Safe Haskell  None 

Language  Haskell2010 
Main functions for manipulating types and typerelated things
 data TyThing
 data Type
 data ArgFlag
 type KindOrType = Type
 type PredType = Type
 type ThetaType = [PredType]
 data Var
 type TyVar = Var
 isTyVar :: Var > Bool
 type TyCoVar = Id
 data TyBinder
 type TyVarBinder = TyVarBndr TyVar ArgFlag
 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)
 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 :: HasDebugCallStack => Type > Maybe (TyCon, [Type])
 splitTyConApp :: Type > (TyCon, [Type])
 tyConAppArgN :: Int > Type > Type
 nextRole :: Type > Role
 tcRepSplitTyConApp_maybe :: HasCallStack => Type > Maybe (TyCon, [Type])
 tcSplitTyConApp_maybe :: HasCallStack => Type > Maybe (TyCon, [Type])
 splitListTyConApp_maybe :: Type > Maybe Type
 repSplitTyConApp_maybe :: HasDebugCallStack => Type > Maybe (TyCon, [Type])
 mkForAllTy :: TyVar > ArgFlag > Type > Type
 mkForAllTys :: [TyVarBinder] > Type > Type
 mkInvForAllTys :: [TyVar] > Type > Type
 mkSpecForAllTys :: [TyVar] > Type > Type
 mkVisForAllTys :: [TyVar] > Type > Type
 mkInvForAllTy :: TyVar > Type > Type
 splitForAllTys :: Type > ([TyVar], Type)
 splitForAllTyVarBndrs :: Type > ([TyVarBinder], Type)
 splitForAllTy_maybe :: Type > Maybe (TyVar, Type)
 splitForAllTy :: Type > (TyVar, Type)
 splitPiTy_maybe :: Type > Maybe (TyBinder, Type)
 splitPiTy :: Type > (TyBinder, Type)
 splitPiTys :: Type > ([TyBinder], Type)
 mkPiTy :: TyBinder > Type > Type
 mkPiTys :: [TyBinder] > Type > Type
 mkTyConBindersPreferAnon :: [TyVar] > Type > [TyConBinder]
 mkLamType :: Var > Type > Type
 mkLamTypes :: [Var] > Type > Type
 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
 getRuntimeRep_maybe :: HasDebugCallStack => Type > Maybe Type
 getRuntimeRepFromKind_maybe :: HasDebugCallStack => Type > Maybe Type
 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
 modifyJoinResTy :: Int > (Type > Type) > Type > Type
 setJoinResTy :: Int > Type > Type > Type
 data TyCoMapper env m = TyCoMapper {}
 mapType :: Monad m => TyCoMapper env m > env > Type > m Type
 mapCoercion :: 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 :: ArgFlag > ArgFlag > Bool
 mkTyVarBinder :: ArgFlag > Var > TyVarBinder
 mkTyVarBinders :: ArgFlag > [TyVar] > [TyVarBinder]
 mkAnonBinder :: Type > TyBinder
 isAnonTyBinder :: TyBinder > Bool
 isNamedTyBinder :: TyBinder > Bool
 binderVar :: TyVarBndr tv argf > tv
 binderVars :: [TyVarBndr tv argf] > [tv]
 binderKind :: TyVarBndr TyVar argf > Kind
 binderArgFlag :: TyVarBndr tv argf > argf
 tyBinderType :: TyBinder > Type
 binderRelevantType_maybe :: TyBinder > Maybe Type
 caseBinder :: TyBinder > (TyVarBinder > a) > (Type > a) > a
 isVisibleArgFlag :: ArgFlag > Bool
 isInvisibleArgFlag :: ArgFlag > Bool
 isVisibleBinder :: TyBinder > Bool
 isInvisibleBinder :: TyBinder > Bool
 tyConBindersTyBinders :: [TyConBinder] > [TyBinder]
 mkTyBinderTyConBinder :: TyBinder > SrcSpan > Unique > OccName > TyConBinder
 funTyCon :: TyCon
 isTyVarTy :: Type > Bool
 isFunTy :: Type > Bool
 isDictTy :: Type > Bool
 isPredTy :: Type > Bool
 isCoercionTy :: Type > Bool
 isCoercionTy_maybe :: Type > Maybe Coercion
 isCoercionType :: Type > Bool
 isForAllTy :: Type > Bool
 isPiTy :: Type > Bool
 isTauTy :: Type > Bool
 isFamFreeTy :: Type > Bool
 isValidJoinPointType :: JoinArity > Type > Bool
 isLiftedType_maybe :: HasDebugCallStack => Type > Maybe Bool
 isUnliftedType :: HasDebugCallStack => Type > Bool
 isUnboxedTupleType :: Type > Bool
 isUnboxedSumType :: Type > Bool
 isAlgType :: Type > Bool
 isClosedAlgType :: Type > Bool
 isDataFamilyAppType :: Type > Bool
 isPrimitiveType :: Type > Bool
 isStrictType :: HasDebugCallStack => Type > Bool
 isRuntimeRepTy :: Type > Bool
 isRuntimeRepVar :: TyVar > Bool
 isRuntimeRepKindedTy :: Type > Bool
 dropRuntimeRepArgs :: [Type] > [Type]
 getRuntimeRep :: HasDebugCallStack => String > Type > Type
 getRuntimeRepFromKind :: HasDebugCallStack => String > Type > Type
 type Kind = Type
 typeKind :: Type > Kind
 isTypeLevPoly :: Type > Bool
 resultIsLevPoly :: Type > Bool
 liftedTypeKind :: Kind
 tyCoFVsOfType :: Type > FV
 tyCoFVsBndr :: TyVarBinder > FV > FV
 tyCoVarsOfType :: Type > TyCoVarSet
 tyCoVarsOfTypes :: [Type] > TyCoVarSet
 tyCoVarsOfTypeDSet :: Type > DTyCoVarSet
 coVarsOfType :: Type > CoVarSet
 coVarsOfTypes :: [Type] > TyCoVarSet
 closeOverKinds :: TyVarSet > TyVarSet
 closeOverKindsList :: [TyVar] > [TyVar]
 noFreeVarsOfType :: Type > Bool
 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
 nonDetCmpType :: Type > Type > Ordering
 nonDetCmpTypes :: [Type] > [Type] > Ordering
 nonDetCmpTypeX :: RnEnv2 > Type > Type > Ordering
 nonDetCmpTypesX :: RnEnv2 > [Type] > [Type] > Ordering
 nonDetCmpTc :: TyCon > TyCon > Ordering
 eqVarBndrs :: RnEnv2 > [Var] > [Var] > Maybe RnEnv2
 seqType :: Type > ()
 seqTypes :: [Type] > ()
 coreView :: Type > Maybe Type
 tcView :: Type > Maybe Type
 tyConsOfType :: Type > UniqSet TyCon
 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
 extendTvSubstBinder :: TCvSubst > TyBinder > Type > TCvSubst
 extendTvSubstList :: TCvSubst > [Var] > [Type] > TCvSubst
 extendTvSubstAndInScope :: TCvSubst > TyVar > Type > TCvSubst
 extendTvSubstWithClone :: TCvSubst > TyVar > TyVar > 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 :: HasCallStack => TCvSubst > Type > Type
 substTys :: HasCallStack => TCvSubst > [Type] > [Type]
 substTyWith :: HasCallStack => [TyVar] > [Type] > Type > Type
 substTysWith :: [TyVar] > [Type] > [Type] > [Type]
 substTheta :: HasCallStack => TCvSubst > ThetaType > ThetaType
 substTyAddInScope :: TCvSubst > Type > Type
 substTyUnchecked :: TCvSubst > Type > Type
 substTysUnchecked :: TCvSubst > [Type] > [Type]
 substThetaUnchecked :: TCvSubst > ThetaType > ThetaType
 substTyWithUnchecked :: [TyVar] > [Type] > Type > Type
 substCoUnchecked :: TCvSubst > Coercion > Coercion
 substCoWithUnchecked :: [TyVar] > [Type] > Coercion > Coercion
 substTyVarBndr :: HasCallStack => 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
 pprShortTyThing :: TyThing > SDoc
 pprTvBndr :: TyVarBinder > SDoc
 pprTvBndrs :: [TyVarBinder] > SDoc
 pprForAll :: [TyVarBinder] > SDoc
 pprUserForAll :: [TyVarBinder] > SDoc
 pprSigmaType :: Type > SDoc
 ppSuggestExplicitKinds :: 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
 pprTyVars :: [TyVar] > 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
 tidyTyVarBinder :: TidyEnv > TyVarBndr TyVar vis > (TidyEnv, TyVarBndr TyVar vis)
 tidyTyVarBinders :: TidyEnv > [TyVarBndr TyVar vis] > (TidyEnv, [TyVarBndr TyVar vis])
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 #) 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.
type KindOrType = Type Source #
The key representation of types within the compiler
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 Note [TyBinders]
type TyVarBinder = TyVarBndr TyVar ArgFlag Source #
Type Variable Binder
A TyVarBinder
is the binder of a ForAllTy
It's convenient to define this synonym here rather its natural
home in TyCoRep, because it's used in DataCon.hsboot
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
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 :: HasDebugCallStack => 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 wellkinded when applied for this
to work!
tcRepSplitTyConApp_maybe :: HasCallStack => Type > Maybe (TyCon, [Type]) Source #
Like tcSplitTyConApp_maybe
but doesn't look through type synonyms.
tcSplitTyConApp_maybe :: HasCallStack => Type > Maybe (TyCon, [Type]) Source #
Split a type constructor application into its type constructor and
applied types. Note that this may fail in the case of a FunTy
with an
argument of unknown kind FunTy
(e.g. FunTy (a :: k) Int
. since the kind
of a
isn't of the form TYPE rep
). Consequently, you may need to zonk your
type before using this function.
If you only need the TyCon
, consider using tcTyConAppTyCon_maybe
.
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 :: HasDebugCallStack => Type > Maybe (TyCon, [Type]) Source #
Like splitTyConApp_maybe
, but doesn't look through synonyms. This
assumes the synonyms have already been dealt with.
mkForAllTys :: [TyVarBinder] > 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 Inferred, 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
mkInvForAllTy :: TyVar > Type > Type Source #
Make a dependent forall over an Inferred (as opposed to Specified) variable
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.
splitForAllTyVarBndrs :: Type > ([TyVarBinder], Type) Source #
Like splitPiTys
but split off only named binders.
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
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
mkTyConBindersPreferAnon :: [TyVar] > Type > [TyConBinder] Source #
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.
mkLamType :: 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 Inferred binders.
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 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 Source #
Drops all 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.
getRuntimeRep_maybe :: HasDebugCallStack => Type > Maybe Type Source #
Extract the RuntimeRep classifier of a type. For instance,
getRuntimeRep_maybe Int = LiftedRep
. Returns Nothing
if this is not
possible.
getRuntimeRepFromKind_maybe :: HasDebugCallStack => Type > Maybe Type Source #
Extract the RuntimeRep classifier of a type from its kind. For example,
getRuntimeRepFromKind * = LiftedRep
; Returns Nothing
if this is not
possible.
mkCastTy :: Type > Coercion > Type Source #
Make a CastTy
. The Coercion must be nominal. Checks the
Coercion for reflexivity, dropping it if it's reflexive.
See Note [No reflexive casts in types]
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 Inferred or Specified ones and Required 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  

mapCoercion :: 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 etareduced 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
mkTyVarBinder :: ArgFlag > Var > TyVarBinder Source #
Make a named binder
mkTyVarBinders :: ArgFlag > [TyVar] > [TyVarBinder] Source #
Make many named binders
mkAnonBinder :: Type > TyBinder Source #
Make an anonymous binder
isAnonTyBinder :: TyBinder > Bool Source #
Does this binder bind a variable that is not erased? Returns
True
for anonymous binders.
isNamedTyBinder :: TyBinder > Bool Source #
binderVars :: [TyVarBndr tv argf] > [tv] Source #
binderArgFlag :: TyVarBndr tv argf > argf Source #
tyBinderType :: TyBinder > Type Source #
binderRelevantType_maybe :: TyBinder > Maybe Type Source #
Extract a relevant type, if there is one.
:: TyBinder  binder to scrutinize 
> (TyVarBinder > a)  named case 
> (Type > a)  anonymous case 
> a 
Like maybe
, but for binders.
isVisibleArgFlag :: ArgFlag > Bool Source #
Does this ArgFlag
classify an argument that is written in Haskell?
isInvisibleArgFlag :: ArgFlag > Bool Source #
Does this ArgFlag
classify an argument that is not written in Haskell?
isVisibleBinder :: TyBinder > Bool Source #
Does this binder bind a visible argument?
isInvisibleBinder :: TyBinder > Bool Source #
Does this binder bind an invisible argument?
tyConBindersTyBinders :: [TyConBinder] > [TyBinder] Source #
mkTyBinderTyConBinder :: TyBinder > SrcSpan > Unique > OccName > TyConBinder Source #
Manufacture a new TyConBinder
from a TyBinder
. Anonymous
TyBinder
s are still assigned names as TyConBinder
s, so we need
the extra gunk with which to construct a Name
. Used when producing
tyConTyVars from a datatype kind signature. Defined here to avoid module
loops.
Common type constructors
The (>)
type constructor.
(>) :: forall (rep1 :: RuntimeRep) (rep2 :: RuntimeRep). TYPE rep1 > TYPE rep2 > *
Predicates on types
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)
isFamFreeTy :: Type > Bool Source #
isValidJoinPointType :: JoinArity > Type > Bool Source #
Determine whether a type could be the type of a join point of given total
arity, according to the polymorphism rule. A join point cannot be polymorphic
in its return type, since given
join j a
b x y z = e1 in e2,
the types of e1 and e2 must be the same, and a and b are not in scope for e2.
(See Note [The polymorphism rule of join points] in CoreSyn.) Returns False
also if the type simply doesn't have enough arguments.
Note that we need to know how many arguments (type *and* value) the putative join point takes; for instance, if j :: forall a. a > Int then j could be a binary join point returning an Int, but it could *not* be a unary join point returning a > Int.
TODO: See Note [Excess polymorphism and join points]
isLiftedType_maybe :: HasDebugCallStack => Type > Maybe Bool Source #
Returns Just True if this type is surely lifted, Just False if it is surely unlifted, Nothing if we can't be sure (i.e., it is levity polymorphic), and panics if the kind does not have the shape TYPE r.
isUnliftedType :: HasDebugCallStack => Type > Bool Source #
See Type for what an unlifted type is. Panics on levity polymorphic types.
isUnboxedTupleType :: Type > Bool Source #
isUnboxedSumType :: 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
isDataFamilyAppType :: Type > Bool Source #
Check whether a type is a data family type
isPrimitiveType :: Type > Bool Source #
Returns true of types that are opaque to Haskell.
isStrictType :: HasDebugCallStack => 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
. Panics on levitypolymorphic types.
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. LiftedRep)
dropRuntimeRepArgs :: [Type] > [Type] Source #
:: HasDebugCallStack  
=> String  Printed in case of an error 
> Type  
> Type 
Extract the RuntimeRep classifier of a type. For instance,
getRuntimeRep_maybe Int = LiftedRep
. Panics if this is not possible.
getRuntimeRepFromKind :: HasDebugCallStack => String > Type > Type Source #
Extract the RuntimeRep classifier of a type from its kind. For example,
getRuntimeRepFromKind * = LiftedRep
; Panics if this is not possible.
Main data types representing Kinds
Finding the kind of a type
isTypeLevPoly :: Type > Bool Source #
Returns True if a type is levity polymorphic. Should be the same as (isKindLevPoly . typeKind) but much faster. Precondition: The type has kind (TYPE blah)
resultIsLevPoly :: Type > Bool Source #
Looking past all pitypes, is the end result potentially levity polymorphic? Example: True for (forall r (a :: TYPE r). String > a) Example: False for (forall r1 r2 (a :: TYPE r1) (b :: TYPE r2). a > b > Type)
Common Kind
Type free variables
tyCoFVsOfType :: 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.
Etaexpanded because that makes it run faster (apparently) See Note [FV eta expansion] in FV for explanation.
tyCoFVsBndr :: TyVarBinder > FV > FV Source #
tyCoVarsOfType :: Type > TyCoVarSet Source #
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 Source #
Returns free variables of types, including kind variables as a nondeterministic set. For type synonyms it does not expand the synonym.
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 nondeterministic set.
closeOverKindsList :: [TyVar] > [TyVar] Source #
Add the kind variables free in the kinds of the tyvars in the given set. Returns a deterministically ordered list.
noFreeVarsOfType :: Type > Bool Source #
Returns True if this type has no free variables. Should be the same as isEmptyVarSet . tyCoVarsOfType, but faster in the nonforall case.
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.
Keep this synchronized with synonymTyConsOfType
Wellscoped lists of variables
dVarSetElemsWellScoped :: DVarSet > [Var] Source #
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] Source #
Do a topological sort on a list of tyvars, so that binders occur before occurrences E.g. given [ a::k, k::*, b::k ] it'll return a wellscoped list [ k::*, a::k, b::k ]
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 [Nontrivial definitional equality] in TyCoRep.
eqTypeX :: RnEnv2 > Type > Type > Bool Source #
Compare types with respect to a (presumably) nonempty RnEnv2
.
eqTypes :: [Type] > [Type] > Bool Source #
Type equality on lists of types, looking through type synonyms but not newtypes.
nonDetCmpTc :: 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.
See Note [nonDetCmpType nondeterminism]
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.
This function considers Constraint
to be a synonym of TYPE LiftedRep
.
By being nonrecursive and inlined, this case analysis gets efficiently joined onto the case analysis that the caller is already doing
tcView :: Type > Maybe Type Source #
Gives the typechecker view of a type. This unwraps synonyms but
leaves Constraint
alone. c.f. coreView, which turns Constraint into
TYPE LiftedRep. Returns Nothing if no unwrapping happens.
See also Note [coreView vs tcView] in Type.
tyConsOfType :: Type > UniqSet 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.
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 Source #
mkTCvSubst :: InScopeSet > (TvSubstEnv, CvSubstEnv) > TCvSubst Source #
zipTvSubst :: [TyVar] > [Type] > TCvSubst Source #
Generates the inscope set for the TCvSubst
from the types in the incoming
environment. No CoVars, please!
mkTvSubstPrs :: [(TyVar, Type)] > TCvSubst Source #
Generates the inscope 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 #
getTCvSubstRangeFVs :: TCvSubst > VarSet Source #
Returns the free variables of the types in the range of a substitution as a nondeterministic set.
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 :: HasCallStack => TCvSubst > Type > Type Source #
Substitute within a Type
The substitution has to satisfy the invariants described in
Note [The substitution invariant].
substTys :: HasCallStack => TCvSubst > [Type] > [Type] Source #
Substitute within several Type
s
The substitution has to satisfy the invariants described in
Note [The substitution invariant].
substTyWith :: HasCallStack => [TyVar] > [Type] > Type > Type Source #
Type substitution, see zipTvSubst
substTysWith :: [TyVar] > [Type] > [Type] > [Type] Source #
Type substitution, see zipTvSubst
substTheta :: HasCallStack => 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 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 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.
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.
substTyVarBndr :: HasCallStack => TCvSubst > TyVar > (TCvSubst, TyVar) Source #
cloneTyVarBndrs :: TCvSubst > [TyVar] > UniqSupply > (TCvSubst, [TyVar]) Source #
Prettyprinting
pprParendType :: Type > SDoc Source #
pprTyThingCategory :: TyThing > SDoc Source #
pprShortTyThing :: TyThing > SDoc Source #
pprTvBndr :: TyVarBinder > SDoc Source #
pprTvBndrs :: [TyVarBinder] > SDoc Source #
pprForAll :: [TyVarBinder] > SDoc Source #
pprUserForAll :: [TyVarBinder] > SDoc Source #
Print a userlevel forall; see Note [When to print foralls]
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 > [TyCoVar] > 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