base-4.11.0.0: 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: base-4.7.0.0

Constructors

Coercion :: Coercible a b => Coercion a b 
Instances
Category (Coercion :: k -> k -> *) Source #

Since: base-4.7.0.0

Instance details

Defined in Control.Category

Methods

id :: Coercion a a Source #

(.) :: Coercion b c -> Coercion a b -> Coercion a c Source #

TestCoercion (Coercion a :: k -> *) Source #

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Coercion

Methods

testCoercion :: Coercion a a0 -> Coercion a b -> Maybe (Coercion a0 b) Source #

Coercible a b => Bounded (Coercion a b) Source #

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Coercion

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 #

Eq (Coercion a b) Source # 
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) 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 :: (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) Source # 
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) Source #

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Coercion

Show (Coercion a b) Source # 
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 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.

Minimal complete definition

testCoercion

Methods

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

Conditionally prove the representational equality of a and b.

Instances
TestCoercion (Coercion a :: k -> *) Source #

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Coercion

Methods

testCoercion :: Coercion a a0 -> Coercion a b -> Maybe (Coercion a0 b) Source #

TestCoercion ((:~:) a :: k -> *) Source #

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Coercion

Methods

testCoercion :: (a :~: a0) -> (a :~: b) -> Maybe (Coercion a0 b) Source #

TestCoercion ((:~~:) a :: k -> *) Source #

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Coercion

Methods

testCoercion :: (a :~~: a0) -> (a :~~: b) -> Maybe (Coercion a0 b) Source #