Type.Reflection

This provides a type-indexed type representation mechanism, similar to that described by,

• Simon Peyton-Jones, Stephanie Weirich, Richard Eisenberg, Dimitrios Vytiniotis. "A reflection on types". Proc. Philip Wadler's 60th birthday Festschrift, Edinburgh (April 2016).

The interface provides TypeRep, a type representation which can be safely decomposed and composed. See Data.Dynamic for an example of this.

Since: base-4.10.0.0

The Typeable class

class Typeable (a :: k)

The class Typeable allows a concrete representation of a type to be calculated.

Minimal complete definition

typeRep#

typeRep :: Typeable a => TypeRep a

withTypeable :: forall k (a :: k) rep (r :: TYPE rep). TypeRep a -> (Typeable a => r) -> r

Use a TypeRep as Typeable evidence.

The TypeRep pattern synonym brings a Typeable constraint into scope and can be used in place of withTypeable.

f :: TypeRep a -> ..
f rep = withTypeable {- Typeable a in scope -}

f :: TypeRep a -> ..
f TypeRep = {- Typeable a in scope -}

Propositional equality

data a :~: b where infix 4

Propositional equality. If a :~: b is inhabited by some terminating value, then the type a is the same as the type b. To use this equality in practice, pattern-match on the a :~: b to get out the Refl constructor; in the body of the pattern-match, the compiler knows that a ~ b.

Since: base-4.7.0.0

Constructors

Refl :: a :~: a

Instances

Category ((:~:) :: k -> k -> Type)

Since: base-4.7.0.0

Defined in Control.Category

Methods

id :: forall (a :: k0). a :~: a

(.) :: forall (b :: k0) (c :: k0) (a :: k0). (b :~: c) -> (a :~: b) -> a :~: c

TestCoercion ((:~:) a :: k -> Type)

Since: base-4.7.0.0

Defined in Data.Type.Coercion

Methods

testCoercion :: forall (a0 :: k0) (b :: k0). (a :~: a0) -> (a :~: b) -> Maybe (Coercion a0 b)

TestEquality ((:~:) a :: k -> Type)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

testEquality :: forall (a0 :: k0) (b :: k0). (a :~: a0) -> (a :~: b) -> Maybe (a0 :~: b)

(a ~ b, Data a) => Data (a :~: b)

Since: base-4.7.0.0

Defined in Data.Data

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> (a :~: b) -> c (a :~: b)

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (a :~: b)

toConstr :: (a :~: b) -> Constr

dataTypeOf :: (a :~: b) -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (a :~: b))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (a :~: b))

gmapT :: (forall b0. Data b0 => b0 -> b0) -> (a :~: b) -> a :~: b

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> (a :~: b) -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> (a :~: b) -> r

gmapQ :: (forall d. Data d => d -> u) -> (a :~: b) -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> (a :~: b) -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> (a :~: b) -> m (a :~: b)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> (a :~: b) -> m (a :~: b)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> (a :~: b) -> m (a :~: b)

a ~ b => Bounded (a :~: b)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

minBound :: a :~: b

maxBound :: a :~: b

a ~ b => Enum (a :~: b)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

succ :: (a :~: b) -> a :~: b

pred :: (a :~: b) -> a :~: b

toEnum :: Int -> a :~: b

fromEnum :: (a :~: b) -> Int

enumFrom :: (a :~: b) -> [a :~: b]

enumFromThen :: (a :~: b) -> (a :~: b) -> [a :~: b]

enumFromTo :: (a :~: b) -> (a :~: b) -> [a :~: b]

enumFromThenTo :: (a :~: b) -> (a :~: b) -> (a :~: b) -> [a :~: b]

a ~ b => Read (a :~: b)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

readsPrec :: Int -> ReadS (a :~: b)

readList :: ReadS [a :~: b]

readPrec :: ReadPrec (a :~: b)

readListPrec :: ReadPrec [a :~: b]

Show (a :~: b)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

showsPrec :: Int -> (a :~: b) -> ShowS

show :: (a :~: b) -> String

showList :: [a :~: b] -> ShowS

Eq (a :~: b)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

(==) :: (a :~: b) -> (a :~: b) -> Bool

(/=) :: (a :~: b) -> (a :~: b) -> Bool

Ord (a :~: b)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

compare :: (a :~: b) -> (a :~: b) -> Ordering

(<) :: (a :~: b) -> (a :~: b) -> Bool

(<=) :: (a :~: b) -> (a :~: b) -> Bool

(>) :: (a :~: b) -> (a :~: b) -> Bool

(>=) :: (a :~: b) -> (a :~: b) -> Bool

max :: (a :~: b) -> (a :~: b) -> a :~: b

min :: (a :~: b) -> (a :~: b) -> a :~: b

data a :~~: b where infix 4

Kind heterogeneous propositional equality. Like :~:, a :~~: b is inhabited by a terminating value if and only if a is the same type as b.

Since: base-4.10.0.0

Constructors

HRefl :: a :~~: a

Instances

Category ((:~~:) :: k -> k -> Type)

Since: base-4.10.0.0

Defined in Control.Category

Methods

id :: forall (a :: k0). a :~~: a

(.) :: forall (b :: k0) (c :: k0) (a :: k0). (b :~~: c) -> (a :~~: b) -> a :~~: c

TestCoercion ((:~~:) a :: k -> Type)

Since: base-4.10.0.0

Defined in Data.Type.Coercion

Methods

testCoercion :: forall (a0 :: k0) (b :: k0). (a :~~: a0) -> (a :~~: b) -> Maybe (Coercion a0 b)

TestEquality ((:~~:) a :: k -> Type)

Since: base-4.10.0.0

Defined in Data.Type.Equality

Methods

testEquality :: forall (a0 :: k0) (b :: k0). (a :~~: a0) -> (a :~~: b) -> Maybe (a0 :~: b)

(Typeable i, Typeable j, Typeable a, Typeable b, a ~~ b) => Data (a :~~: b)

Since: base-4.10.0.0

Defined in Data.Data

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> (a :~~: b) -> c (a :~~: b)

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (a :~~: b)

toConstr :: (a :~~: b) -> Constr

dataTypeOf :: (a :~~: b) -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (a :~~: b))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (a :~~: b))

gmapT :: (forall b0. Data b0 => b0 -> b0) -> (a :~~: b) -> a :~~: b

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> (a :~~: b) -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> (a :~~: b) -> r

gmapQ :: (forall d. Data d => d -> u) -> (a :~~: b) -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> (a :~~: b) -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> (a :~~: b) -> m (a :~~: b)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> (a :~~: b) -> m (a :~~: b)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> (a :~~: b) -> m (a :~~: b)

a ~~ b => Bounded (a :~~: b)

Since: base-4.10.0.0

Defined in Data.Type.Equality

Methods

minBound :: a :~~: b

maxBound :: a :~~: b

a ~~ b => Enum (a :~~: b)

Since: base-4.10.0.0

Defined in Data.Type.Equality

Methods

succ :: (a :~~: b) -> a :~~: b

pred :: (a :~~: b) -> a :~~: b

toEnum :: Int -> a :~~: b

fromEnum :: (a :~~: b) -> Int

enumFrom :: (a :~~: b) -> [a :~~: b]

enumFromThen :: (a :~~: b) -> (a :~~: b) -> [a :~~: b]

enumFromTo :: (a :~~: b) -> (a :~~: b) -> [a :~~: b]

enumFromThenTo :: (a :~~: b) -> (a :~~: b) -> (a :~~: b) -> [a :~~: b]

a ~~ b => Read (a :~~: b)

Since: base-4.10.0.0

Defined in Data.Type.Equality

Methods

readsPrec :: Int -> ReadS (a :~~: b)

readList :: ReadS [a :~~: b]

readPrec :: ReadPrec (a :~~: b)

readListPrec :: ReadPrec [a :~~: b]

Show (a :~~: b)

Since: base-4.10.0.0

Defined in Data.Type.Equality

Methods

showsPrec :: Int -> (a :~~: b) -> ShowS

show :: (a :~~: b) -> String

showList :: [a :~~: b] -> ShowS

Eq (a :~~: b)

Since: base-4.10.0.0

Defined in Data.Type.Equality

Methods

(==) :: (a :~~: b) -> (a :~~: b) -> Bool

(/=) :: (a :~~: b) -> (a :~~: b) -> Bool

Ord (a :~~: b)

Since: base-4.10.0.0

Defined in Data.Type.Equality

Methods

compare :: (a :~~: b) -> (a :~~: b) -> Ordering

(<) :: (a :~~: b) -> (a :~~: b) -> Bool

(<=) :: (a :~~: b) -> (a :~~: b) -> Bool

(>) :: (a :~~: b) -> (a :~~: b) -> Bool

(>=) :: (a :~~: b) -> (a :~~: b) -> Bool

max :: (a :~~: b) -> (a :~~: b) -> a :~~: b

min :: (a :~~: b) -> (a :~~: b) -> a :~~: b

Type representations

Type-Indexed

data TypeRep a

A concrete representation of a (monomorphic) type. TypeRep supports reasonably efficient equality.

Instances

TestEquality (TypeRep :: k -> Type)

Defined in Data.Typeable.Internal

Methods

testEquality :: forall (a :: k0) (b :: k0). TypeRep a -> TypeRep b -> Maybe (a :~: b)

Show (TypeRep a)

Defined in Data.Typeable.Internal

Methods

showsPrec :: Int -> TypeRep a -> ShowS

show :: TypeRep a -> String

showList :: [TypeRep a] -> ShowS

Eq (TypeRep a)

Since: base-2.1

Defined in Data.Typeable.Internal

Methods

(==) :: TypeRep a -> TypeRep a -> Bool

(/=) :: TypeRep a -> TypeRep a -> Bool

Ord (TypeRep a)

Since: base-4.4.0.0

Defined in Data.Typeable.Internal

Methods

compare :: TypeRep a -> TypeRep a -> Ordering

(<) :: TypeRep a -> TypeRep a -> Bool

(<=) :: TypeRep a -> TypeRep a -> Bool

(>) :: TypeRep a -> TypeRep a -> Bool

(>=) :: TypeRep a -> TypeRep a -> Bool

max :: TypeRep a -> TypeRep a -> TypeRep a

min :: TypeRep a -> TypeRep a -> TypeRep a

pattern TypeRep :: forall {k :: Type} (a :: k). () => Typeable @k a => TypeRep @k a

A explicitly bidirectional pattern synonym to construct a concrete representation of a type.

As an expression: Constructs a singleton TypeRep a given a implicit 'Typeable a' constraint:

TypeRep @a :: Typeable a => TypeRep a

As a pattern: Matches on an explicit TypeRep a witness bringing an implicit Typeable a constraint into scope.

f :: TypeRep a -> ..
f TypeRep = {- Typeable a in scope -}

Since: base-4.17.0.0

typeOf :: Typeable a => a -> TypeRep a

pattern App :: forall k2 (t :: k2). () => forall k1 (a :: k1 -> k2) (b :: k1). t ~ a b => TypeRep a -> TypeRep b -> TypeRep t

A type application.

For instance,

typeRep @(Maybe Int) === App (typeRep @Maybe) (typeRep @Int)

Note that this will also match a function type,

typeRep @(Int# -> Char)
  ===
App (App arrow (typeRep @Int#)) (typeRep @Char)

where arrow :: TypeRep ((->) :: TYPE IntRep -> Type -> Type).

pattern Con :: forall k (a :: k). () => NotApplication a => TyCon -> TypeRep a

Pattern match on a type constructor

pattern Con' :: forall k (a :: k). () => NotApplication a => TyCon -> [SomeTypeRep] -> TypeRep a

Pattern match on a type constructor including its instantiated kind variables.

For instance,

App (Con' proxyTyCon ks) intRep = typeRep @(Proxy @Int)

will bring into scope,

proxyTyCon :: TyCon
ks         == [someTypeRep Type] :: [SomeTypeRep]
intRep     == typeRep Int

pattern Fun :: forall k (fun :: k). () => forall (r1 :: RuntimeRep) (r2 :: RuntimeRep) (arg :: TYPE r1) (res :: TYPE r2). (k ~ Type, fun ~~ (arg -> res)) => TypeRep arg -> TypeRep res -> TypeRep fun

The function type constructor.

For instance,

typeRep @(Int -> Char) === Fun (typeRep @Int) (typeRep @Char)

typeRepTyCon :: TypeRep a -> TyCon

Observe the type constructor of a type representation

rnfTypeRep :: TypeRep a -> ()

Helper to fully evaluate TypeRep for use as NFData(rnf) implementation

Since: base-4.8.0.0

eqTypeRep :: forall k1 k2 (a :: k1) (b :: k2). TypeRep a -> TypeRep b -> Maybe (a :~~: b)

Type equality

Since: base-4.10

typeRepKind :: TypeRep (a :: k) -> TypeRep k

Observe the kind of a type.

splitApps :: TypeRep a -> (TyCon, [SomeTypeRep])

Quantified

data SomeTypeRep where

A non-indexed type representation.

Constructors

SomeTypeRep :: forall k (a :: k). !(TypeRep a) -> SomeTypeRep

Instances

Show SomeTypeRep

Since: base-4.10.0.0

Defined in Data.Typeable.Internal

Methods

showsPrec :: Int -> SomeTypeRep -> ShowS

show :: SomeTypeRep -> String

showList :: [SomeTypeRep] -> ShowS

Eq SomeTypeRep

Defined in Data.Typeable.Internal

Methods

(==) :: SomeTypeRep -> SomeTypeRep -> Bool

(/=) :: SomeTypeRep -> SomeTypeRep -> Bool

Ord SomeTypeRep

Defined in Data.Typeable.Internal

Methods

compare :: SomeTypeRep -> SomeTypeRep -> Ordering

(<) :: SomeTypeRep -> SomeTypeRep -> Bool

(<=) :: SomeTypeRep -> SomeTypeRep -> Bool

(>) :: SomeTypeRep -> SomeTypeRep -> Bool

(>=) :: SomeTypeRep -> SomeTypeRep -> Bool

max :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep

min :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep

someTypeRep :: forall proxy a. Typeable a => proxy a -> SomeTypeRep

Takes a value of type a and returns a concrete representation of that type.

Since: base-4.7.0.0

someTypeRepTyCon :: SomeTypeRep -> TyCon

Observe the type constructor of a quantified type representation.

rnfSomeTypeRep :: SomeTypeRep -> ()

Helper to fully evaluate SomeTypeRep for use as NFData(rnf) implementation

Since: base-4.10.0.0

Type constructors

data TyCon

Instances

Show TyCon

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> TyCon -> ShowS

show :: TyCon -> String

showList :: [TyCon] -> ShowS

Eq TyCon

Defined in GHC.Classes

Methods

(==) :: TyCon -> TyCon -> Bool

(/=) :: TyCon -> TyCon -> Bool

Ord TyCon

Defined in GHC.Classes

Methods

compare :: TyCon -> TyCon -> Ordering

(<) :: TyCon -> TyCon -> Bool

(<=) :: TyCon -> TyCon -> Bool

(>) :: TyCon -> TyCon -> Bool

(>=) :: TyCon -> TyCon -> Bool

max :: TyCon -> TyCon -> TyCon

min :: TyCon -> TyCon -> TyCon

tyConPackage :: TyCon -> String

tyConModule :: TyCon -> String

tyConName :: TyCon -> String

rnfTyCon :: TyCon -> ()

Module names

data Module

Instances

Show Module

Since: base-4.9.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> Module -> ShowS

show :: Module -> String

showList :: [Module] -> ShowS

Eq Module

Defined in GHC.Classes

Methods

(==) :: Module -> Module -> Bool

(/=) :: Module -> Module -> Bool

moduleName :: Module -> String

modulePackage :: Module -> String

rnfModule :: Module -> ()

Helper to fully evaluate TyCon for use as NFData(rnf) implementation

Since: base-4.8.0.0