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

Data.Type.Coercion

Description

Definition of representational equality (Coercion).

Since: base-4.7.0.0

Synopsis

data Coercion (a :: k) (b :: k) where
- Coercion :: forall {k} (a :: k) (b :: k). Coercible a b => Coercion a b
coerceWith :: Coercion a b -> a -> b
gcoerceWith :: forall {k} (a :: k) (b :: k) r. Coercion a b -> (Coercible a b => r) -> r
sym :: forall {k} (a :: k) (b :: k). Coercion a b -> Coercion b a
trans :: forall {k} (a :: k) (b :: k) (c :: k). Coercion a b -> Coercion b c -> Coercion a c
repr :: forall {k} (a :: k) (b :: k). (a :~: b) -> Coercion a b
class TestCoercion (f :: k -> Type) where
- testCoercion :: forall (a :: k) (b :: k). f a -> f b -> Maybe (Coercion a b)

Documentation

data Coercion (a :: k) (b :: k) 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 :: forall {k} (a :: k) (b :: k). Coercible a b => Coercion a b

Instances

Instances details

Category (Coercion :: k -> k -> Type) Source #	Since: base-4.7.0.0
Instance details Defined in Control.Category Methods id :: forall (a :: k). Coercion a a Source # (.) :: forall (b :: k) (c :: k) (a :: k). Coercion b c -> Coercion a b -> Coercion a c Source #
TestCoercion (Coercion a :: k -> Type) Source #	Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods testCoercion :: forall (a0 :: k) (b :: k). Coercion a a0 -> Coercion a b -> Maybe (Coercion a0 b) 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 :: 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 #
Coercible a b => Bounded (Coercion a b) Source #	Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods minBound :: Coercion a b Source # maxBound :: Coercion a b Source #
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 #
Coercible a b => Read (Coercion a b) Source #	Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods readsPrec :: Int -> ReadS (Coercion a b) Source # readList :: ReadS [Coercion a b] Source # readPrec :: ReadPrec (Coercion a b) Source # readListPrec :: ReadPrec [Coercion a b] Source #
Show (Coercion a b) Source #	Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods showsPrec :: Int -> Coercion a b -> ShowS Source # show :: Coercion a b -> String Source # showList :: [Coercion a b] -> ShowS Source #
Eq (Coercion a b) Source #	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 #
Ord (Coercion a b) Source #	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 #

coerceWith :: Coercion a b -> a -> b Source #

Type-safe cast, using representational equality

gcoerceWith :: forall {k} (a :: k) (b :: k) r. 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 :: forall {k} (a :: k) (b :: k). Coercion a b -> Coercion b a Source #

Symmetry of representational equality

trans :: forall {k} (a :: k) (b :: k) (c :: k). Coercion a b -> Coercion b c -> Coercion a c Source #

Transitivity of representational equality

repr :: forall {k} (a :: k) (b :: k). (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.

Methods

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

Conditionally prove the representational equality of a and b.

Instances

Instances details

TestCoercion SNat Source #	Since: base-4.18.0.0
Instance details Defined in GHC.TypeNats Methods testCoercion :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (Coercion a b) Source #
TestCoercion SChar Source #	Since: base-4.18.0.0
Instance details Defined in GHC.TypeLits Methods testCoercion :: forall (a :: Char) (b :: Char). SChar a -> SChar b -> Maybe (Coercion a b) Source #
TestCoercion SSymbol Source #	Since: base-4.18.0.0
Instance details Defined in GHC.TypeLits Methods testCoercion :: forall (a :: Symbol) (b :: Symbol). SSymbol a -> SSymbol b -> Maybe (Coercion a b) Source #
TestCoercion (Coercion a :: k -> Type) Source #	Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods testCoercion :: forall (a0 :: k) (b :: k). Coercion a a0 -> Coercion a b -> Maybe (Coercion a0 b) Source #
TestCoercion ((:~:) a :: k -> Type) Source #	Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods testCoercion :: forall (a0 :: k) (b :: k). (a :~: a0) -> (a :~: b) -> Maybe (Coercion a0 b) Source #
TestCoercion ((:~~:) a :: k -> Type) Source #	Since: base-4.10.0.0
Instance details Defined in Data.Type.Coercion Methods testCoercion :: forall (a0 :: k) (b :: k). (a :~~: a0) -> (a :~~: b) -> Maybe (Coercion a0 b) Source #