base-4.10.1.0: Basic libraries

Copyright | (c) The University of Glasgow CWI 2001--2017
License | BSD-style (see the file libraries/base/LICENSE)
Maintainer | libraries@haskell.org
Stability | experimental
Portability | non-portable (requires GADTs and compiler support)
Safe Haskell | Trustworthy
Language | Haskell2010

Type.Reflection

Contents

- The Typeable class
- Propositional equality
- Type representations
  - Type-Indexed
  - Quantified
- Type constructors
- Module names

Description

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

Synopsis

- class Typeable (a :: k)
- typeRep :: Typeable a => TypeRep a
- withTypeable :: forall a r. TypeRep a -> (Typeable a => r) -> r
- data a :~: b where
  - Refl :: a :~: a
- data (a :: k1) :~~: (b :: k2) where
  - HRefl :: a :~~: a
- data TypeRep (a :: k)
- 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 Con :: forall k (a :: k). TyCon -> TypeRep a
- pattern Con' :: forall k (a :: k). TyCon -> [SomeTypeRep] -> TypeRep a
- 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
- rnfTypeRep :: TypeRep a -> ()
- eqTypeRep :: forall k1 k2 (a :: k1) (b :: k2). TypeRep a -> TypeRep b -> Maybe (a :~~: b)
- typeRepKind :: TypeRep (a :: k) -> TypeRep k
- splitApps :: TypeRep a -> (TyCon, [SomeTypeRep])
- data SomeTypeRep where
  - SomeTypeRep :: forall k (a :: k). !(TypeRep a) -> SomeTypeRep
- someTypeRep :: forall proxy a. Typeable a => proxy a -> SomeTypeRep
- someTypeRepTyCon :: SomeTypeRep -> TyCon
- rnfSomeTypeRep :: SomeTypeRep -> ()
- data TyCon :: *
- tyConPackage :: TyCon -> String
- tyConModule :: TyCon -> String
- tyConName :: TyCon -> String
- rnfTyCon :: TyCon -> ()
- data Module :: *
- moduleName :: Module -> String
- modulePackage :: Module -> String
- rnfModule :: Module -> ()

# 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 Source # (/=) :: (k :~: a) b -> (k :~: a) b -> Bool Source #
((~) * 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 Source # (<) :: (k :~: a) b -> (k :~: a) b -> Bool Source # (<=) :: (k :~: a) b -> (k :~: a) b -> Bool Source # (>) :: (k :~: a) b -> (k :~: a) b -> Bool Source # (>=) :: (k :~: a) b -> (k :~: a) b -> Bool Source # max :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b Source # min :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b Source #
(~) 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 Source # (/=) :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Bool Source #
(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 Source #

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

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

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

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

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

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

(~~) 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 Source # (/=) :: TypeRep k a -> TypeRep k a -> Bool Source #
Ord (TypeRep k a) # | Since: 4.4.0.0
Methods compare :: TypeRep k a -> TypeRep k a -> Ordering Source # (<) :: TypeRep k a -> TypeRep k a -> Bool Source # (<=) :: TypeRep k a -> TypeRep k a -> Bool Source # (>) :: TypeRep k a -> TypeRep k a -> Bool Source # (>=) :: TypeRep k a -> TypeRep k a -> Bool Source # max :: TypeRep k a -> TypeRep k a -> TypeRep k a Source # min :: TypeRep k a -> TypeRep k a -> TypeRep k a Source #
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 #

A type application.

For instance, `typeRep @(Maybe Int) === App (typeRep @Maybe) (typeRep @Int)` Note that this will never match a function type (e.g. `Int -> Char`).

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.

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: 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 Source # (/=) :: SomeTypeRep -> SomeTypeRep -> Bool Source #
Ord SomeTypeRep # |
Methods compare :: SomeTypeRep -> SomeTypeRep -> Ordering Source # (<) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (<=) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (>) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (>=) :: SomeTypeRep -> SomeTypeRep -> Bool Source # max :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep Source # min :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep Source #
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 :: * Source #

Instances

Eq TyCon |
Methods (==) :: TyCon -> TyCon -> Bool Source # (/=) :: TyCon -> TyCon -> Bool Source #
Ord TyCon |
Methods compare :: TyCon -> TyCon -> Ordering Source # (<) :: TyCon -> TyCon -> Bool Source # (<=) :: TyCon -> TyCon -> Bool Source # (>) :: TyCon -> TyCon -> Bool Source # (>=) :: TyCon -> TyCon -> Bool Source # max :: TyCon -> TyCon -> TyCon Source # min :: TyCon -> TyCon -> TyCon Source #
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 :: * Source #

Instances

Eq Module |
Methods (==) :: Module -> Module -> Bool Source # (/=) :: Module -> Module -> Bool Source #
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