Propositional equality. If a :~: b is inhabited by some terminating value, then the type a is the same as the type b. To use this equality in practice, pattern-match on the a :~: b to get out the Refl constructor; in the body of the pattern-match, the compiler knows that a ~ b.

Since: 4.7.0.0

Constructors

Refl :: (:~:) k a a

Instances

TestEquality k ((:~:) k a)
Methods testEquality :: f a -> f b -> Maybe (((k :~: a) :~: a) b) #
(Rep a, Rep b, Sat (ctx a), Sat (ctx b)) => Rep1 ctx ((:~:) * a b) Source #
Methods rep1 :: R1 ctx ((* :~: a) b) Source #
(~) k a b => Bounded ((:~:) k a b)
Methods minBound :: (k :~: a) b # maxBound :: (k :~: a) b #
(~) k a b => Enum ((:~:) k a b)
Methods succ :: (k :~: a) b -> (k :~: a) b # pred :: (k :~: a) b -> (k :~: a) b # toEnum :: Int -> (k :~: a) b # fromEnum :: (k :~: a) b -> Int # enumFrom :: (k :~: a) b -> [(k :~: a) b] # enumFromThen :: (k :~: a) b -> (k :~: a) b -> [(k :~: a) b] # enumFromTo :: (k :~: a) b -> (k :~: a) b -> [(k :~: a) b] # enumFromThenTo :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b -> [(k :~: a) b] #
Eq ((:~:) k a b)
Methods (==) :: (k :~: a) b -> (k :~: a) b -> Bool # (/=) :: (k :~: a) b -> (k :~: a) b -> Bool #
((~) * a b, Data a) => Data ((:~:) * a b)
Methods gfoldl :: (forall d c. Data d => c (d -> c) -> d -> c c) -> (forall g. g -> c g) -> (* :~: a) b -> c ((* :~: a) b) # gunfold :: (forall c r. Data c => c (c -> 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 c. Data c => c -> c) -> (* :~: a) b -> (* :~: a) b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> (* :~: a) b -> r # gmapQr :: (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) #
Ord ((:~:) k a b)
Methods compare :: (k :~: a) b -> (k :~: a) b -> Ordering # (<) :: (k :~: a) b -> (k :~: a) b -> Bool # (<=) :: (k :~: a) b -> (k :~: a) b -> Bool # (>) :: (k :~: a) b -> (k :~: a) b -> Bool # (>=) :: (k :~: a) b -> (k :~: a) b -> Bool # max :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b # min :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b #
(~) k a b => Read ((:~:) k a b)
Methods readsPrec :: Int -> ReadS ((k :~: a) b) # readList :: ReadS [(k :~: a) b] # readPrec :: ReadPrec ((k :~: a) b) # readListPrec :: ReadPrec [(k :~: a) b] #
Show ((:~:) k a b)
Methods showsPrec :: Int -> (k :~: a) b -> ShowS # show :: (k :~: a) b -> String # showList :: [(k :~: a) b] -> ShowS #
(Rep a, Rep b) => Rep ((:~:) * a b) Source #
Methods rep :: R ((* :~: a) b) Source #

class TestEquality k 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.

Instances

TestEquality k ((:~:) k a)
Methods testEquality :: f a -> f b -> Maybe (((k :~: a) :~: a) b) #