Data.Type.Coercion

Definition of representational equality (Coercion).

Since: base-4.7.0.0

Documentation

data Coercion a b where

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 -> *)

Since: base-4.7.0.0

Defined in Control.Category

Methods

id :: Coercion a a

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

TestCoercion (Coercion a :: k -> *)

Since: base-4.7.0.0

Defined in Data.Type.Coercion

Methods

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

Coercible a b => Bounded (Coercion a b)

Since: base-4.7.0.0

Defined in Data.Type.Coercion

Methods

minBound :: Coercion a b

maxBound :: Coercion a b

Coercible a b => Enum (Coercion a b)

Since: base-4.7.0.0

Defined in Data.Type.Coercion

Methods

succ :: Coercion a b -> Coercion a b

pred :: Coercion a b -> Coercion a b

toEnum :: Int -> Coercion a b

fromEnum :: Coercion a b -> Int

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

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

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

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

Eq (Coercion a b)

Defined in Data.Type.Coercion

Methods

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

(/=) :: Coercion a b -> Coercion a b -> Bool

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

Since: base-4.7.0.0

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)

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

toConstr :: Coercion a b -> Constr

dataTypeOf :: Coercion a b -> DataType

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

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

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

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

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

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

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

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

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

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

Ord (Coercion a b)

Defined in Data.Type.Coercion

Methods

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

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

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

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

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

max :: Coercion a b -> Coercion a b -> Coercion a b

min :: Coercion a b -> Coercion a b -> Coercion a b

Coercible a b => Read (Coercion a b)

Since: base-4.7.0.0

Defined in Data.Type.Coercion

Methods

readsPrec :: Int -> ReadS (Coercion a b)

readList :: ReadS [Coercion a b]

readPrec :: ReadPrec (Coercion a b)

readListPrec :: ReadPrec [Coercion a b]

Show (Coercion a b)

Defined in Data.Type.Coercion

Methods

showsPrec :: Int -> Coercion a b -> ShowS

show :: Coercion a b -> String

showList :: [Coercion a b] -> ShowS

coerceWith :: Coercion a b -> a -> b

Type-safe cast, using representational equality

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

Generalized form of type-safe cast using representational equality

Since: base-4.10.0.0

sym :: Coercion a b -> Coercion b a

Symmetry of representational equality

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

Transitivity of representational equality

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

Convert propositional (nominal) equality to representational equality

class TestCoercion f where

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)

Conditionally prove the representational equality of a and b.

Instances

TestCoercion (Coercion a :: k -> *)

Since: base-4.7.0.0

Defined in Data.Type.Coercion

Methods

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

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

Since: base-4.7.0.0

Defined in Data.Type.Coercion

Methods

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

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

Since: base-4.10.0.0

Defined in Data.Type.Coercion

Methods

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