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: 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 a r. TypeRep a -> (Typeable a => r) -> r

Use a TypeRep as Typeable evidence.

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: 4.7.0.0

Constructors

Refl :: a :~: a

Instances

Category k ((:~:) k)

Since: 4.7.0.0

Methods

id :: cat a a

(.) :: cat b c -> cat a b -> cat a c

TestEquality k ((:~:) k a)

Since: 4.7.0.0

Methods

testEquality :: f a -> f b -> Maybe (((k :~: a) :~: a) b)

TestCoercion k ((:~:) k a)

Since: 4.7.0.0

Methods

testCoercion :: f a -> f b -> Maybe (Coercion (k :~: a) a b)

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

Since: 4.7.0.0

Methods

minBound :: (k :~: a) b

maxBound :: (k :~: a) b

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

Since: 4.7.0.0

Methods

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

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

toEnum :: Int -> (k :~: a) b

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

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

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

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

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

Eq ((:~:) k a b)

Methods

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

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

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

Since: 4.7.0.0

Methods

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

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

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

gmapQr :: (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)

Ord ((:~:) k a b)

Methods

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

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

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

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

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

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

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

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

Since: 4.7.0.0

Methods

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

readList :: ReadS [(k :~: a) b]

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

readListPrec :: ReadPrec [(k :~: a) b]

Show ((:~:) k a b)

Methods

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

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

showList :: [(k :~: a) b] -> ShowS

data (a :: k1) :~~: (b :: k2) 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: 4.10.0.0

Constructors

HRefl :: a :~~: a

Instances

Category k ((:~~:) k k)

Since: 4.10.0.0

Methods

id :: cat a a

(.) :: cat b c -> cat a b -> cat a c

TestEquality k ((:~~:) k1 k a)

Since: 4.10.0.0

Methods

testEquality :: f a -> f b -> Maybe (((k1 :~~: k) a :~: a) b)

TestCoercion k ((:~~:) k1 k a)

Since: 4.10.0.0

Methods

testCoercion :: f a -> f b -> Maybe (Coercion ((k1 :~~: k) a) a b)

(~~) k1 k2 a b => Bounded ((:~~:) k1 k2 a b)

Since: 4.10.0.0

Methods

minBound :: (k1 :~~: k2) a b

maxBound :: (k1 :~~: k2) a b

(~~) k1 k2 a b => Enum ((:~~:) k1 k2 a b)

Since: 4.10.0.0

Methods

succ :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b

pred :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b

toEnum :: Int -> (k1 :~~: k2) a b

fromEnum :: (k1 :~~: k2) a b -> Int

enumFrom :: (k1 :~~: k2) a b -> [(k1 :~~: k2) a b]

enumFromThen :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> [(k1 :~~: k2) a b]

enumFromTo :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> [(k1 :~~: k2) a b]

enumFromThenTo :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> [(k1 :~~: k2) a b]

Eq ((:~~:) k1 k2 a b)

Since: 4.10.0.0

Methods

(==) :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Bool

(/=) :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Bool

(Typeable * i2, Typeable * j2, Typeable i2 a, Typeable j2 b, (~~) i2 j2 a b) => Data ((:~~:) i2 j2 a b)

Since: 4.10.0.0

Methods

gfoldl :: (forall d c. Data d => c (d -> c) -> d -> c c) -> (forall g. g -> c g) -> (i2 :~~: j2) a b -> c ((i2 :~~: j2) a b)

gunfold :: (forall c r. Data c => c (c -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c ((i2 :~~: j2) a b)

toConstr :: (i2 :~~: j2) a b -> Constr

dataTypeOf :: (i2 :~~: j2) a b -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c ((i2 :~~: j2) a b))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c ((i2 :~~: j2) a b))

gmapT :: (forall c. Data c => c -> c) -> (i2 :~~: j2) a b -> (i2 :~~: j2) a b

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> (i2 :~~: j2) a b -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> (i2 :~~: j2) a b -> r

gmapQ :: (forall d. Data d => d -> u) -> (i2 :~~: j2) a b -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> (i2 :~~: j2) a b -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> (i2 :~~: j2) a b -> m ((i2 :~~: j2) a b)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> (i2 :~~: j2) a b -> m ((i2 :~~: j2) a b)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> (i2 :~~: j2) a b -> m ((i2 :~~: j2) a b)

Ord ((:~~:) k1 k2 a b)

Since: 4.10.0.0

Methods

compare :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Ordering

(<) :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Bool

(<=) :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Bool

(>) :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Bool

(>=) :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Bool

max :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> (k1 :~~: k2) a b

min :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> (k1 :~~: k2) a b

(~~) k1 k2 a b => Read ((:~~:) k1 k2 a b)

Since: 4.10.0.0

Methods

readsPrec :: Int -> ReadS ((k1 :~~: k2) a b)

readList :: ReadS [(k1 :~~: k2) a b]

readPrec :: ReadPrec ((k1 :~~: k2) a b)

readListPrec :: ReadPrec [(k1 :~~: k2) a b]

Show ((:~~:) k1 k2 a b)

Since: 4.10.0.0

Methods

showsPrec :: Int -> (k1 :~~: k2) a b -> ShowS

show :: (k1 :~~: k2) a b -> String

showList :: [(k1 :~~: k2) a b] -> ShowS

Type representations

Type-Indexed

data TypeRep (a :: k)

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

Instances

TestEquality k (TypeRep k)

Methods

testEquality :: f a -> f b -> Maybe ((TypeRep k :~: a) b)

Eq (TypeRep k a)

Since: 2.1

Methods

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

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

Ord (TypeRep k a)

Since: 4.4.0.0

Methods

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

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

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

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

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

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

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

Show (TypeRep k a)

Methods

showsPrec :: Int -> TypeRep k a -> ShowS

show :: TypeRep k a -> String

showList :: [TypeRep k a] -> ShowS

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

Pattern match on a type application

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

Pattern match on a type constructor

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

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

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

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: 4.8.0.0

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

Type equality

Since: 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

Eq SomeTypeRep

Methods

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

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

Ord SomeTypeRep

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

Show SomeTypeRep

Since: 4.10.0.0

Methods

showsPrec :: Int -> SomeTypeRep -> ShowS

show :: SomeTypeRep -> String

showList :: [SomeTypeRep] -> ShowS

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

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

Since: 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: 4.10.0.0

Type constructors

data TyCon :: *

Instances

Eq TyCon

Methods

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

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

Ord TyCon

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

Show TyCon

Since: 2.1

Methods

showsPrec :: Int -> TyCon -> ShowS

show :: TyCon -> String

showList :: [TyCon] -> ShowS

tyConPackage :: TyCon -> String

tyConModule :: TyCon -> String

tyConName :: TyCon -> String

rnfTyCon :: TyCon -> ()

Module names

data Module :: *

Instances

Eq Module

Methods

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

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

Show Module

Since: 4.9.0.0

Methods

showsPrec :: Int -> Module -> ShowS

show :: Module -> String

showList :: [Module] -> ShowS

moduleName :: Module -> String

modulePackage :: Module -> String

rnfModule :: Module -> ()

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

Since: 4.8.0.0