License	BSD-style (see the LICENSE file in the distribution)
Maintainer	libraries@haskell.org
Stability	experimental
Portability	not portable
Safe Haskell	None
Language	Haskell2010

Data.Type.Coercion (signature^[?])

Description

Definition of representational equality (Coercion).

Since: 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

Constructors

Coercion :: Coercible a b => Coercion a b

Instances

Category k (Coercion k) #	Since: 4.7.0.0
Methods id :: cat a a Source # (.) :: cat b c -> cat a b -> cat a c Source #
TestCoercion k (Coercion k a) #	Since: 4.7.0.0
Methods testCoercion :: f a -> f b -> Maybe (Coercion (Coercion k a) a b) Source #
Coercible k a b => Bounded (Coercion k a b) #	Since: 4.7.0.0
Methods minBound :: Coercion k a b Source # maxBound :: Coercion k a b Source #
Coercible k a b => Enum (Coercion k a b) #	Since: 4.7.0.0
Methods succ :: Coercion k a b -> Coercion k a b Source # pred :: Coercion k a b -> Coercion k a b Source # toEnum :: Int -> Coercion k a b Source # fromEnum :: Coercion k a b -> Int Source # enumFrom :: Coercion k a b -> [Coercion k a b] Source # enumFromThen :: Coercion k a b -> Coercion k a b -> [Coercion k a b] Source # enumFromTo :: Coercion k a b -> Coercion k a b -> [Coercion k a b] Source # enumFromThenTo :: Coercion k a b -> Coercion k a b -> Coercion k a b -> [Coercion k a b] Source #
Eq (Coercion k a b) #
Methods (==) :: Coercion k a b -> Coercion k a b -> Bool Source # (/=) :: Coercion k a b -> Coercion k a b -> Bool Source #
(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) Source # gunfold :: (forall c r. Data c => c (c -> 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 c. Data c => c -> c) -> 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 k a b) #
Methods compare :: Coercion k a b -> Coercion k a b -> Ordering Source # (<) :: Coercion k a b -> Coercion k a b -> Bool Source # (<=) :: Coercion k a b -> Coercion k a b -> Bool Source # (>) :: Coercion k a b -> Coercion k a b -> Bool Source # (>=) :: Coercion k a b -> Coercion k a b -> Bool Source # max :: Coercion k a b -> Coercion k a b -> Coercion k a b Source # min :: Coercion k a b -> Coercion k a b -> Coercion k a b Source #
Coercible k a b => Read (Coercion k a b) #	Since: 4.7.0.0
Methods readsPrec :: Int -> ReadS (Coercion k a b) Source # readList :: ReadS [Coercion k a b] Source # readPrec :: ReadPrec (Coercion k a b) Source # readListPrec :: ReadPrec [Coercion k a b] Source #
Show (Coercion k a b) #
Methods showsPrec :: Int -> Coercion k a b -> ShowS Source # show :: Coercion k a b -> String Source # showList :: [Coercion k a b] -> ShowS 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: 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 k (Coercion k a) #	Since: 4.7.0.0
Methods testCoercion :: f a -> f b -> Maybe (Coercion (Coercion k a) a b) Source #
TestCoercion k ((:~:) k a) #	Since: 4.7.0.0
Methods testCoercion :: f a -> f b -> Maybe (Coercion (k :~: a) a b) Source #
TestCoercion k ((:~~:) k1 k a) #	Since: 4.10.0.0
Methods testCoercion :: f a -> f b -> Maybe (Coercion ((k1 :~~: k) a) a b) Source #