ghc-8.0.0.20160204: The GHC API

Safe HaskellNone
LanguageHaskell2010

Type

Contents

Description

Main functions for manipulating types and type-related things

Synopsis

Main data types representing Types

 
 

data TyThing

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

data Type

The key representation of types within the compiler

Instances

Data Type 

Methods

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

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

toConstr :: Type -> Constr Source

dataTypeOf :: Type -> DataType Source

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

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

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

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

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

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

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

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

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

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

Outputable Type 

Methods

ppr :: Type -> SDoc

pprPrec :: Rational -> Type -> SDoc

data VisibilityFlag

Is something required to appear in source Haskell (Visible), permitted by request (Specified) (visible type application), or prohibited entirely from appearing in source Haskell (Invisible)? Examples in Note [VisibilityFlag]

Constructors

Visible 
Specified 
Invisible 

Instances

Eq VisibilityFlag 
Data VisibilityFlag 

Methods

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

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

toConstr :: VisibilityFlag -> Constr Source

dataTypeOf :: VisibilityFlag -> DataType Source

dataCast1 :: Typeable (TYPE Lifted -> TYPE Lifted) t => (forall d. Data d => c (t d)) -> Maybe (c VisibilityFlag) Source

dataCast2 :: Typeable (TYPE Lifted -> TYPE Lifted -> TYPE Lifted) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c VisibilityFlag) Source

gmapT :: (forall b. Data b => b -> b) -> VisibilityFlag -> VisibilityFlag Source

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

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

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

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

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

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

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

Outputable VisibilityFlag 
Binary VisibilityFlag 

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

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 Source

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

toConstr :: Var -> Constr Source

dataTypeOf :: Var -> DataType Source

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

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

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

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

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

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

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

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

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

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

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

NamedThing Var 

Methods

getOccName :: Var -> OccName

getName :: Var -> Name

type PostRn Id ty = ty 
type PostTc Id ty = ty 

type TyVar = Var

type TyCoVar = Id

data TyBinder

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

Instances

Data TyBinder 

Methods

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

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

toConstr :: TyBinder -> Constr Source

dataTypeOf :: TyBinder -> DataType Source

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

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

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

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

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

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

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

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

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

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

Outputable TyBinder 

Constructing and deconstructing types

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

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.

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

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

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

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

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!

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.

mkForAllTys :: [TyBinder] -> 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 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

splitPiTy :: Type -> (TyBinder, Type)

Takes a forall type apart, or panics

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.

mkPiTypes :: [Var] -> Type -> Type

mkPiType for multiple type or value arguments

mkPiTypesPreferFunTy :: [TyVar] -> Type -> Type

Given a list of type-level vars, makes ForAllTys, preferring anonymous binders if the variable is, in fact, not dependent. All binders are visible.

piResultTy :: Type -> Type -> Type

Essentially funResultTy on kinds handling pi-types too

piResultTys :: Type -> [Type] -> Type

Fold piResultTy over many types

applyTys :: Type -> [KindOrType] -> Type

This function is interesting because:

  1. The function may have more for-alls than there are args
  2. Less obviously, it may have fewer for-alls

For case 2. think of:

applyTys (forall a.a) [forall b.b, Int]

This really can happen, but only (I think) in situations involving undefined. For example: undefined :: forall a. a Term: undefined (forall b. b->b) Int This term should have type (Int -> Int), but notice that there are more type args than foralls in undefineds type.

applyTysD :: SDoc -> Type -> [Type] -> Type

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

dropForAlls :: Type -> Type

Drops all non-anonymous ForAllTys

isNumLitTy :: Type -> Maybe Integer

Is this a numeric literal. We also look through type synonyms.

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.

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.

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

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

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 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

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

data TyCoMapper env m

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

Constructors

TyCoMapper 

Fields

mapType :: (Applicative m, Monad m) => TyCoMapper env m -> env -> Type -> m Type

mapCoercion :: (Applicative m, Monad m) => TyCoMapper env m -> env -> Coercion -> m Coercion

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

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

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

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

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

Where the instance tycon is :RTL, so:

mkFamilyTyConApp :RTL Int  =  T (Maybe Int)

mkPrimEqPred :: Type -> Type -> Type

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

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

Makes a lifted equality predicate at the given role

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

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

predTypeEqRel :: PredType -> EqRel

Get the equality relation relevant for a pred type.

Binders

sameVis :: VisibilityFlag -> VisibilityFlag -> Bool

Do these denote the same level of visibility? Except that Specified and Invisible are considered the same. Used for printing.

mkNamedBinder :: Var -> VisibilityFlag -> TyBinder

Make a named binder

mkAnonBinder :: Type -> TyBinder

Make an anonymous binder

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

binderVar

Arguments

:: String

printed if there is a panic

-> TyBinder 
-> Var 

Extract a bound variable in a binder, or panics

binderRelevantType_maybe :: TyBinder -> Maybe Type

Extract a relevant type, if there is one.

caseBinder

Arguments

:: TyBinder

binder to scrutinize

-> (TyVar -> a)

named case

-> (Type -> a)

anonymous case

-> a 

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.

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

isPredTy :: Type -> Bool

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

isCoercionType :: Type -> Bool

Does this type classify a core Coercion?

isForAllTy :: Type -> Bool

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

isPiTy :: Type -> Bool

Is this a function or forall?

isUnLiftedType :: Type -> Bool

See Type for what an unlifted type is

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

isPrimitiveType :: Type -> Bool

Returns true of types that are opaque to Haskell.

isStrictType :: Type -> Bool

Computes whether an argument (or let right hand side) should be computed strictly or lazily, based only on its type. Currently, it's just isUnLiftedType.

isLevityTy :: Type -> Bool

Is this the type Levity?

isLevityVar :: TyVar -> Bool

Is a tyvar of type Levity?

getLevity

Arguments

:: String

Printed in case of an error

-> Type 
-> Type 

Extract the levity classifier of a type. Panics if this is not possible.

getLevityFromKind

Arguments

:: String

Printed in case of an error

-> Type 
-> Type 

Extract the levity classifier of a type from its kind. For example, getLevityFromKind * = Lifted; getLevityFromKind # = Unlifted. Panics if this is not possible.

Main data types representing Kinds

type Kind = Type

The key type representing kinds in the compiler.

Finding the kind of a type

Common Kind

Type free variables

tyCoVarsOfType :: Type -> TyCoVarSet

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

tyCoVarsOfTypes :: [Type] -> TyCoVarSet

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

tyCoVarsOfTypeAcc :: Type -> FV

The worker for tyVarsOfType and tyVarsOfTypeList. The previous implementation used unionVarSet which is O(n+m) and can make the function quadratic. It's exported, so that it can be composed with other functions that compute free variables. See Note [FV naming conventions] in FV.

Eta-expanded because that makes it run faster (apparently)

tyCoVarsOfTypeDSet :: Type -> DTyCoVarSet

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

closeOverKinds :: TyVarSet -> TyVarSet

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

splitDepVarsOfType :: Type -> Pair TyCoVarSet

Retrieve the free variables in this type, splitting them based on whether the variable was used in a dependent context. It's possible for a variable to be reported twice, if it's used both dependently and non-dependently. (This isn't the most precise analysis, because it's used in the typechecking knot. It might list some dependent variables as also non-dependent.)

splitDepVarsOfTypes :: [Type] -> Pair TyCoVarSet

Like splitDepVarsOfType, but over a list of types

splitVisVarsOfType :: Type -> Pair TyCoVarSet

Retrieve the free variables in this type, splitting them based on whether they are used visibly or invisibly. Invisible ones come first.

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.

Well-scoped lists of variables

varSetElemsWellScoped :: VarSet -> [Var]

Extract a well-scoped list of variables from a set of variables.

toposortTyVars :: [TyVar] -> [TyVar]

Do a topological sort on a list of tyvars. This is a deterministic sorting operation (that is, doesn't depend on Uniques).

tyCoVarsOfTypeWellScoped :: Type -> [TyVar]

Get the free vars of a type in scoped order

Type comparison

eqType :: Type -> Type -> Bool

Type equality on source types. Does not look through newtypes or 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.

cmpTypes :: [Type] -> [Type] -> Ordering

cmpTc :: 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.

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.

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

coreViewOneStarKind :: Type -> Maybe Type

Like coreView, but it also "expands" Constraint to become TYPE Lifted.

repType :: Type -> RepType

Looks through:

  1. For-alls
  2. Synonyms
  3. Predicates
  4. All newtypes, including recursive ones, but not newtype families
  5. Casts

It's useful in the back end of the compiler.

tyConsOfType :: Type -> NameEnv TyCon

All type constructors occurring in the type; looking through type synonyms, but not newtypes. When it finds a Class, it returns the class TyCon.

Type representation for the code generator

typePrimRep :: UnaryType -> PrimRep

Discovers the primitive representation of a more abstract UnaryType

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.

Instances

Manipulating type substitutions

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!

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.

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 :: TCvSubst -> [Type] -> [Type]

Substitute within several Types

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

Type substitution, see zipTvSubst

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

Type substitution, see zipTvSubst

substTheta :: TCvSubst -> ThetaType -> ThetaType

Substitute within a ThetaType

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.

substTelescope :: [TyCoVar] -> [Type] -> ([Type], TCvSubst)

Create a substitution from tyvars to types, but later types may depend on earlier ones. Return the substed types and the built substitution.

Pretty-printing

pprForAll :: [TyBinder] -> SDoc

Render the "forall ... ." or "forall ... ->" bit of a type. Do not pass in anonymous binders!

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

Instances

pprTyVar :: TyVar -> SDoc

Print a tyvar with its kind

pprTcAppTy :: TyPrec -> (TyPrec -> Type -> SDoc) -> TyCon -> [Type] -> SDoc

Tidying type related things up for printing

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

tidyOpenType :: 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 -> TyCoVarSet -> 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

tidyTopType :: Type -> Type

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