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Description |
Main functions for manipulating types and type-related things
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Synopsis |
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| | data 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 | | expandTypeSynonyms :: Type -> Type | | 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 | | | | 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 |
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Main data types representing Types
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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
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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, PredTys 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.
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A typecheckable-thing, essentially anything that has a name
| Constructors | | Instances | |
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The key representation of types within the compiler
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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 | | Instances | |
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A collection of PredTypes
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Constructing and deconstructing types
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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
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Attempts to obtain the type variable underlying a Type
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Applies a type to another, as in e.g. k a
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Attempts to take a type application apart, as in splitAppTy_maybe,
and panics if this is not possible
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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.
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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!
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Does the AppTy split as in splitAppTy_maybe, but assumes that
any Core view stuff is already done
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Creates a function type from the given argument and result type
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Attempts to extract the argument and result types from a type, and
panics if that is not possible. See also splitFunTy_maybe
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Attempts to extract the argument and result types from a type
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Split off exactly the given number argument types, and panics if that is not possible
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Extract the function result type and panic if that is not possible
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Extract the function argument type and panic if that is not possible
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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.
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A key function: builds a TyConApp or FunTy as apppropriate to its arguments.
Applies its arguments to the constructor from left to right
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Create the plain type constructor type which has been applied to no type arguments at all.
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The same as fst . splitTyConApp
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The same as snd . splitTyConApp
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Attempts to tease a type apart into a type constructor and the application
of a number of arguments to that constructor
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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
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Wraps foralls over the type using the provided TyVars from left to right
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Attempts to take a forall type apart, returning the bound type variable
and the remainder of the type
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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 TyVars
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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.
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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 ()
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Equivalent to snd . splitForAllTys
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Unwrap one layer of newtype on a type constructor and its arguments, using an
eta-reduced version of the newtype if possible
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Finds type family instances occuring in a type after expanding synonyms.
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Finds type family instances occuring in a predicate type after expanding
synonyms.
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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)
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Common type constructors
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Predicates on types
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See Type for what an unlifted type is
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See Type for what an algebraic type is.
Should only be applied to types, as opposed to e.g. partially
saturated type constructors
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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
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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
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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)
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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.)
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Main data types representing Kinds
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There's a little subtyping at the kind level:
?
/ \
/ \
?? (#)
/ \
* #
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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)
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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)
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Deconstructing Kinds
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Essentially funResultTy on kinds
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Essentially splitFunTys on kinds
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Essentially splitFunTysN on kinds
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Common Kinds and SuperKinds
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See Type for details of the distinction between these Kinds
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tySuperKind :: SuperKind | Source |
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coSuperKind :: SuperKind | Source |
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Common Kind type constructors
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Predicates on Kinds
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See Type for details of the distinction between these Kinds
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Is this a kind (i.e. a type-of-types)?
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Is this a super-kind (i.e. a type-of-kinds)?
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Given two kinds k1 and k2, creates the Kind k1 -> k2
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Iterated application of mkArrowKind
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True of any sub-kind of ArgTypeKind
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True of any sub-kind of OpenTypeKind (i.e. anything except arrow)
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k1 `isSubKind` k2 checks that k1 <: k2
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Used when generalising: default kind ? and ?? to *. See Type for more
information on what that means
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kc1 `isSubKindCon` kc2 checks that kc1 <: kc2
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Type free variables
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NB: for type synonyms tyVarsOfType does not expand the synonym
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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.
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Tidying type related things up for printing
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Grabs the free type variables, tidies them
and then uses tidyType to work over the type itself
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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.
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Add the free TyVars to the env in tidy form,
so that we can tidy the type they are free in
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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
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Calls tidyType on a top-level type (i.e. with an empty tidying environment)
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Type comparison
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Type equality test for Core types (i.e. ignores predicate-types, synonyms etc.)
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Type equality on source types. Does not look through newtypes or
PredTypes, but it does look through type synonyms.
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Type ordering on source types. Does not look through newtypes or
PredTypes, but it does look through type synonyms.
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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.)
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Forcing evaluation of types
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Other views onto Types
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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 newtypes, 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)
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Similar to coreView, but for the type checker, which just looks through synonyms
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Similar to coreView or tcView, but works on Kinds
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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.
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Type representation for the code generator
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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 | |
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Discovers the primitive representation of a more abstract Type
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Convert a PredType to its representation type. However, it unwraps
only the outermost level; for example, the result might be a newtype application
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Main type substitution data types
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A substitition of Types for TyVars
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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.
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Manipulating type substitutions
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Generates the in-scope set for the TvSubst from the types in the incoming
environment, hence open
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Generates the in-scope set for the TvSubst from the types in the incoming
environment, hence open
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Called when doing top-level substitutions. Here we expect that the
free vars of the range of the substitution will be empty.
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(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
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Performing substitution on types
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Substitute within a Type
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Substitute within several Types
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Type substitution making use of an TvSubst that
is assumed to be open, see zipOpenTvSubst
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Type substitution making use of an TvSubst that
is assumed to be open, see zipOpenTvSubst
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Substitute within a ThetaType
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Substitute within a PredType
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Remove any nested binders mentioning the TyVars in the TyVarSet
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Pretty-printing
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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
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Produced by Haddock version 2.6.1 |