Data.Type.Coercion

Definition of representational equality (Coercion).

Since: 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: 4.7.0.0

Constructors

Coercion :: Coercible a b => Coercion a b

Instances

Category k (Coercion k)

Since: 4.7.0.0

Methods

id :: cat a a

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

TestCoercion k (Coercion k a)

Since: 4.7.0.0

Methods

testCoercion :: f a -> f b -> Maybe (Coercion (Coercion k a) a b)

Coercible k a b => Bounded (Coercion k a b)

Since: 4.7.0.0

Methods

minBound :: Coercion k a b

maxBound :: Coercion k a b

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

Since: 4.7.0.0

Methods

succ :: Coercion k a b -> Coercion k a b

pred :: Coercion k a b -> Coercion k a b

toEnum :: Int -> Coercion k a b

fromEnum :: Coercion k a b -> Int

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

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

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

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

Eq (Coercion k a b)

Methods

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

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

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

Since: 4.7.0.0

Methods

gfoldl :: (forall d c. Data d => c (d -> c) -> d -> c c) -> (forall g. g -> c g) -> Coercion * a b -> c (Coercion * a b)

gunfold :: (forall c r. Data c => c (c -> 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 c. Data c => c -> c) -> 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 k a b)

Methods

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

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

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

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

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

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

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

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

Since: 4.7.0.0

Methods

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

readList :: ReadS [Coercion k a b]

readPrec :: ReadPrec (Coercion k a b)

readListPrec :: ReadPrec [Coercion k a b]

Show (Coercion k a b)

Methods

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

show :: Coercion k a b -> String

showList :: [Coercion k 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: 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 k (Coercion k a)

Since: 4.7.0.0

Methods

testCoercion :: f a -> f b -> Maybe (Coercion (Coercion k a) a b)

TestCoercion k ((:~:) k a)

Since: 4.7.0.0

Methods

testCoercion :: f a -> f b -> Maybe (Coercion (k :~: a) a b)

TestCoercion k ((:~~:) k1 k a)

Since: 4.10.0.0

Methods

testCoercion :: f a -> f b -> Maybe (Coercion ((k1 :~~: k) a) a b)