Type
Contents
Description
Main functions for manipulating types and type-related things
- data TyThing
- data Type
- data Pred a
- type PredType = Pred 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 :: 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
- mkDictTy :: Class -> [Type] -> Type
- isDictLikeTy :: Type -> Bool
- isClassPred :: Pred a -> Bool
- isEqPred :: Pred a -> Bool
- allPred :: (a -> Bool) -> Pred a -> Bool
- mkEqPred :: (a, a) -> Pred a
- mkClassPred :: Class -> [Type] -> PredType
- getClassPredTys :: PredType -> (Class, [Type])
- getClassPredTys_maybe :: PredType -> Maybe (Class, [Type])
- isTyVarClassPred :: PredType -> Bool
- mkIPPred :: IPName Name -> Type -> PredType
- isIPPred :: Pred a -> Bool
- funTyCon :: TyCon
- isTyVarTy :: Type -> Bool
- isFunTy :: Type -> Bool
- isPredTy :: Type -> Bool
- isDictTy :: Type -> Bool
- isEqPredTy :: Type -> Bool
- isReflPredTy :: Type -> Bool
- splitPredTy_maybe :: Type -> Maybe PredType
- splitEqPredTy_maybe :: Type -> Maybe (Type, Type)
- 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
- liftedTypeKind, ubxTupleKind, argTypeKind, openTypeKind, unliftedTypeKind :: Kind
- tySuperKind :: SuperKind
- argTypeKindTyCon, ubxTupleKindTyCon, unliftedTypeKindTyCon, openTypeKindTyCon, liftedTypeKindTyCon :: TyCon
- tyVarsOfType :: Type -> VarSet
- tyVarsOfTypes :: [Type] -> TyVarSet
- tyVarsOfPred :: PredType -> TyCoVarSet
- tyVarsOfTheta :: ThetaType -> TyCoVarSet
- exactTyVarsOfType :: Type -> TyVarSet
- exactTyVarsOfTypes :: [Type] -> TyVarSet
- expandTypeSynonyms :: Type -> Type
- typeSize :: Type -> Int
- 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
- seqType :: Type -> ()
- seqTypes :: [Type] -> ()
- seqPred :: (a -> ()) -> Pred a -> ()
- coreView :: Type -> Maybe Type
- tcView :: Type -> Maybe Type
- repType :: Type -> Type
- data PrimRep
- 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 :: TyCoVar -> 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
- substPred :: TvSubst -> PredType -> PredType
- 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
- pprType, pprParendType :: Type -> SDoc
- pprTypeApp :: NamedThing a => a -> [Type] -> SDoc
- pprTyThingCategory :: TyThing -> SDoc
- pprTyThing :: TyThing -> SDoc
- pprForAll :: [TyVar] -> SDoc
- pprPred :: (Prec -> a -> SDoc) -> Pred a -> SDoc
- pprPredTy :: PredType -> SDoc
- pprEqPred :: Pair Type -> SDoc
- pprTheta :: ThetaType -> SDoc
- pprThetaArrowTy :: ThetaType -> SDoc
- pprClassPred :: Class -> [Type] -> SDoc
- pprKind, 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
ornewtype
. An algebraic type is one that can be deconstructed with a case expression. This is not the same as lifted types, because we also include unboxed tuples in this classification. - Data
- Iff it is a type declared with
data
, or a boxed tuple. - Primitive
- Iff it is a 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 Type
The key representation of types within the compiler
data Pred a
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"
data Var
Constructing and deconstructing types
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
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
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
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
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:
- The function may have more for-alls than there are args
- 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 ()
isForAllTy :: Type -> Bool
dropForAlls :: Type -> Type
Equivalent to snd . splitForAllTys
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
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.
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
isClassPred :: Pred a -> Bool
mkClassPred :: Class -> [Type] -> PredType
getClassPredTys :: PredType -> (Class, [Type])
getClassPredTys_maybe :: PredType -> Maybe (Class, [Type])
isTyVarClassPred :: PredType -> Bool
Common type constructors
Predicates on types
isEqPredTy :: Type -> Bool
isReflPredTy :: Type -> Bool
splitPredTy_maybe :: Type -> Maybe PredType
splitEqPredTy_maybe :: Type -> Maybe (Type, Type)
isUnLiftedType :: Type -> Bool
See Type for what an unlifted type is
isUnboxedTupleType :: 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)
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
Common Kinds and SuperKinds
tySuperKind :: SuperKind
Common Kind type constructors
argTypeKindTyCon, ubxTupleKindTyCon, unliftedTypeKindTyCon, openTypeKindTyCon, liftedTypeKindTyCon :: TyCon
Type free variables
tyVarsOfType :: Type -> VarSet
NB: for type synonyms tyVarsOfType does not expand the synonym
tyVarsOfTypes :: [Type] -> TyVarSet
tyVarsOfPred :: PredType -> TyCoVarSet
tyVarsOfTheta :: ThetaType -> TyCoVarSet
exactTyVarsOfType :: Type -> TyVarSet
exactTyVarsOfTypes :: [Type] -> 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.
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.
Forcing evaluation of types
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
Similar to coreView
, but for the type checker, which just looks through synonyms
Looks through:
- 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.
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
data TvSubst
Type substitution
The following invariants must hold of a TvSubst
:
- The in-scope set is needed only to guide the generation of fresh uniques
- In particular, the kind of the type variables in the in-scope set is not relevant
- The substition is only applied ONCE! This is because in general such application will not reached a fixed point.
Constructors
TvSubst InScopeSet TvSubstEnv |
Instances
Manipulating type substitutions
mkTvSubst :: InScopeSet -> TvSubstEnv -> TvSubst
mkOpenTvSubst :: TvSubstEnv -> TvSubst
zipOpenTvSubst :: [TyVar] -> [Type] -> TvSubst
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 :: TyCoVar -> 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
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
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)
deShadowTy :: TyVarSet -> Type -> Type
lookupTyVar :: TvSubst -> TyVar -> Maybe Type
Pretty-printing
pprType, pprParendType :: Type -> SDoc
pprTypeApp :: NamedThing a => a -> [Type] -> SDoc
pprTyThingCategory :: TyThing -> SDoc
pprTyThing :: TyThing -> SDoc
pprThetaArrowTy :: ThetaType -> SDoc
pprClassPred :: Class -> [Type] -> SDoc
pprKind, pprParendKind :: Kind -> SDoc
pprSourceTyCon :: TyCon -> SDoc