base-4.18.1.0: Basic libraries

License | BSD-style (see the LICENSE file in the distribution)
Maintainer | libraries@haskell.org
Stability | stable
Portability | not portable
Safe Haskell | Safe-Inferred
Language | Haskell2010

Data.Type.Coercion

Description

Definition of representational equality (`Coercion`).

Since: base-4.7.0.0

Synopsis

- data Coercion a b where
  - Coercion :: Coercible a b => Coercion a b
- coerceWith :: Coercion a b -> a -> b
- gcoerceWith :: Coercion a b -> (Coercible a b => r) -> r
- sym :: Coercion a b -> Coercion b a
- trans :: Coercion a b -> Coercion b c -> Coercion a c
- repr :: (a :~: b) -> Coercion a b
- class TestCoercion f where
  - testCoercion :: f a -> f b -> Maybe (Coercion a b)

# Documentation

data Coercion a b where Source #

Representational equality. If `Coercion a b` is inhabited by some terminating value, then the type `a` has the same underlying representation as the type `b`.

To use this equality in practice, pattern-match on the `Coercion a b` to get out the `Coercible a b` instance, and then use `coerce` to apply it.

Since: base-4.7.0.0

Constructors

Coercion :: Coercible a b => Coercion a b |

#### Instances

Instances details

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

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

toConstr :: Coercion a b -> Constr Source #

dataTypeOf :: Coercion a b -> DataType Source #

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

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

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

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

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

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

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

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

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

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

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

Instance details

Defined in Data.Type.Coercion

Methods

succ :: Coercion a b -> Coercion a b Source #

pred :: Coercion a b -> Coercion a b Source #

toEnum :: Int -> Coercion a b Source #

fromEnum :: Coercion a b -> Int Source #

enumFrom :: Coercion a b -> [Coercion a b] Source #

enumFromThen :: Coercion a b -> Coercion a b -> [Coercion a b] Source #

enumFromTo :: Coercion a b -> Coercion a b -> [Coercion a b] Source #

enumFromThenTo :: Coercion a b -> Coercion a b -> Coercion a b -> [Coercion a b] Source #

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

Instance details

Defined in Data.Type.Coercion

Methods

compare :: Coercion a b -> Coercion a b -> Ordering Source #

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

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

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

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

max :: Coercion a b -> Coercion a b -> Coercion a b Source #

min :: Coercion a b -> Coercion a b -> Coercion a b Source #

coerceWith :: Coercion a b -> a -> b Source #

Type-safe cast, using representational equality

gcoerceWith :: Coercion a b -> (Coercible a b => r) -> r Source #

Generalized form of type-safe cast using representational equality

Since: base-4.10.0.0

sym :: Coercion a b -> Coercion b a Source #

Symmetry of representational equality

trans :: Coercion a b -> Coercion b c -> Coercion a c Source #

Transitivity of representational equality

repr :: (a :~: b) -> Coercion a b Source #

Convert propositional (nominal) equality to representational equality

class TestCoercion f where Source #

This class contains types where you can learn the equality of two types from information contained in terms. Typically, only singleton types should inhabit this class.

Methods

testCoercion :: f a -> f b -> Maybe (Coercion a b) Source #

Conditionally prove the representational equality of `a` and `b`.

#### Instances

Instances details

TestCoercion SNat Source # | Since: base-4.18.0.0
Instance details Defined in GHC.TypeNats Methods testCoercion :: forall (a :: k) (b :: k). SNat a -> SNat b -> Maybe (Coercion a b) Source #
TestCoercion SChar Source # | Since: base-4.18.0.0
Instance details Defined in GHC.TypeLits Methods testCoercion :: forall (a :: k) (b :: k). SChar a -> SChar b -> Maybe (Coercion a b) Source #
TestCoercion SSymbol Source # | Since: base-4.18.0.0
Instance details Defined in GHC.TypeLits Methods testCoercion :: forall (a :: k) (b :: k). SSymbol a -> SSymbol b -> Maybe (Coercion a b) Source #
TestCoercion (Coercion a :: k -> Type) Source # | Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods testCoercion :: forall (a0 :: k0) (b :: k0). Coercion a a0 -> Coercion a b -> Maybe (Coercion a0 b) 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 #
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 #