getClassPredTys :: PredType > (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 :: VisibilityFlag > Var > TyBinder #
Make a named binder
mkNamedBinders :: VisibilityFlag > [TyVar] > [TyBinder] #
Make many named binders
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 #
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
.
isRuntimeRepTy :: Type > Bool #
Is this the type RuntimeRep
?
isRuntimeRepVar :: TyVar > Bool #
Is a tyvar of type RuntimeRep
?
isRuntimeRepKindedTy :: Type > Bool #
Is this a type of kind RuntimeRep? (e.g. PtrRep)
dropRuntimeRepArgs :: [Type] > [Type] #
Extract the RuntimeRep classifier of a type. Panics if this is not possible.
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
liftedTypeKind :: Kind #
Type free variables
tyCoVarsOfType :: Type > TyCoVarSet #
Returns free variables of a type, including kind variables as a nondeterministic set. For type synonyms it does not expand the synonym.
tyCoVarsOfTypes :: [Type] > TyCoVarSet #
Returns free variables of types, including kind variables as a nondeterministic set. For type synonyms it does not expand the synonym.
tyCoFVsOfType :: 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.
Etaexpanded 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 nondeterministic set.
closeOverKindsList :: [TyVar] > [TyVar] #
Add the kind variables free in the kinds of the tyvars in the given set. Returns a deterministically ordered list.
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.
expandTypeSynonyms
only expands out type synonyms mentioned in the type,
not in the kinds of any TyCon or TyVar mentioned in the type.
Wellscoped lists of variables
dVarSetElemsWellScoped :: DVarSet > [Var] #
Extract a wellscoped list of variables from a deterministic set of variables. The result is deterministic. NB: There used to exist varSetElemsWellScoped :: VarSet > [Var] which took a nondeterministic set and produced a nondeterministic wellscoped list. If you care about the list being wellscoped you also most likely care about it being in deterministic order.
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
tyCoVarsOfTypesWellScoped :: [Type] > [TyVar] #
Get the free vars of types 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 [Nontrivial definitional equality] in TyCoRep.
eqTypeX :: RnEnv2 > Type > Type > Bool #
Compare types with respect to a (presumably) nonempty 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.
See Note [cmpType nondeterminism]
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 nonrecursive 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 PtrRepLifted
.
flattenRepType :: RepType > [UnaryType] #
repType
figure out how a type will be represented
at runtime. It looks through
 Foralls
 Synonyms
 Predicates
 All newtypes, including recursive ones, but not newtype families
 Casts
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 #
tyConPrimRep :: TyCon > PrimRep #
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 inscope set is needed only to guide the generation of fresh uniques
 In particular, the kind of the type variables in the inscope 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 #
mkTCvSubst :: InScopeSet > (TvSubstEnv, CvSubstEnv) > TCvSubst #
zipTvSubst :: [TyVar] > [Type] > TCvSubst #
Generates the inscope set for the TCvSubst
from the types in the incoming
environment. No CoVars, please!
mkTvSubstPrs :: [(TyVar, Type)] > TCvSubst #
Generates the inscope set for the TCvSubst
from the types in the
incoming environment. No CoVars, please!
notElemTCvSubst :: Var > TCvSubst > Bool #
getTvSubstEnv :: TCvSubst > TvSubstEnv #
setTvSubstEnv :: TCvSubst > TvSubstEnv > TCvSubst #
zapTCvSubst :: TCvSubst > TCvSubst #
getTCvInScope :: TCvSubst > InScopeSet #
getTCvSubstRangeFVs :: TCvSubst > VarSet #
Returns the free variables of the types in the range of a substitution as a nondeterministic set.
extendTCvInScope :: TCvSubst > Var > TCvSubst #
extendTCvInScopeList :: TCvSubst > [Var] > TCvSubst #
extendTCvInScopeSet :: TCvSubst > VarSet > 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
substTy :: (?callStack :: CallStack) => TCvSubst > Type > Type #
Substitute within a Type
The substitution has to satisfy the invariants described in
Note [The substitution invariant].
substTys :: (?callStack :: CallStack) => TCvSubst > [Type] > [Type] #
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 #
Type substitution, see zipTvSubst
substTysWith :: [TyVar] > [Type] > [Type] > [Type] #
Type substitution, see zipTvSubst
substTheta :: (?callStack :: CallStack) => TCvSubst > ThetaType > ThetaType #
Substitute within a ThetaType
The substitution has to satisfy the invariants described in
Note [The substitution invariant].
substTyAddInScope :: TCvSubst > Type > Type #
Substitute within a Type
after adding the free variables of the type
to the inscope set. This is useful for the case when the free variables
aren't already in the inscope set or easily available.
See also Note [The substitution invariant].
substTyUnchecked :: TCvSubst > Type > Type #
Substitute within a Type
disabling the sanity checks.
The problems that the sanity checks in substTy catch are described in
Note [The substitution invariant].
The goal of #11371 is to migrate all the calls of substTyUnchecked to
substTy and remove this function. Please don't use in new code.
substTysUnchecked :: TCvSubst > [Type] > [Type] #
Substitute within several Type
s disabling the sanity checks.
The problems that the sanity checks in substTys catch are described in
Note [The substitution invariant].
The goal of #11371 is to migrate all the calls of substTysUnchecked to
substTys and remove this function. Please don't use in new code.
substThetaUnchecked :: TCvSubst > ThetaType > ThetaType #
Substitute within a ThetaType
disabling the sanity checks.
The problems that the sanity checks in substTys catch are described in
Note [The substitution invariant].
The goal of #11371 is to migrate all the calls of substThetaUnchecked to
substTheta and remove this function. Please don't use in new code.
substTyWithBindersUnchecked :: [TyBinder] > [Type] > Type > Type #
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 #
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 #
Substitute within a Coercion
disabling sanity checks.
The problems that the sanity checks in substCo catch are described in
Note [The substitution invariant].
The goal of #11371 is to migrate all the calls of substCoUnchecked to
substCo and remove this function. Please don't use in new code.
substCoWithUnchecked :: [TyVar] > [Type] > Coercion > Coercion #
Coercion substitution, see zipTvSubst
. Disables sanity checks.
The problems that the sanity checks in substCo catch are described in
Note [The substitution invariant].
The goal of #11371 is to migrate all the calls of substCoUnchecked to
substCo and remove this function. Please don't use in new code.
substTyVar :: TCvSubst > TyVar > Type #
substTyVars :: TCvSubst > [TyVar] > [Type] #
cloneTyVarBndrs :: TCvSubst > [TyVar] > UniqSupply > (TCvSubst, [TyVar]) #
Prettyprinting
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 #
pprArrowChain :: TyPrec > [SDoc] > SDoc #
Tidying type related things up for printing
tidyOpenTypes :: TidyEnv > [Type] > (TidyEnv, [Type]) #
Grabs the free type variables, tidies them
and then uses tidyType
to work over the type itself
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 > [TyCoVar] > 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
tidyTyVarOcc :: TidyEnv > TyVar > TyVar #
tidyTopType :: Type > Type #
Calls tidyType
on a toplevel type (i.e. with an empty tidying environment)