| ghc-6.10.4: The GHC API | Contents | Index

Type

Contents

Main data types representing Types
  Constructing and deconstructing types
  Common type constructors
  Predicates on types
Main data types representing Kinds
  Deconstructing Kinds
  Common Kinds and SuperKinds
  Common Kind type constructors
  Predicates on Kinds
Type free variables
Tidying type related things up for printing
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
Pretty-printing

Description
Main functions for manipulating types and type-related things
Synopsis

data TyThing

= AnId Id
| ADataCon DataCon
| ATyCon TyCon
| AClass Class

data Type

data PredType

= ClassP Class [Type]
| IParam (IPName Name) Type
| EqPred Type Type

type ThetaType = [PredType]
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 :: Type -> TyCon
tyConAppArgs :: Type -> [Type]
splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
splitTyConApp :: Type -> (TyCon, [Type])
mkForAllTy :: TyVar -> Type -> Type
mkForAllTys :: [TyVar] -> Type -> Type
splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
splitForAllTys :: Type -> ([TyVar], Type)
applyTy :: Type -> Type -> Type
applyTys :: Type -> [Type] -> Type
applyTysD :: SDoc -> Type -> [Type] -> Type
isForAllTy :: Type -> Bool
dropForAlls :: Type -> Type
newTyConInstRhs :: TyCon -> [Type] -> Type
carefullySplitNewType_maybe :: [TyCon] -> TyCon -> [Type] -> Maybe ([TyCon], Type)
tyFamInsts :: Type -> [(TyCon, [Type])]
predFamInsts :: PredType -> [(TyCon, [Type])]
mkPredTy :: PredType -> Type
mkPredTys :: ThetaType -> [Type]
mkFamilyTyConApp :: TyCon -> [Type] -> Type
funTyCon :: TyCon
isTyVarTy :: Type -> Bool
isFunTy :: Type -> Bool
isUnLiftedType :: Type -> Bool
isUnboxedTupleType :: Type -> Bool
isAlgType :: Type -> Bool
isClosedAlgType :: Type -> Bool
isPrimitiveType :: Type -> Bool
isStrictType :: Type -> Bool
isStrictPred :: PredType -> Bool
type Kind = Type
type SimpleKind = Kind
type KindVar = TyVar
kindFunResult :: Kind -> Kind
splitKindFunTys :: Kind -> ([Kind], Kind)
splitKindFunTysN :: Int -> Kind -> ([Kind], Kind)
liftedTypeKind :: Kind
unliftedTypeKind :: Kind
openTypeKind :: Kind
argTypeKind :: Kind
ubxTupleKind :: Kind
tySuperKind :: SuperKind
coSuperKind :: SuperKind
liftedTypeKindTyCon :: TyCon
openTypeKindTyCon :: TyCon
unliftedTypeKindTyCon :: TyCon
argTypeKindTyCon :: TyCon
ubxTupleKindTyCon :: TyCon
isLiftedTypeKind :: Kind -> Bool
isUnliftedTypeKind :: Kind -> Bool
isOpenTypeKind :: Kind -> Bool
isUbxTupleKind :: Kind -> Bool
isArgTypeKind :: Kind -> Bool
isKind :: Kind -> Bool
isTySuperKind :: SuperKind -> Bool
isCoSuperKind :: SuperKind -> Bool
isSuperKind :: Type -> Bool
isCoercionKind :: Kind -> Bool
isEqPred :: PredType -> Bool
mkArrowKind :: Kind -> Kind -> Kind
mkArrowKinds :: [Kind] -> Kind -> Kind
isSubArgTypeKind :: Kind -> Bool
isSubOpenTypeKind :: Kind -> Bool
isSubKind :: Kind -> Kind -> Bool
defaultKind :: Kind -> Kind
eqKind :: Kind -> Kind -> Bool
isSubKindCon :: TyCon -> TyCon -> Bool
tyVarsOfType :: Type -> TyVarSet
tyVarsOfTypes :: [Type] -> TyVarSet
tyVarsOfPred :: PredType -> TyVarSet
tyVarsOfTheta :: ThetaType -> TyVarSet
typeKind :: Type -> Kind
tidyType :: TidyEnv -> Type -> Type
tidyTypes :: TidyEnv -> [Type] -> [Type]
tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
tidyTyVarBndr :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
tidyFreeTyVars :: TidyEnv -> TyVarSet -> TidyEnv
tidyOpenTyVar :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
tidyOpenTyVars :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
tidyTopType :: Type -> Type
tidyPred :: TidyEnv -> PredType -> PredType
tidyKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
coreEqType :: Type -> Type -> Bool
tcEqType :: Type -> Type -> Bool
tcEqTypes :: [Type] -> [Type] -> Bool
tcCmpType :: Type -> Type -> Ordering
tcCmpTypes :: [Type] -> [Type] -> Ordering
tcEqPred :: PredType -> PredType -> Bool
tcEqPredX :: RnEnv2 -> PredType -> PredType -> Bool
tcCmpPred :: PredType -> PredType -> Ordering
tcEqTypeX :: RnEnv2 -> Type -> Type -> Bool
tcPartOfType :: Type -> Type -> Bool
tcPartOfPred :: Type -> PredType -> Bool
seqType :: Type -> ()
seqTypes :: [Type] -> ()
coreView :: Type -> Maybe Type
tcView :: Type -> Maybe Type
kindView :: Kind -> Maybe Kind
repType :: Type -> Type

data PrimRep

= VoidRep
| PtrRep
| IntRep
| WordRep
| Int64Rep
| Word64Rep
| AddrRep
| FloatRep
| DoubleRep

typePrimRep :: Type -> PrimRep
predTypeRep :: PredType -> Type
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 :: TyVar -> TvSubst -> Bool
getTvSubstEnv :: TvSubst -> TvSubstEnv
setTvSubstEnv :: TvSubst -> TvSubstEnv -> TvSubst
getTvInScope :: TvSubst -> InScopeSet
extendTvInScope :: 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
substTy :: TvSubst -> Type -> Type
substTys :: TvSubst -> [Type] -> [Type]
substTyWith :: [TyVar] -> [Type] -> Type -> Type
substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type]
substTheta :: TvSubst -> ThetaType -> ThetaType
substPred :: TvSubst -> PredType -> PredType
substTyVar :: TvSubst -> TyVar -> Type
substTyVars :: TvSubst -> [TyVar] -> [Type]
substTyVarBndr :: TvSubst -> TyVar -> (TvSubst, TyVar)
deShadowTy :: TyVarSet -> Type -> Type
lookupTyVar :: TvSubst -> TyVar -> Maybe Type
pprType :: Type -> SDoc
pprParendType :: Type -> SDoc
pprTypeApp :: NamedThing a => a -> [Type] -> SDoc
pprTyThingCategory :: TyThing -> SDoc
pprTyThing :: TyThing -> SDoc
pprForAll :: [TyVar] -> SDoc
pprPred :: PredType -> SDoc
pprTheta :: ThetaType -> SDoc
pprThetaArrow :: ThetaType -> SDoc
pprClassPred :: Class -> [Type] -> SDoc
pprKind :: Kind -> SDoc
pprParendKind :: Kind -> SDoc
pprSourceTyCon :: TyCon -> SDoc

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. Notably, `PredTy`s are removed from the representation type while they do exist in the source types.

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 |
ADataCon DataCon |
ATyCon TyCon |
AClass Class |

Instances

Outputable TyThing
NamedThing TyThing

data Type

The key representation of types within the compiler
Instances

Outputable Type

data PredType

A type of the form `PredTy p` represents a value whose type is the Haskell predicate `p`, where a predicate is what occurs before the `=>` in a Haskell type. 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"

Constructors

ClassP Class [Type] | Class predicate e.g. `Eq a`
IParam (IPName Name) Type | Implicit parameter e.g. `?x :: Int`
EqPred Type Type | Equality predicate e.g `ty1 ~ ty2`

Instances

Eq PredType
Ord PredType
Outputable PredType

type ThetaType = [PredType]
A collection of `PredType`s
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
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 apppropriate 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 :: Type -> TyCon
The same as `fst . splitTyConApp`
tyConAppArgs :: Type -> [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`
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
applyTy :: Type -> Type -> 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 -> [Type] -> 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, via dressing up polymorphic types with newtype clothing. Here's an example:

     newtype R = R (forall a. a->a)
     foo = case undefined :: R of
                R f -> f ()

applyTysD :: SDoc -> Type -> [Type] -> Type
isForAllTy :: Type -> Bool
dropForAlls :: Type -> Type
Equivalent to `snd . splitForAllTys`
newTyConInstRhs :: TyCon -> [Type] -> Type
Unwrap one layer of newtype on a type constructor and it's arguments, using an eta-reduced version of the `newtype` if possible
carefullySplitNewType_maybe :: [TyCon] -> TyCon -> [Type] -> Maybe ([TyCon], Type)
tyFamInsts :: Type -> [(TyCon, [Type])]
Finds type family instances occuring in a type after expanding synonyms.
predFamInsts :: PredType -> [(TyCon, [Type])]
Finds type family instances occuring in a predicate type after expanding synonyms.
mkPredTy :: PredType -> Type
mkPredTys :: ThetaType -> [Type]
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)

Common type constructors
funTyCon :: TyCon
Predicates on types
isTyVarTy :: Type -> Bool
isFunTy :: 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. Most of these are unlifted, but now that we interact with .NET, we may have primtive (foreign-imported) types that are lifted
isStrictType :: Type -> Bool
Computes whether an argument (or let right hand side) should be computed strictly or lazily, based only on its type. Works just like `isUnLiftedType`, except that it has a special case for dictionaries (i.e. does not work purely on representation types)
isStrictPred :: PredType -> Bool
We may be strict in dictionary types, but only if it has more than one component. (Being strict in a single-component dictionary risks poking the dictionary component, which is wrong.)
Main data types representing Kinds

There's a little subtyping at the kind level:

                   ?
                  / \
                 /   \
                ??   (#)
               /  \
              *    #
     .
     Where:        *    [LiftedTypeKind]   means boxed type
                  #    [UnliftedTypeKind] means unboxed type
                  (#)  [UbxTupleKind]     means unboxed tuple
                  ??   [ArgTypeKind]      is the lub of {*, #}
                  ?    [OpenTypeKind]	means any type at all

In particular:

     error :: forall a:?. String -> a
     (->)  :: ?? -> ? -> \*
     (\\(x::t) -> ...)

Where in the last example `t :: ??` (i.e. is not an unboxed tuple)

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 KindVar = TyVar
Deconstructing Kinds
kindFunResult :: Kind -> Kind
Essentially `funResultTy` on kinds
splitKindFunTys :: Kind -> ([Kind], Kind)
Essentially `splitFunTys` on kinds
splitKindFunTysN :: Int -> Kind -> ([Kind], Kind)
Essentially `splitFunTysN` on kinds
Common Kinds and SuperKinds
liftedTypeKind :: Kind
unliftedTypeKind :: Kind
See Type for details of the distinction between these `Kind`s
openTypeKind :: Kind
argTypeKind :: Kind
ubxTupleKind :: Kind
tySuperKind :: SuperKind
coSuperKind :: SuperKind
Common Kind type constructors
liftedTypeKindTyCon :: TyCon
openTypeKindTyCon :: TyCon
unliftedTypeKindTyCon :: TyCon
argTypeKindTyCon :: TyCon
ubxTupleKindTyCon :: TyCon
Predicates on Kinds
isLiftedTypeKind :: Kind -> Bool
isUnliftedTypeKind :: Kind -> Bool
isOpenTypeKind :: Kind -> Bool
See Type for details of the distinction between these `Kind`s
isUbxTupleKind :: Kind -> Bool
isArgTypeKind :: Kind -> Bool
isKind :: Kind -> Bool
Is this a kind (i.e. a type-of-types)?
isTySuperKind :: SuperKind -> Bool
isCoSuperKind :: SuperKind -> Bool
isSuperKind :: Type -> Bool
Is this a super-kind (i.e. a type-of-kinds)?
isCoercionKind :: Kind -> Bool
isEqPred :: PredType -> Bool
mkArrowKind :: Kind -> Kind -> Kind
Given two kinds `k1` and `k2`, creates the `Kind` `k1 -> k2`
mkArrowKinds :: [Kind] -> Kind -> Kind
Iterated application of `mkArrowKind`
isSubArgTypeKind :: Kind -> Bool
True of any sub-kind of ArgTypeKind
isSubOpenTypeKind :: Kind -> Bool
True of any sub-kind of OpenTypeKind (i.e. anything except arrow)
isSubKind :: Kind -> Kind -> Bool
`k1 `isSubKind` k2` checks that `k1` <: `k2`
defaultKind :: Kind -> Kind
Used when generalising: default kind ? and ?? to *. See Type for more information on what that means
eqKind :: Kind -> Kind -> Bool
isSubKindCon :: TyCon -> TyCon -> Bool
`kc1 `isSubKindCon` kc2` checks that `kc1` <: `kc2`
Type free variables
tyVarsOfType :: Type -> TyVarSet
NB: for type synonyms tyVarsOfType does not expand the synonym
tyVarsOfTypes :: [Type] -> TyVarSet
tyVarsOfPred :: PredType -> TyVarSet
tyVarsOfTheta :: ThetaType -> TyVarSet
typeKind :: Type -> Kind
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])
tidyTyVarBndr :: 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])
tidyTopType :: Type -> Type
Calls `tidyType` on a top-level type (i.e. with an empty tidying environment)
tidyPred :: TidyEnv -> PredType -> PredType
tidyKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
Type comparison
coreEqType :: Type -> Type -> Bool
Type equality test for Core types (i.e. ignores predicate-types, synonyms etc.)
tcEqType :: Type -> Type -> Bool
Type equality on source types. Does not look through `newtypes` or `PredType`s, but it does look through type synonyms.
tcEqTypes :: [Type] -> [Type] -> Bool
tcCmpType :: Type -> Type -> Ordering
Type ordering on source types. Does not look through `newtypes` or `PredType`s, but it does look through type synonyms.
tcCmpTypes :: [Type] -> [Type] -> Ordering
tcEqPred :: PredType -> PredType -> Bool
tcEqPredX :: RnEnv2 -> PredType -> PredType -> Bool
tcCmpPred :: PredType -> PredType -> Ordering
tcEqTypeX :: RnEnv2 -> Type -> Type -> Bool
tcPartOfType :: Type -> Type -> Bool
Checks whether the second argument is a subterm of the first. (We don't care about binders, as we are only interested in syntactic subterms.)
tcPartOfPred :: Type -> PredType -> Bool
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.

In the case of `newtype`s, it returns one of:

1) A vanilla `TyConApp` (recursive newtype, or non-saturated)

2) The newtype representation (otherwise), meaning the type written in the RHS of the newtype declaration, which may itself be a newtype

For example, with:

     newtype R = MkR S
     newtype S = MkS T
     newtype T = MkT (T -> T)

expandNewTcApp on:

- `R` gives `Just S` * `S` gives `Just T` * `T` gives `Nothing` (no expansion)

tcView :: Type -> Maybe Type
Similar to `coreView`, but for the type checker, which just looks through synonyms
kindView :: Kind -> Maybe Kind
Similar to `coreView` or `tcView`, but works on `Kind`s
repType :: Type -> Type
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.
Type representation for the code generator
data PrimRep

A `PrimRep` is an abstraction of a type. It contains information that the code generator needs in order to pass arguments, return results, and store values of this type.
Constructors

VoidRep |
PtrRep |
IntRep | Signed, word-sized value
WordRep | Unsigned, word-sized value
Int64Rep | Signed, 64 bit value (with 32-bit words only)
Word64Rep | Unsigned, 64 bit value (with 32-bit words only)
AddrRep | A pointer, but not to a Haskell value (use `PtrRep`)
FloatRep |
DoubleRep |

Instances

Eq PrimRep
Show PrimRep
Outputable PrimRep

typePrimRep :: Type -> PrimRep
Discovers the primitive representation of a more abstract `Type`
predTypeRep :: PredType -> Type
Convert a `PredType` to its representation type. However, it unwraps only the outermost level; for example, the result might be a newtype application
Main type substitution data types
type TvSubstEnv = TyVarEnv Type
A substitition of `Type`s for `TyVar`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 substition is only applied ONCE! This is because in general such application will not reached a fixed point.
Constructors

TvSubst InScopeSet TvSubstEnv |

Instances

Outputable TvSubst

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 :: TyVar -> TvSubst -> Bool
getTvSubstEnv :: TvSubst -> TvSubstEnv
setTvSubstEnv :: TvSubst -> TvSubstEnv -> TvSubst
getTvInScope :: TvSubst -> InScopeSet
extendTvInScope :: 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
Performing substitution on types
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`
substPred :: TvSubst -> PredType -> PredType
Substitute within a `PredType`
substTyVar :: TvSubst -> TyVar -> Type
substTyVars :: TvSubst -> [TyVar] -> [Type]
substTyVarBndr :: TvSubst -> TyVar -> (TvSubst, TyVar)
deShadowTy :: TyVarSet -> Type -> Type
Remove any nested binders mentioning the `TyVar`s in the `TyVarSet`
lookupTyVar :: TvSubst -> TyVar -> Maybe Type
Pretty-printing
pprType :: Type -> SDoc
pprParendType :: Type -> SDoc
pprTypeApp :: NamedThing a => a -> [Type] -> SDoc
pprTyThingCategory :: TyThing -> SDoc
pprTyThing :: TyThing -> SDoc
pprForAll :: [TyVar] -> SDoc
pprPred :: PredType -> SDoc
pprTheta :: ThetaType -> SDoc
pprThetaArrow :: 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`

Produced by Haddock version 2.4.2