Type

ghc-7.10.3: The GHC API

Safe Haskell | None
Language | Haskell2010

Type

Contents

- Main data types representing Types
  - Constructing and deconstructing types
  - Common type constructors
  - Predicates on types
- Main data types representing Kinds
  - Finding the kind of a type
  - Common Kinds and SuperKinds
  - Common Kind type constructors
- Type free variables
- Type comparison
- Forcing evaluation of types
- Other views onto Types
- Type representation for the code generator
- Main type substitution data types
  - Manipulating type substitutions
  - Performing substitution on types and kinds
- Pretty-printing
- Tidying type related things up for printing

Description

Main functions for manipulating types and type-related things

Synopsis

- data TyThing
  - = AnId Id
  - | AConLike ConLike
  - | ATyCon TyCon
  - | ACoAxiom (CoAxiom Branched)
- data Type
- type KindOrType = Type
- type PredType = Type
- type ThetaType = [PredType]
- data Var
- type TyVar = Var
- isTyVar :: Var -> Bool
- mkTyVarTy :: TyVar -> Type
- mkTyVarTys :: [TyVar] -> [Type]
- getTyVar :: String -> Type -> TyVar
- getTyVar_maybe :: Type -> Maybe TyVar
- mkAppTy :: Type -> Type -> Type
- mkAppTys :: Type -> [Type] -> Type
- splitAppTy :: Type -> (Type, Type)
- splitAppTys :: Type -> (Type, [Type])
- splitAppTy_maybe :: Type -> Maybe (Type, Type)
- repSplitAppTy_maybe :: Type -> Maybe (Type, Type)
- mkFunTy :: Type -> Type -> Type
- mkFunTys :: [Type] -> Type -> Type
- splitFunTy :: Type -> (Type, Type)
- splitFunTy_maybe :: Type -> Maybe (Type, Type)
- splitFunTys :: Type -> ([Type], Type)
- splitFunTysN :: Int -> Type -> ([Type], Type)
- funResultTy :: Type -> Type
- funArgTy :: Type -> Type
- zipFunTys :: Outputable a => [a] -> Type -> ([(a, Type)], Type)
- mkTyConApp :: TyCon -> [Type] -> Type
- mkTyConTy :: TyCon -> Type
- tyConAppTyCon_maybe :: Type -> Maybe TyCon
- tyConAppArgs_maybe :: Type -> Maybe [Type]
- tyConAppTyCon :: Type -> TyCon
- tyConAppArgs :: Type -> [Type]
- splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
- splitTyConApp :: Type -> (TyCon, [Type])
- tyConAppArgN :: Int -> Type -> Type
- nextRole :: Type -> Role
- mkForAllTy :: TyVar -> Type -> Type
- mkForAllTys :: [TyVar] -> Type -> Type
- splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
- splitForAllTys :: Type -> ([TyVar], Type)
- mkPiKinds :: [TyVar] -> Kind -> Kind
- mkPiType :: Var -> Type -> Type
- mkPiTypes :: [Var] -> Type -> Type
- applyTy :: Type -> KindOrType -> Type
- applyTys :: Type -> [KindOrType] -> Type
- applyTysD :: SDoc -> 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
- coAxNthLHS :: CoAxiom br -> Int -> Type
- newTyConInstRhs :: TyCon -> [Type] -> Type
- mkFamilyTyConApp :: TyCon -> [Type] -> Type
- isDictLikeTy :: Type -> Bool
- mkEqPred :: Type -> Type -> PredType
- mkCoerciblePred :: Type -> Type -> PredType
- mkPrimEqPred :: Type -> Type -> Type
- mkReprPrimEqPred :: Type -> Type -> Type
- mkClassPred :: Class -> [Type] -> PredType
- isClassPred :: PredType -> Bool
- isEqPred :: PredType -> Bool
- isIPPred :: PredType -> Bool
- isIPPred_maybe :: Type -> Maybe (FastString, Type)
- isIPTyCon :: TyCon -> Bool
- isIPClass :: Class -> Bool
- data PredTree
  - = ClassPred Class [Type]
  - | EqPred EqRel Type Type
  - | TuplePred [PredType]
  - | IrredPred PredType
- data EqRel
  - = NomEq
  - | ReprEq
- 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
- funTyCon :: TyCon
- isTypeVar :: Var -> Bool
- isKindVar :: Var -> Bool
- allDistinctTyVars :: [KindOrType] -> Bool
- isForAllTy :: Type -> Bool
- isTyVarTy :: Type -> Bool
- isFunTy :: Type -> Bool
- isDictTy :: Type -> Bool
- isPredTy :: Type -> Bool
- isVoidTy :: Type -> Bool
- isUnLiftedType :: Type -> Bool
- isUnboxedTupleType :: Type -> Bool
- isAlgType :: Type -> Bool
- isClosedAlgType :: Type -> Bool
- isPrimitiveType :: Type -> Bool
- isStrictType :: Type -> Bool
- type Kind = Type
- type SimpleKind = Kind
- type MetaKindVar = TyVar
- typeKind :: Type -> Kind
- anyKind :: Kind
- liftedTypeKind :: Kind
- unliftedTypeKind :: Kind
- openTypeKind :: Kind
- constraintKind :: Kind
- superKind :: Kind
- liftedTypeKindTyCon :: TyCon
- openTypeKindTyCon :: TyCon
- unliftedTypeKindTyCon :: TyCon
- constraintKindTyCon :: TyCon
- anyKindTyCon :: TyCon
- tyVarsOfType :: Type -> VarSet
- tyVarsOfTypes :: [Type] -> TyVarSet
- closeOverKinds :: TyVarSet -> TyVarSet
- expandTypeSynonyms :: Type -> Type
- typeSize :: Type -> Int
- varSetElemsKvsFirst :: VarSet -> [TyVar]
- eqType :: Type -> Type -> Bool
- eqTypeX :: RnEnv2 -> Type -> Type -> Bool
- eqTypes :: [Type] -> [Type] -> Bool
- cmpType :: Type -> Type -> Ordering
- cmpTypes :: [Type] -> [Type] -> Ordering
- eqPred :: PredType -> PredType -> Bool
- eqPredX :: RnEnv2 -> PredType -> PredType -> Bool
- cmpPred :: PredType -> PredType -> Ordering
- eqKind :: Kind -> Kind -> Bool
- eqTyVarBndrs :: RnEnv2 -> [TyVar] -> [TyVar] -> Maybe RnEnv2
- seqType :: Type -> ()
- seqTypes :: [Type] -> ()
- coreView :: Type -> Maybe Type
- tcView :: Type -> Maybe Type
- type UnaryType = Type
- data RepType
  - = UbxTupleRep [UnaryType]
  - | UnaryRep UnaryType
- flattenRepType :: RepType -> [UnaryType]
- repType :: Type -> RepType
- tyConsOfType :: Type -> NameEnv TyCon
- typePrimRep :: UnaryType -> PrimRep
- typeRepArity :: Arity -> Type -> RepArity
- type TvSubstEnv = TyVarEnv Type
- data TvSubst = TvSubst InScopeSet TvSubstEnv
- emptyTvSubstEnv :: TvSubstEnv
- emptyTvSubst :: TvSubst
- mkTvSubst :: InScopeSet -> TvSubstEnv -> TvSubst
- mkOpenTvSubst :: TvSubstEnv -> TvSubst
- zipOpenTvSubst :: [TyVar] -> [Type] -> TvSubst
- zipTopTvSubst :: [TyVar] -> [Type] -> TvSubst
- mkTopTvSubst :: [(TyVar, Type)] -> TvSubst
- notElemTvSubst :: CoVar -> TvSubst -> Bool
- getTvSubstEnv :: TvSubst -> TvSubstEnv
- setTvSubstEnv :: TvSubst -> TvSubstEnv -> TvSubst
- zapTvSubstEnv :: TvSubst -> TvSubst
- getTvInScope :: TvSubst -> InScopeSet
- extendTvInScope :: TvSubst -> Var -> TvSubst
- extendTvInScopeList :: TvSubst -> [Var] -> TvSubst
- extendTvSubst :: TvSubst -> TyVar -> Type -> TvSubst
- extendTvSubstList :: TvSubst -> [TyVar] -> [Type] -> TvSubst
- isInScope :: Var -> TvSubst -> Bool
- composeTvSubst :: InScopeSet -> TvSubstEnv -> TvSubstEnv -> TvSubstEnv
- zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
- isEmptyTvSubst :: TvSubst -> Bool
- unionTvSubst :: TvSubst -> TvSubst -> TvSubst
- substTy :: TvSubst -> Type -> Type
- substTys :: TvSubst -> [Type] -> [Type]
- substTyWith :: [TyVar] -> [Type] -> Type -> Type
- substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type]
- substTheta :: TvSubst -> ThetaType -> ThetaType
- substTyVar :: TvSubst -> TyVar -> Type
- substTyVars :: TvSubst -> [TyVar] -> [Type]
- substTyVarBndr :: TvSubst -> TyVar -> (TvSubst, TyVar)
- cloneTyVarBndr :: TvSubst -> TyVar -> Unique -> (TvSubst, TyVar)
- deShadowTy :: TyVarSet -> Type -> Type
- lookupTyVar :: TvSubst -> TyVar -> Maybe Type
- substKiWith :: [KindVar] -> [Kind] -> Kind -> Kind
- substKisWith :: [KindVar] -> [Kind] -> [Kind] -> [Kind]
- pprType :: Type -> SDoc
- pprParendType :: Type -> SDoc
- pprTypeApp :: TyCon -> [Type] -> SDoc
- pprTyThingCategory :: TyThing -> SDoc
- pprTyThing :: TyThing -> SDoc
- pprTvBndr :: TyVar -> SDoc
- pprTvBndrs :: [TyVar] -> SDoc
- pprForAll :: [TyVar] -> SDoc
- pprUserForAll :: [TyVar] -> SDoc
- pprSigmaType :: Type -> SDoc
- pprTheta :: ThetaType -> SDoc
- pprThetaArrowTy :: ThetaType -> SDoc
- pprClassPred :: Class -> [Type] -> SDoc
- pprKind :: Kind -> SDoc
- pprParendKind :: Kind -> SDoc
- pprSourceTyCon :: TyCon -> SDoc
- data TyPrec
  - = TopPrec
  - | FunPrec
  - | TyOpPrec
  - | TyConPrec
- maybeParen :: TyPrec -> TyPrec -> SDoc -> SDoc
- pprSigmaTypeExtraCts :: Bool -> Type -> SDoc
- tidyType :: TidyEnv -> Type -> Type
- tidyTypes :: TidyEnv -> [Type] -> [Type]
- tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
- tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
- tidyOpenKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
- tidyTyVarBndr :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
- tidyTyVarBndrs :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
- tidyFreeTyVars :: TidyEnv -> TyVarSet -> TidyEnv
- tidyOpenTyVar :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
- tidyOpenTyVars :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
- tidyTyVarOcc :: TidyEnv -> TyVar -> TyVar
- tidyTopType :: Type -> Type
- tidyKind :: TidyEnv -> Kind -> Kind

# 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  )   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 typecheckable-thing, essentially anything that has a name

Constructors

AnId Id |
AConLike ConLike |
ATyCon TyCon |
ACoAxiom (CoAxiom Branched) |

Instances

Eq TyThing |
Ord TyThing |
Outputable TyThing |
NamedThing TyThing |

data Type

The key representation of types within the compiler

Instances

Data Type |
Outputable Type |

type KindOrType = Type

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 `PredType`s

data Var

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

Instances

Eq Var |
Data Var |
Ord Var |
Outputable Var |
Uniquable Var |
NamedThing Var |
type PostRn Id ty = ty |
type PostTc Id ty = ty |

type TyVar = Var

isTyVar :: Var -> Bool

## 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`

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

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

Creates a function type from the given argument and result type

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

splitFunTy :: Type -> (Type, Type)

Attempts to extract the argument and result types from a type, and panics if that is not possible. See also `splitFunTy_maybe`

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

Attempts to extract the argument and result types from a type

splitFunTys :: Type -> ([Type], Type)

splitFunTysN :: Int -> Type -> ([Type], Type)

Split off exactly the given number argument types, and panics if that is not possible

funResultTy :: Type -> Type

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

funArgTy :: Type -> Type

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

zipFunTys :: Outputable a => [a] -> Type -> ([(a, Type)], Type)

Splits off argument types from the given type and associating them with the things in the input list from left to right. The final result type is returned, along with the resulting pairs of objects and types, albeit with the list of pairs in reverse order. Panics if there are not enough argument types for the input list.

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`

tyConAppArgs_maybe :: Type -> Maybe [Type]

The same as `snd . splitTyConApp`

tyConAppTyCon :: Type -> TyCon

tyConAppArgs :: Type -> [Type]

splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])

Attempts to tease a type apart into a type constructor and the application of a number of arguments to that constructor

splitTyConApp :: Type -> (TyCon, [Type])

Attempts to tease a type apart into a type constructor and the application of a number of arguments to that constructor. Panics if that is not possible. See also `splitTyConApp_maybe`

tyConAppArgN :: Int -> Type -> Type

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!

mkForAllTy :: TyVar -> Type -> Type

mkForAllTys :: [TyVar] -> Type -> Type

Wraps foralls over the type using the provided `TyVar`s from left to right

splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)

Attempts to take a forall type apart, returning the bound type variable and the remainder of the type

splitForAllTys :: Type -> ([TyVar], Type)

Attempts to take a forall type apart, returning all the immediate such bound type variables and the remainder of the type. Always suceeds, even if that means returning an empty list of `TyVar`s

mkPiKinds :: [TyVar] -> Kind -> Kind

mkPiType :: Var -> Type -> Type

Makes a `(->)` type or a forall type, depending on whether it is given a type variable or a term variable.

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

`mkPiType` for multiple type or value arguments

applyTy :: Type -> KindOrType -> Type

Instantiate a forall type with one or more type arguments. Used when we have a polymorphic function applied to type args:

    f t1 t2

We use `applyTys type-of-f [t1,t2]` to compute the type of the expression. Panics if no application is possible.

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 `undefined`s type.

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

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

dropForAlls :: Type -> Type

Equivalent to `snd . splitForAllTys`

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.

coAxNthLHS :: CoAxiom br -> Int -> Type

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

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

mkEqPred :: Type -> Type -> PredType

Creates a type equality predicate

mkCoerciblePred :: Type -> Type -> PredType

mkPrimEqPred :: Type -> Type -> Type

mkReprPrimEqPred :: Type -> Type -> Type

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

isClassPred :: PredType -> Bool

isEqPred :: PredType -> Bool

isIPPred :: PredType -> Bool

isIPPred_maybe :: Type -> Maybe (FastString, Type)

isIPTyCon :: TyCon -> Bool

isIPClass :: Class -> Bool

data PredTree

Constructors

ClassPred Class [Type] |
EqPred EqRel Type Type |
TuplePred [PredType] |
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 |
Ord EqRel |
Outputable 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

Get the equality relation relevant for a pred type.

## Common type constructors

funTyCon :: TyCon

## Predicates on types

isTypeVar :: Var -> Bool

isKindVar :: Var -> Bool

allDistinctTyVars :: [KindOrType] -> Bool

isForAllTy :: Type -> Bool

isTyVarTy :: Type -> Bool

isFunTy :: Type -> Bool

isDictTy :: Type -> Bool

isPredTy :: Type -> Bool

isVoidTy :: Type -> Bool

isUnLiftedType :: Type -> Bool

See Type for what an unlifted type is

isUnboxedTupleType :: 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

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`.

# Main data types representing Kinds

type Kind = Type

The key type representing kinds in the compiler. Invariant: a kind is always in one of these forms:

    FunTy k1 k2
    TyConApp PrimTyCon [...]
    TyVar kv   -- (during inference only)
    ForAll ... -- (for top-level coercions)

type SimpleKind = Kind

type MetaKindVar = TyVar

## Finding the kind of a type

typeKind :: Type -> Kind

## Common Kinds and SuperKinds

anyKind :: Kind

See Type for details of the distinction between these `Kind`s

liftedTypeKind :: Kind

See Type for details of the distinction between these `Kind`s

unliftedTypeKind :: Kind

See Type for details of the distinction between these `Kind`s

openTypeKind :: Kind

See Type for details of the distinction between these `Kind`s

constraintKind :: Kind

See Type for details of the distinction between these `Kind`s

superKind :: Kind

See Type for details of the distinction between these `Kind`s

## Common Kind type constructors

liftedTypeKindTyCon :: TyCon

See Type for details of the distinction between the `Kind` `TyCon`s

openTypeKindTyCon :: TyCon

See Type for details of the distinction between the `Kind` `TyCon`s

unliftedTypeKindTyCon :: TyCon

See Type for details of the distinction between the `Kind` `TyCon`s

constraintKindTyCon :: TyCon

See Type for details of the distinction between the `Kind` `TyCon`s

anyKindTyCon :: TyCon

See Type for details of the distinction between the `Kind` `TyCon`s

# Type free variables

tyVarsOfType :: Type -> VarSet

NB: for type synonyms tyVarsOfType does not expand the synonym tyVarsOfType returns only the free variables of a type For example, tyVarsOfType (a::k) returns {a}, not including the kind variable {k}

tyVarsOfTypes :: [Type] -> TyVarSet

closeOverKinds :: TyVarSet -> TyVarSet

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.

typeSize :: Type -> Int

varSetElemsKvsFirst :: VarSet -> [TyVar]

# Type comparison

eqType :: Type -> Type -> Bool

Type equality on source types. Does not look through `newtypes` or `PredType`s, but it does look through type synonyms. Watch out for horrible hack: See Note [Comparison with OpenTypeKind]

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

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

cmpType :: Type -> Type -> Ordering

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

eqPred :: PredType -> PredType -> Bool

eqPredX :: RnEnv2 -> PredType -> PredType -> Bool

cmpPred :: PredType -> PredType -> Ordering

eqKind :: Kind -> Kind -> Bool

eqTyVarBndrs :: RnEnv2 -> [TyVar] -> [TyVar] -> Maybe RnEnv2

# Forcing evaluation of types

seqType :: Type -> ()

seqTypes :: [Type] -> ()

# Other views onto Types

coreView :: Type -> Maybe Type

In Core, we "look through" non-recursive newtypes and `PredTypes`: this function tries to obtain a different view of the supplied type given this

Strips off the top layer only of a type to give 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

tcView :: Type -> Maybe Type

Similar to `coreView`, but for the type checker, which just looks through synonyms

type UnaryType = Type

data RepType

Constructors

UbxTupleRep [UnaryType] |
UnaryRep UnaryType |

flattenRepType :: RepType -> [UnaryType]

repType :: Type -> RepType

Looks through:

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

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`

typeRepArity :: Arity -> Type -> RepArity

# Main type substitution data types

type TvSubstEnv = TyVarEnv Type

A substitution of `Type`s for `TyVar`s and `Kind`s for `KindVar`s

data TvSubst

Type substitution

The following invariants must hold of a `TvSubst`:

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 reached a fixed point.

Constructors

TvSubst InScopeSet TvSubstEnv |

## Manipulating type substitutions

emptyTvSubstEnv :: TvSubstEnv

emptyTvSubst :: TvSubst

mkTvSubst :: InScopeSet -> TvSubstEnv -> TvSubst

mkOpenTvSubst :: TvSubstEnv -> TvSubst

Generates the in-scope set for the `TvSubst` from the types in the incoming environment, hence "open"

zipOpenTvSubst :: [TyVar] -> [Type] -> TvSubst

Generates the in-scope set for the `TvSubst` from the types in the incoming environment, hence "open"

zipTopTvSubst :: [TyVar] -> [Type] -> TvSubst

mkTopTvSubst :: [(TyVar, Type)] -> TvSubst

Called when doing top-level substitutions. Here we expect that the free vars of the range of the substitution will be empty.

notElemTvSubst :: CoVar -> TvSubst -> Bool

getTvSubstEnv :: TvSubst -> TvSubstEnv

setTvSubstEnv :: TvSubst -> TvSubstEnv -> TvSubst

zapTvSubstEnv :: TvSubst -> TvSubst

getTvInScope :: TvSubst -> InScopeSet

extendTvInScope :: TvSubst -> Var -> TvSubst

extendTvInScopeList :: TvSubst -> [Var] -> TvSubst

extendTvSubst :: TvSubst -> TyVar -> Type -> TvSubst

extendTvSubstList :: TvSubst -> [TyVar] -> [Type] -> TvSubst

isInScope :: Var -> TvSubst -> Bool

composeTvSubst :: InScopeSet -> TvSubstEnv -> TvSubstEnv -> TvSubstEnv

`(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`

zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv

isEmptyTvSubst :: TvSubst -> Bool

unionTvSubst :: TvSubst -> TvSubst -> TvSubst

## Performing substitution on types and kinds

substTy :: TvSubst -> Type -> Type

Substitute within a `Type`

substTys :: TvSubst -> [Type] -> [Type]

Substitute within several `Type`s

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

Type substitution making use of an `TvSubst` that is assumed to be open, see `zipOpenTvSubst`

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

Type substitution making use of an `TvSubst` that is assumed to be open, see `zipOpenTvSubst`

substTheta :: TvSubst -> ThetaType -> ThetaType

Substitute within a `ThetaType`

substTyVar :: TvSubst -> TyVar -> Type

substTyVars :: TvSubst -> [TyVar] -> [Type]

substTyVarBndr :: TvSubst -> TyVar -> (TvSubst, TyVar)

cloneTyVarBndr :: TvSubst -> TyVar -> Unique -> (TvSubst, TyVar)

deShadowTy :: TyVarSet -> Type -> Type

Remove any nested binders mentioning the `TyVar`s in the `TyVarSet`

lookupTyVar :: TvSubst -> TyVar -> Maybe Type

substKiWith :: [KindVar] -> [Kind] -> Kind -> Kind

substKisWith :: [KindVar] -> [Kind] -> [Kind] -> [Kind]

# Pretty-printing

pprType :: Type -> SDoc

pprParendType :: Type -> SDoc

pprTypeApp :: TyCon -> [Type] -> SDoc

pprTyThingCategory :: TyThing -> SDoc

pprTyThing :: TyThing -> SDoc

pprTvBndr :: TyVar -> SDoc

pprTvBndrs :: [TyVar] -> SDoc

pprForAll :: [TyVar] -> SDoc

pprUserForAll :: [TyVar] -> SDoc

pprSigmaType :: Type -> 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 |
Ord TyPrec |

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

pprSigmaTypeExtraCts :: Bool -> Type -> SDoc

# Tidying type related things up for printing

tidyType :: TidyEnv -> Type -> Type

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

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

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

tidyTyVarBndr :: TidyEnv -> TyVar -> (TidyEnv, TyVar)

tidyTyVarBndrs :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])

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.

tidyFreeTyVars :: TidyEnv -> TyVarSet -> TidyEnv

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

tidyOpenTyVar :: TidyEnv -> TyVar -> (TidyEnv, TyVar)

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

tidyOpenTyVars :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])

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