Type

Main functions for manipulating types and type-related things

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 or newtype. 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 #) 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 TyThing

A global typecheckable-thing, essentially anything that has a name. Not to be confused with a TcTyThing, which is also a typecheckable thing but in the *local* context. See TcEnv for how to retrieve a TyThing given a Name.

Constructors

AnId Id

AConLike ConLike

ATyCon TyCon

ACoAxiom (CoAxiom Branched)

Instances

Outputable TyThing

Methods

ppr :: TyThing -> SDoc

pprPrec :: Rational -> TyThing -> SDoc

NamedThing TyThing

Methods

getOccName :: TyThing -> OccName

getName :: TyThing -> Name

data Type

Instances

Data Type

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Type -> c Type

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Type

toConstr :: Type -> Constr

dataTypeOf :: Type -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Type)

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Type)

gmapT :: (forall b. Data b => b -> b) -> Type -> Type

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Type -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Type -> r

gmapQ :: (forall d. Data d => d -> u) -> Type -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Type -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Type -> m Type

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Type -> m Type

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Type -> m Type

Outputable Type

Methods

ppr :: Type -> SDoc

pprPrec :: Rational -> Type -> SDoc

data ArgFlag

Argument Flag

Is something required to appear in source Haskell (Required), permitted by request (Specified) (visible type application), or prohibited entirely from appearing in source Haskell (Inferred)? See Note [TyBinders and ArgFlags] in TyCoRep

Constructors

Required

Specified

Inferred

Instances

Eq ArgFlag

Methods

(==) :: ArgFlag -> ArgFlag -> Bool

(/=) :: ArgFlag -> ArgFlag -> Bool

Data ArgFlag

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> ArgFlag -> c ArgFlag

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c ArgFlag

toConstr :: ArgFlag -> Constr

dataTypeOf :: ArgFlag -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c ArgFlag)

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c ArgFlag)

gmapT :: (forall b. Data b => b -> b) -> ArgFlag -> ArgFlag

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ArgFlag -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ArgFlag -> r

gmapQ :: (forall d. Data d => d -> u) -> ArgFlag -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> ArgFlag -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> ArgFlag -> m ArgFlag

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ArgFlag -> m ArgFlag

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ArgFlag -> m ArgFlag

Outputable ArgFlag

Methods

ppr :: ArgFlag -> SDoc

pprPrec :: Rational -> ArgFlag -> SDoc

Binary ArgFlag

Methods

put_ :: BinHandle -> ArgFlag -> IO ()

put :: BinHandle -> ArgFlag -> IO (Bin * ArgFlag)

get :: BinHandle -> IO ArgFlag

Outputable tv => Outputable (TyVarBndr tv ArgFlag)

Methods

ppr :: TyVarBndr tv ArgFlag -> SDoc

pprPrec :: Rational -> TyVarBndr tv ArgFlag -> SDoc

type KindOrType = Type

The key representation of types within the compiler

type PredType = 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"

type ThetaType = [PredType]

A collection of PredTypes

data Var

Variable

Essentially a typed Name, that may also contain some additional information about the Var and it's use sites.

Instances

Eq Var

Methods

(==) :: Var -> Var -> Bool

(/=) :: Var -> Var -> Bool

Data Var

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Var -> c Var

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Var

toConstr :: Var -> Constr

dataTypeOf :: Var -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Var)

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Var)

gmapT :: (forall b. Data b => b -> b) -> Var -> Var

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Var -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Var -> r

gmapQ :: (forall d. Data d => d -> u) -> Var -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Var -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Var -> m Var

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Var -> m Var

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Var -> m Var

Ord Var

Methods

compare :: Var -> Var -> Ordering

(<) :: Var -> Var -> Bool

(<=) :: Var -> Var -> Bool

(>) :: Var -> Var -> Bool

(>=) :: Var -> Var -> Bool

max :: Var -> Var -> Var

min :: Var -> Var -> Var

Outputable Var

Methods

ppr :: Var -> SDoc

pprPrec :: Rational -> Var -> SDoc

Uniquable Var

Methods

getUnique :: Var -> Unique

HasOccName Var

Methods

occName :: Var -> OccName

NamedThing Var

Methods

getOccName :: Var -> OccName

getName :: Var -> Name

type PostRn Id ty

type PostRn Id ty = ty

type PostTc Id ty

type PostTc Id ty = ty

type TyVar = Var

Type or kind Variable

isTyVar :: Var -> Bool

type TyCoVar = Id

Type or Coercion Variable

data TyBinder

A TyBinder represents an argument to a function. TyBinders can be dependent (Named) or nondependent (Anon). They may also be visible or not. See Note [TyBinders]

Instances

Data TyBinder

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TyBinder -> c TyBinder

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TyBinder

toConstr :: TyBinder -> Constr

dataTypeOf :: TyBinder -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c TyBinder)

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TyBinder)

gmapT :: (forall b. Data b => b -> b) -> TyBinder -> TyBinder

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TyBinder -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TyBinder -> r

gmapQ :: (forall d. Data d => d -> u) -> TyBinder -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> TyBinder -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> TyBinder -> m TyBinder

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> TyBinder -> m TyBinder

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> TyBinder -> m TyBinder

Outputable TyBinder

Methods

ppr :: TyBinder -> SDoc

pprPrec :: Rational -> TyBinder -> SDoc

type TyVarBinder = TyVarBndr TyVar ArgFlag

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.hs-boot

Constructing and deconstructing types

mkTyVarTy :: TyVar -> Type

mkTyVarTys :: [TyVar] -> [Type]

getTyVar :: String -> Type -> TyVar

Attempts to obtain the type variable underlying a Type, and panics with the given message if this is not a type variable type. See also getTyVar_maybe

getTyVar_maybe :: Type -> Maybe TyVar

Attempts to obtain the type variable underlying a Type

repGetTyVar_maybe :: Type -> Maybe TyVar

Attempts to obtain the type variable underlying a Type, without any expansion

getCastedTyVar_maybe :: Type -> Maybe (TyVar, Coercion)

If the type is a tyvar, possibly under a cast, returns it, along with the coercion. Thus, the co is :: kind tv ~R kind type

tyVarKind :: TyVar -> Kind

mkAppTy :: Type -> Type -> Type

Applies a type to another, as in e.g. k a

mkAppTys :: Type -> [Type] -> 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)

mkFunTy :: Type -> Type -> Type infixr 3

Make an arrow type

mkFunTys :: [Type] -> Type -> Type

Make nested arrow types

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)

funResultTy :: Type -> Type

Extract the function result type and panic if that is not possible

funArgTy :: Type -> Type

Extract the function argument 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.

mkTyConTy :: TyCon -> Type

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 :: HasDebugCallStack => 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

nextRole :: Type -> Role

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!

tcRepSplitTyConApp_maybe :: HasCallStack => Type -> Maybe (TyCon, [Type])

Like tcSplitTyConApp_maybe but doesn't look through type synonyms.

tcSplitTyConApp_maybe :: HasCallStack => Type -> Maybe (TyCon, [Type])

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

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])

Like splitTyConApp_maybe, but doesn't look through synonyms. This assumes the synonyms have already been dealt with.

mkForAllTy :: TyVar -> ArgFlag -> Type -> Type

mkForAllTys :: [TyVarBinder] -> Type -> Type

Wraps foralls over the type using the provided TyVars from left to right

mkInvForAllTys :: [TyVar] -> Type -> Type

Like mkForAllTys, but assumes all variables are dependent and Inferred, 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

mkInvForAllTy :: TyVar -> Type -> Type

Make a dependent forall over an Inferred (as opposed to Specified) variable

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.

splitForAllTyVarBndrs :: Type -> ([TyVarBinder], Type)

Like splitPiTys but split off only named binders.

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

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

splitPiTy :: Type -> (TyBinder, Type)

Takes a forall type apart, or panics

splitPiTys :: Type -> ([TyBinder], Type)

Split off all TyBinders to a type, splitting both proper foralls and functions

mkPiTy :: TyBinder -> Type -> Type

mkPiTys :: [TyBinder] -> Type -> Type

mkTyConBindersPreferAnon :: [TyVar] -> Type -> [TyConBinder]

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.

mkLamType :: 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 Inferred binders.

mkLamTypes :: [Var] -> Type -> Type

mkLamType for multiple type or value arguments

piResultTy :: Type -> Type -> Type

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 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 undefineds type.

applyTysX :: [TyVar] -> Type -> [Type] -> Type

dropForAlls :: Type -> Type

Drops all 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.

getRuntimeRep_maybe :: HasDebugCallStack => Type -> Maybe Type

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

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

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

splitCastTy_maybe :: Type -> Maybe (Type, Coercion)

userTypeError_maybe :: Type -> Maybe Type

Is this type a custom user error? If so, give us the kind and the error message.

pprUserTypeErrorTy :: Type -> SDoc

Render a type corresponding to a user type error into a SDoc.

coAxNthLHS :: CoAxiom br -> Int -> Type

Get the type on the LHS of a coercion induced by a type/data family instance.

stripCoercionTy :: Type -> Coercion

splitCoercionType_maybe :: Type -> Maybe (Type, Type)

Try to split up a coercion type into the types that it coerces

splitPiTysInvisible :: Type -> ([TyBinder], Type)

filterOutInvisibleTypes :: TyCon -> [Type] -> [Type]

Given a tycon and its arguments, filters out any invisible arguments

filterOutInvisibleTyVars :: TyCon -> [TyVar] -> [TyVar]

Like filterOutInvisibles, but works on TyVars

partitionInvisibles :: TyCon -> (a -> Type) -> [a] -> ([a], [a])

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

Find the result Kind of a type synonym, after applying it to its arity number of type variables Actually this function works fine on data types too, but they'd always return *, so we never need to ask

modifyJoinResTy :: Int -> (Type -> Type) -> Type -> Type

setJoinResTy :: Int -> Type -> Type -> Type

data TyCoMapper env m

This describes how a "map" operation over a type/coercion should behave

Constructors

TyCoMapper

Fields

• tcm_smart :: Bool

  Should the new type be created with smart constructors?

• tcm_tyvar :: env -> TyVar -> m Type
• tcm_covar :: env -> CoVar -> m Coercion
• tcm_hole :: env -> CoercionHole -> Role -> Type -> Type -> m Coercion

  What to do with coercion holes. See Note [Coercion holes] in TyCoRep.

• tcm_tybinder :: env -> TyVar -> ArgFlag -> m (env, TyVar)

  The returned env is used in the extended scope

mapType :: Monad m => TyCoMapper env m -> env -> Type -> m Type

mapCoercion :: Monad m => TyCoMapper env m -> env -> Coercion -> m Coercion

newTyConInstRhs :: TyCon -> [Type] -> Type

Unwrap one layer of newtype on a type constructor and its arguments, using an eta-reduced version of the newtype if possible. This requires tys to have at least newTyConInstArity tycon elements.

mkFamilyTyConApp :: TyCon -> [Type] -> Type

Given a family instance TyCon and its arg types, return the corresponding family type. E.g:

data family T a
data instance T (Maybe b) = MkT b

Where the instance tycon is :RTL, so:

mkFamilyTyConApp :RTL Int  =  T (Maybe Int)

isDictLikeTy :: Type -> Bool

mkPrimEqPred :: Type -> Type -> Type

Creates a primitive type equality predicate. Invariant: the types are not Coercions

mkReprPrimEqPred :: Type -> Type -> Type

mkPrimEqPredRole :: Role -> Type -> Type -> PredType

Makes a lifted equality predicate at the given role

equalityTyCon :: Role -> TyCon

mkHeteroPrimEqPred :: Kind -> Kind -> Type -> Type -> Type

Creates a primite type equality predicate with explicit kinds

mkHeteroReprPrimEqPred :: Kind -> Kind -> Type -> Type -> Type

Creates a primitive representational type equality predicate with explicit kinds

mkClassPred :: Class -> [Type] -> PredType

isClassPred :: PredType -> Bool

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

Constructors

ClassPred Class [Type]

EqPred EqRel Type Type

IrredPred PredType

data EqRel

A choice of equality relation. This is separate from the type Role because Phantom does not define a (non-trivial) equality relation.

Constructors

NomEq

ReprEq

Instances

Eq EqRel

Methods

(==) :: EqRel -> EqRel -> Bool

(/=) :: EqRel -> EqRel -> Bool

Ord EqRel

Methods

compare :: EqRel -> EqRel -> Ordering

(<) :: EqRel -> EqRel -> Bool

(<=) :: EqRel -> EqRel -> Bool

(>) :: EqRel -> EqRel -> Bool

(>=) :: EqRel -> EqRel -> Bool

max :: EqRel -> EqRel -> EqRel

min :: EqRel -> EqRel -> EqRel

Outputable EqRel

Methods

ppr :: EqRel -> SDoc

pprPrec :: Rational -> EqRel -> SDoc

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

Get the equality relation relevant for a pred type.

Binders

sameVis :: ArgFlag -> ArgFlag -> Bool

Do these denote the same level of visibility? Required arguments are visible, others are not. So this function equates Specified and Inferred. Used for printing.

mkTyVarBinder :: ArgFlag -> Var -> TyVarBinder

Make a named binder

mkTyVarBinders :: ArgFlag -> [TyVar] -> [TyVarBinder]

Make many named binders

mkAnonBinder :: Type -> TyBinder

Make an anonymous binder

isAnonTyBinder :: TyBinder -> Bool

Does this binder bind a variable that is not erased? Returns True for anonymous binders.

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

Extract a relevant type, if there is one.

caseBinder

Arguments

:: TyBinder

binder to scrutinize

-> (TyVarBinder -> a)

named case

-> (Type -> a)

anonymous case

-> a

Like maybe, but for binders.

isVisibleArgFlag :: ArgFlag -> Bool

Does this ArgFlag classify an argument that is written in Haskell?

isInvisibleArgFlag :: ArgFlag -> Bool

Does this ArgFlag classify an argument that is not written in Haskell?

isVisibleBinder :: TyBinder -> Bool

Does this binder bind a visible argument?

isInvisibleBinder :: TyBinder -> Bool

Does this binder bind an invisible argument?

tyConBindersTyBinders :: [TyConBinder] -> [TyBinder]

mkTyBinderTyConBinder :: TyBinder -> SrcSpan -> Unique -> OccName -> TyConBinder

Manufacture a new TyConBinder from a TyBinder. Anonymous TyBinders are still assigned names as TyConBinders, 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

funTyCon :: TyCon

The (->) type constructor.

(->) :: forall (rep1 :: RuntimeRep) (rep2 :: RuntimeRep).
        TYPE rep1 -> TYPE rep2 -> *

Predicates on types

isTyVarTy :: Type -> Bool

isFunTy :: Type -> Bool

isDictTy :: Type -> Bool

isPredTy :: Type -> Bool

Is the type suitable to classify a given/wanted in the typechecker?

isCoercionTy :: Type -> Bool

isCoercionTy_maybe :: Type -> Maybe Coercion

isCoercionType :: Type -> Bool

Does this type classify a core (unlifted) Coercion? At either role nominal or representational (t1 ~ t2)

isForAllTy :: Type -> Bool

Checks whether this is a proper forall (with a named binder)

isPiTy :: Type -> Bool

Is this a function or forall?

isTauTy :: Type -> Bool

isFamFreeTy :: Type -> Bool

isValidJoinPointType :: JoinArity -> Type -> Bool

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

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

See Type for what an unlifted type is. Panics on levity polymorphic types.

isUnboxedTupleType :: Type -> Bool

isUnboxedSumType :: Type -> Bool

isAlgType :: 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

isDataFamilyAppType :: Type -> Bool

Check whether a type is a data family type

isPrimitiveType :: Type -> Bool

Returns true of types that are opaque to Haskell.

isStrictType :: HasDebugCallStack => 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. Panics on levity-polymorphic types.

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. LiftedRep)

dropRuntimeRepArgs :: [Type] -> [Type]

Drops prefix of RuntimeRep constructors in TyConApps. Useful for e.g. dropping 'LiftedRep arguments of unboxed tuple TyCon applications:

dropRuntimeRepArgs [ 'LiftedRep, 'IntRep , String, Int]

getRuntimeRep

Arguments

:: 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

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

type Kind = Type

The key type representing kinds in the compiler.

Finding the kind of a type

typeKind :: Type -> Kind

isTypeLevPoly :: Type -> Bool

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

Looking past all pi-types, 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

liftedTypeKind :: Kind

Type free variables

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.

Eta-expanded because that makes it run faster (apparently) See Note [FV eta expansion] in FV for explanation.

tyCoFVsBndr :: TyVarBinder -> FV -> FV

tyCoVarsOfType :: Type -> TyCoVarSet

Returns free variables of a type, including kind variables as a non-deterministic set. For type synonyms it does not expand the synonym.

tyCoVarsOfTypes :: [Type] -> TyCoVarSet

Returns free variables of types, including kind variables as a non-deterministic set. For type synonyms it does not expand the synonym.

tyCoVarsOfTypeDSet :: Type -> DTyCoVarSet

tyVarsOfType that returns free variables of a type in a deterministic set. For explanation of why using VarSet is not deterministic see Note [Deterministic FV] in FV.

coVarsOfType :: Type -> CoVarSet

coVarsOfTypes :: [Type] -> TyCoVarSet

closeOverKinds :: TyVarSet -> TyVarSet

Add the kind variables free in the kinds of the tyvars in the given set. Returns a non-deterministic set.

closeOverKindsList :: [TyVar] -> [TyVar]

Add the kind variables free in the kinds of the tyvars in the given set. Returns a deterministically ordered list.

noFreeVarsOfType :: Type -> Bool

Returns True if this type has no free variables. Should be the same as isEmptyVarSet . tyCoVarsOfType, but faster in the non-forall case.

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.

Keep this synchronized with synonymTyConsOfType

typeSize :: Type -> Int

Well-scoped lists of variables

dVarSetElemsWellScoped :: DVarSet -> [Var]

Extract a well-scoped list of variables from a deterministic set of variables. The result is deterministic. NB: There used to exist varSetElemsWellScoped :: VarSet -> [Var] which took a non-deterministic set and produced a non-deterministic well-scoped list. If you care about the list being well-scoped you also most likely care about it being in deterministic order.

toposortTyVars :: [TyVar] -> [TyVar]

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 well-scoped list [ k::*, a::k, b::k ]

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 PredTypes, but it does look through type synonyms. This first checks that the kinds of the types are equal and then checks whether the types are equal, ignoring casts and coercions. (The kind check is a recursive call, but since all kinds have type Type, there is no need to check the types of kinds.) See also Note [Non-trivial definitional equality] in TyCoRep.

eqTypeX :: RnEnv2 -> Type -> Type -> Bool

Compare types with respect to a (presumably) non-empty RnEnv2.

eqTypes :: [Type] -> [Type] -> Bool

Type equality on lists of types, looking through type synonyms but not newtypes.

nonDetCmpType :: Type -> Type -> Ordering

nonDetCmpTypes :: [Type] -> [Type] -> Ordering

nonDetCmpTypeX :: RnEnv2 -> Type -> Type -> Ordering

nonDetCmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering

nonDetCmpTc :: TyCon -> TyCon -> Ordering

Compare two TyCons. 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]

eqVarBndrs :: RnEnv2 -> [Var] -> [Var] -> Maybe RnEnv2

Forcing evaluation of types

seqType :: Type -> ()

seqTypes :: [Type] -> ()

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. This function considers Constraint to be a synonym of TYPE LiftedRep.

By being non-recursive and inlined, this case analysis gets efficiently joined onto the case analysis that the caller is already doing

tcView :: Type -> Maybe Type

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

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 TvSubstEnv = TyVarEnv Type

A substitution of Types for TyVars and Kinds for KindVars

data TCvSubst

Type & coercion substitution

The following invariants must hold of a TCvSubst:

1. The in-scope set is needed only to guide the generation of fresh uniques
2. In particular, the kind of the type variables in the in-scope set is not relevant
3. The substitution is only applied ONCE! This is because in general such application will not reach a fixed point.

Constructors

TCvSubst InScopeSet TvSubstEnv CvSubstEnv

Instances

Outputable TCvSubst

Methods

ppr :: TCvSubst -> SDoc

pprPrec :: Rational -> TCvSubst -> SDoc

Manipulating type substitutions

emptyTvSubstEnv :: TvSubstEnv

emptyTCvSubst :: TCvSubst

mkEmptyTCvSubst :: InScopeSet -> TCvSubst

mkTCvSubst :: InScopeSet -> (TvSubstEnv, CvSubstEnv) -> TCvSubst

zipTvSubst :: [TyVar] -> [Type] -> TCvSubst

Generates the in-scope set for the TCvSubst from the types in the incoming environment. No CoVars, please!

mkTvSubstPrs :: [(TyVar, Type)] -> TCvSubst

Generates the in-scope 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 non-deterministic set.

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)

(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 :: HasCallStack => TCvSubst -> Type -> Type

Substitute within a Type The substitution has to satisfy the invariants described in Note [The substitution invariant].

substTys :: HasCallStack => TCvSubst -> [Type] -> [Type]

Substitute within several Types The substitution has to satisfy the invariants described in Note [The substitution invariant].

substTyWith :: HasCallStack => [TyVar] -> [Type] -> Type -> Type

Type substitution, see zipTvSubst

substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type]

Type substitution, see zipTvSubst

substTheta :: HasCallStack => 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 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

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 Types 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.

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.

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

Pretty-printing

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

Print a user-level forall; see Note [When to print foralls]

pprSigmaType :: Type -> SDoc

ppSuggestExplicitKinds :: SDoc

pprTheta :: ThetaType -> SDoc

pprThetaArrowTy :: ThetaType -> SDoc

pprClassPred :: Class -> [Type] -> SDoc

pprKind :: Kind -> SDoc

pprParendKind :: Kind -> SDoc

pprSourceTyCon :: TyCon -> SDoc

Pretty prints a TyCon, using the family instance in case of a representation tycon. For example:

data T [a] = ...

In that case we want to print T [a], where T is the family TyCon

data TyPrec

Constructors

TopPrec

FunPrec

TyOpPrec

TyConPrec

Instances

Eq TyPrec

Methods

(==) :: TyPrec -> TyPrec -> Bool

(/=) :: TyPrec -> TyPrec -> Bool

Ord TyPrec

Methods

compare :: TyPrec -> TyPrec -> Ordering

(<) :: TyPrec -> TyPrec -> Bool

(<=) :: TyPrec -> TyPrec -> Bool

(>) :: TyPrec -> TyPrec -> Bool

(>=) :: TyPrec -> TyPrec -> Bool

max :: TyPrec -> TyPrec -> TyPrec

min :: TyPrec -> TyPrec -> TyPrec

maybeParen :: TyPrec -> TyPrec -> SDoc -> SDoc

pprTyVar :: TyVar -> SDoc

pprTyVars :: [TyVar] -> SDoc

pprPrefixApp :: TyPrec -> SDoc -> [SDoc] -> SDoc

pprArrowChain :: TyPrec -> [SDoc] -> SDoc

Tidying type related things up for printing

tidyType :: TidyEnv -> Type -> Type

tidyTypes :: TidyEnv -> [Type] -> [Type]

tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)

tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])

Grabs the free type variables, tidies them and then uses tidyType to work over the type itself

tidyOpenKind :: TidyEnv -> Kind -> (TidyEnv, Kind)

tidyTyCoVarBndr :: TidyEnv -> TyCoVar -> (TidyEnv, TyCoVar)

tidyTyCoVarBndrs :: TidyEnv -> [TyCoVar] -> (TidyEnv, [TyCoVar])

This tidies up a type for printing in an error message, or in an interface file.

It doesn't change the uniques at all, just the print names.

tidyFreeTyCoVars :: TidyEnv -> [TyCoVar] -> TidyEnv

Add the free TyVars to the env in tidy form, so that we can tidy the type they are free in

tidyOpenTyCoVar :: TidyEnv -> TyCoVar -> (TidyEnv, TyCoVar)

Treat a new TyCoVar as a binder, and give it a fresh tidy name using the environment if one has not already been allocated. See also tidyTyCoVarBndr

tidyOpenTyCoVars :: TidyEnv -> [TyCoVar] -> (TidyEnv, [TyCoVar])

tidyTyVarOcc :: TidyEnv -> TyVar -> TyVar

tidyTopType :: Type -> Type

Calls tidyType on a top-level type (i.e. with an empty tidying environment)

tidyKind :: TidyEnv -> Kind -> Kind

tidyTyVarBinder :: TidyEnv -> TyVarBndr TyVar vis -> (TidyEnv, TyVarBndr TyVar vis)

tidyTyVarBinders :: TidyEnv -> [TyVarBndr TyVar vis] -> (TidyEnv, [TyVarBndr TyVar vis])