base-4.14.0.0: Basic libraries
LicenseBSD-style (see the LICENSE file in the distribution)
Maintainerlibraries@haskell.org
Stabilityexperimental
Portabilitynot portable
Safe HaskellNone
LanguageHaskell2010

Data.Type.Coercion

Description

Definition of representational equality (Coercion).

Since: base-4.7.0.0

Synopsis

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 4.7.0.0. Kind k explicitly quantified since 4.15.0.0.

Constructors

Coercion :: Coercible @k a b => Coercion @k a b 

Instances

Instances details
Category (Coercion :: k -> k -> Type) #

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) #

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 => Bounded (Coercion a b) #

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Coercion

Coercible a b => Enum (Coercion a b) #

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 #

Eq (Coercion a b) #

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 #

(Coercible a b, Data a, Data b) => Data (Coercion a b) #

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 #

Ord (Coercion a b) #

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 #

Coercible a b => Read (Coercion a b) #

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Coercion

Show (Coercion a b) #

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Coercion

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 :: k -> Type) 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.

Kind k explicitly quantified since 4.15.0.0.

Methods

testCoercion :: forall (a :: k) (b :: k). f a -> f b -> Maybe (Coercion @k a b) Source #

Conditionally prove the representational equality of a and b.

Instances

Instances details
TestCoercion (Coercion a :: k -> Type) #

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) #

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) #

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 #