type-equality-1: Data.Type.Equality compat package
Safe HaskellTrustworthy
LanguageHaskell2010

Data.Type.Equality.Hetero

Description

This module shims kind heterogeneous propositional equality.

Note: some instances: Read, Enum, Bounded and Data would be available only since GHC-8.0 as we need ~~ constraint. Also GH-7.10.3 is nitpicky data constructor ‘HRefl’ cannot be GADT-like in its *kind* arguments, thus this module is available only with GHC >= 8.0

Synopsis
  • data (a :: k1) :~~: (b :: k2) where

Documentation

data (a :: k1) :~~: (b :: k2) where infix 4 #

Kind heterogeneous propositional equality. Like :~:, a :~~: b is inhabited by a terminating value if and only if a is the same type as b.

Since: base-4.10.0.0

Constructors

HRefl :: forall {k1} (a :: k1). a :~~: a 

Instances

Instances details
Category ((:~~:) :: k -> k -> Type)

Since: base-4.10.0.0

Instance details

Defined in Control.Category

Methods

id :: forall (a :: k). a :~~: a #

(.) :: forall (b :: k) (c :: k) (a :: k). (b :~~: c) -> (a :~~: b) -> a :~~: c #

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

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) #

TestEquality ((:~~:) a :: k -> Type)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

testEquality :: forall (a0 :: k) (b :: k). (a :~~: a0) -> (a :~~: b) -> Maybe (a0 :~: b) #

(Typeable i, Typeable j, Typeable a, Typeable b, a ~~ b) => Data (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> (a :~~: b) -> c (a :~~: b) #

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

toConstr :: (a :~~: b) -> Constr #

dataTypeOf :: (a :~~: b) -> DataType #

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

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

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

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

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

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

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

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

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

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

a ~~ b => Bounded (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

minBound :: a :~~: b #

maxBound :: a :~~: b #

a ~~ b => Enum (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

succ :: (a :~~: b) -> a :~~: b #

pred :: (a :~~: b) -> a :~~: b #

toEnum :: Int -> a :~~: b #

fromEnum :: (a :~~: b) -> Int #

enumFrom :: (a :~~: b) -> [a :~~: b] #

enumFromThen :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] #

enumFromTo :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] #

enumFromThenTo :: (a :~~: b) -> (a :~~: b) -> (a :~~: b) -> [a :~~: b] #

a ~~ b => Read (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

readsPrec :: Int -> ReadS (a :~~: b) #

readList :: ReadS [a :~~: b] #

readPrec :: ReadPrec (a :~~: b) #

readListPrec :: ReadPrec [a :~~: b] #

Show (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

showsPrec :: Int -> (a :~~: b) -> ShowS #

show :: (a :~~: b) -> String #

showList :: [a :~~: b] -> ShowS #

Eq (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

(==) :: (a :~~: b) -> (a :~~: b) -> Bool #

(/=) :: (a :~~: b) -> (a :~~: b) -> Bool #

Ord (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

compare :: (a :~~: b) -> (a :~~: b) -> Ordering #

(<) :: (a :~~: b) -> (a :~~: b) -> Bool #

(<=) :: (a :~~: b) -> (a :~~: b) -> Bool #

(>) :: (a :~~: b) -> (a :~~: b) -> Bool #

(>=) :: (a :~~: b) -> (a :~~: b) -> Bool #

max :: (a :~~: b) -> (a :~~: b) -> a :~~: b #

min :: (a :~~: b) -> (a :~~: b) -> a :~~: b #