base-4.18.1.0: 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 | stable
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: base-4.10.0.0

Synopsis

- class Typeable (a :: k)
- typeRep :: Typeable a => TypeRep a
- withTypeable :: forall k (a :: k) rep (r :: TYPE rep). TypeRep a -> (Typeable a => r) -> r
- data a :~: b where
  - Refl :: a :~: a
- data a :~~: b where
  - HRefl :: a :~~: a
- data TypeRep a
- pattern TypeRep :: forall {k :: Type} (a :: k). () => Typeable @k a => TypeRep @k a
- 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). () => NotApplication a => TyCon -> TypeRep a
- pattern Con' :: forall k (a :: k). () => NotApplication a => 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) Source #

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

Minimal complete definition

typeRep#

typeRep :: Typeable a => TypeRep a Source #

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

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 Source #

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

Instances details

Category ((:~:) :: k -> k -> Type) Source # | Since: base-4.7.0.0
Instance details Defined in Control.Category Methods id :: forall (a :: k0). a :~: a Source # (.) :: forall (b :: k0) (c :: k0) (a :: k0). (b :~: c) -> (a :~: b) -> a :~: c Source #
TestCoercion ((:~:) a :: k -> Type) Source # | Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods testCoercion :: forall (a0 :: k0) (b :: k0). (a :~: a0) -> (a :~: b) -> Maybe (Coercion a0 b) Source #
TestEquality ((:~:) a :: k -> Type) Source # | Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods testEquality :: forall (a0 :: k0) (b :: k0). (a :~: a0) -> (a :~: b) -> Maybe (a0 :~: b) Source #
(a ~ b, Data a) => Data (a :~: b) Source # | Since: base-4.7.0.0

Instance details

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) Source #

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

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

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

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

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

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

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

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

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

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

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

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

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

a ~ b => Bounded (a :~: b) Source # | Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods minBound :: a :~: b Source # maxBound :: a :~: b Source #
a ~ b => Enum (a :~: b) Source # | Since: base-4.7.0.0

Instance details

Defined in Data.Type.Equality

Methods

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

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

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

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

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

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

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

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

a ~ b => Read (a :~: b) Source # | Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods readsPrec :: Int -> ReadS (a :~: b) Source # readList :: ReadS [a :~: b] Source # readPrec :: ReadPrec (a :~: b) Source # readListPrec :: ReadPrec [a :~: b] Source #
Show (a :~: b) Source # | Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods showsPrec :: Int -> (a :~: b) -> ShowS Source # show :: (a :~: b) -> String Source # showList :: [a :~: b] -> ShowS Source #
Eq (a :~: b) Source # | Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods (==) :: (a :~: b) -> (a :~: b) -> Bool Source # (/=) :: (a :~: b) -> (a :~: b) -> Bool Source #
Ord (a :~: b) Source # | Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods compare :: (a :~: b) -> (a :~: b) -> Ordering Source # (<) :: (a :~: b) -> (a :~: b) -> Bool Source # (<=) :: (a :~: b) -> (a :~: b) -> Bool Source # (>) :: (a :~: b) -> (a :~: b) -> Bool Source # (>=) :: (a :~: b) -> (a :~: b) -> Bool Source # max :: (a :~: b) -> (a :~: b) -> a :~: b Source # min :: (a :~: b) -> (a :~: b) -> a :~: b Source #

data a :~~: b where infix 4 Source #

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

Instances details

Category ((:~~:) :: k -> k -> Type) Source # | Since: base-4.10.0.0
Instance details Defined in Control.Category Methods id :: forall (a :: k0). a :~~: a Source # (.) :: forall (b :: k0) (c :: k0) (a :: k0). (b :~~: c) -> (a :~~: b) -> a :~~: c Source #
TestCoercion ((:~~:) a :: k -> Type) Source # | Since: base-4.10.0.0
Instance details Defined in Data.Type.Coercion Methods testCoercion :: forall (a0 :: k0) (b :: k0). (a :~~: a0) -> (a :~~: b) -> Maybe (Coercion a0 b) Source #
TestEquality ((:~~:) a :: k -> Type) Source # | Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods testEquality :: forall (a0 :: k0) (b :: k0). (a :~~: a0) -> (a :~~: b) -> Maybe (a0 :~: b) Source #
(Typeable i, Typeable j, Typeable a, Typeable b, a ~~ b) => Data (a :~~: b) Source # | Since: base-4.10.0.0

Instance details

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) Source #

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

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

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

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

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

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

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

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

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

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

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

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

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

a ~~ b => Bounded (a :~~: b) Source # | Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods minBound :: a :~~: b Source # maxBound :: a :~~: b Source #
a ~~ b => Enum (a :~~: b) Source # | Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

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

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

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

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

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

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

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

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

a ~~ b => Read (a :~~: b) Source # | Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods readsPrec :: Int -> ReadS (a :~~: b) Source # readList :: ReadS [a :~~: b] Source # readPrec :: ReadPrec (a :~~: b) Source # readListPrec :: ReadPrec [a :~~: b] Source #
Show (a :~~: b) Source # | Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods showsPrec :: Int -> (a :~~: b) -> ShowS Source # show :: (a :~~: b) -> String Source # showList :: [a :~~: b] -> ShowS Source #
Eq (a :~~: b) Source # | Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods (==) :: (a :~~: b) -> (a :~~: b) -> Bool Source # (/=) :: (a :~~: b) -> (a :~~: b) -> Bool Source #
Ord (a :~~: b) Source # | Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

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

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

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

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

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

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

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

# Type representations

## Type-Indexed

data TypeRep a Source #

TypeRep is a concrete representation of a (monomorphic) type. `TypeRep` supports reasonably efficient equality. See Note [Grand plan for Typeable] in GHC.Tc.Instance.Typeable

#### Instances

Instances details

TestEquality (TypeRep :: k -> Type) Source # |
Instance details Defined in Data.Typeable.Internal Methods testEquality :: forall (a :: k0) (b :: k0). TypeRep a -> TypeRep b -> Maybe (a :~: b) Source #
Show (TypeRep a) Source # |
Instance details Defined in Data.Typeable.Internal Methods showsPrec :: Int -> TypeRep a -> ShowS Source # show :: TypeRep a -> String Source # showList :: [TypeRep a] -> ShowS Source #
Eq (TypeRep a) Source # | Since: base-2.1
Instance details Defined in Data.Typeable.Internal Methods (==) :: TypeRep a -> TypeRep a -> Bool Source # (/=) :: TypeRep a -> TypeRep a -> Bool Source #
Ord (TypeRep a) Source # | Since: base-4.4.0.0

Instance details

Defined in Data.Typeable.Internal

Methods

compare :: TypeRep a -> TypeRep a -> Ordering Source #

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

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

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

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

max :: TypeRep a -> TypeRep a -> TypeRep a Source #

min :: TypeRep a -> TypeRep a -> TypeRep a Source #

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

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 Source #

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

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 Source #

Pattern match on a type constructor

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

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 Source #

The function type constructor.

For instance,

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

typeRepTyCon :: TypeRep a -> TyCon Source #

Observe the type constructor of a type representation

rnfTypeRep :: TypeRep a -> () Source #

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) Source #

Type equality

Since: base-4.10

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

Observe the kind of a type.

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

## Quantified

data SomeTypeRep where Source #

A non-indexed type representation.

Constructors

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

#### Instances

Instances details

Show SomeTypeRep Source # | Since: base-4.10.0.0
Instance details Defined in Data.Typeable.Internal Methods showsPrec :: Int -> SomeTypeRep -> ShowS Source # show :: SomeTypeRep -> String Source # showList :: [SomeTypeRep] -> ShowS Source #
Eq SomeTypeRep Source # |
Instance details Defined in Data.Typeable.Internal Methods (==) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (/=) :: SomeTypeRep -> SomeTypeRep -> Bool Source #
Ord SomeTypeRep Source # |

Instance details

Defined in Data.Typeable.Internal

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 #

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

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

Since: base-4.7.0.0

someTypeRepTyCon :: SomeTypeRep -> TyCon Source #

Observe the type constructor of a quantified type representation.

rnfSomeTypeRep :: SomeTypeRep -> () Source #

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

Since: base-4.10.0.0

# Type constructors

data TyCon Source #

#### Instances

Instances details

Show TyCon Source # | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> TyCon -> ShowS Source # show :: TyCon -> String Source # showList :: [TyCon] -> ShowS Source #
Eq TyCon |
Instance details Defined in GHC.Classes Methods (==) :: TyCon -> TyCon -> Bool Source # (/=) :: TyCon -> TyCon -> Bool Source #
Ord TyCon |
Instance details Defined in GHC.Classes 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 #

tyConPackage :: TyCon -> String Source #

tyConModule :: TyCon -> String Source #

tyConName :: TyCon -> String Source #

rnfTyCon :: TyCon -> () Source #

# Module names

data Module Source #

#### Instances

Instances details

Show Module Source # | Since: base-4.9.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Module -> ShowS Source # show :: Module -> String Source # showList :: [Module] -> ShowS Source #
Eq Module |
Instance details Defined in GHC.Classes Methods (==) :: Module -> Module -> Bool Source # (/=) :: Module -> Module -> Bool Source #

moduleName :: Module -> String Source #

modulePackage :: Module -> String Source #

rnfModule :: Module -> () Source #

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

Since: base-4.8.0.0