License | BSD-style (see the LICENSE file in the distribution) |
---|---|
Maintainer | libraries@haskell.org |
Stability | experimental |
Portability | not portable |
Safe Haskell | Trustworthy |
Language | Haskell2010 |
Data.Type.Equality
Contents
Description
Definition of propositional equality (:~:)
. Pattern-matching on a variable
of type (a :~: b)
produces a proof that a ~ b
.
Since: base-4.7.0.0
Synopsis
- data a :~: b where
- class a ~# b => (a :: k0) ~~ (b :: k1)
- data (a :: k1) :~~: (b :: k2) where
- sym :: (a :~: b) -> b :~: a
- trans :: (a :~: b) -> (b :~: c) -> a :~: c
- castWith :: (a :~: b) -> a -> b
- gcastWith :: (a :~: b) -> (a ~ b => r) -> r
- apply :: (f :~: g) -> (a :~: b) -> f a :~: g b
- inner :: (f a :~: g b) -> a :~: b
- outer :: (f a :~: g b) -> f :~: g
- class TestEquality f where
- type family (a :: k) == (b :: k) :: Bool where ...
The equality types
data a :~: b where infix 4 Source #
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: base-4.7.0.0
Instances
Category ((:~:) :: k -> k -> *) Source # | Since: base-4.7.0.0 |
TestEquality ((:~:) a :: k -> *) Source # | Since: base-4.7.0.0 |
Defined in Data.Type.Equality | |
TestCoercion ((:~:) a :: k -> *) Source # | Since: base-4.7.0.0 |
Defined in Data.Type.Coercion | |
a ~ b => Bounded (a :~: b) Source # | Since: base-4.7.0.0 |
a ~ b => Enum (a :~: b) Source # | Since: base-4.7.0.0 |
Defined in Data.Type.Equality Methods succ :: (a :~: b) -> a :~: b Source # pred :: (a :~: b) -> a :~: b Source # toEnum :: Int -> a :~: b Source # fromEnum :: (a :~: b) -> Int Source # enumFrom :: (a :~: b) -> [a :~: b] Source # enumFromThen :: (a :~: b) -> (a :~: b) -> [a :~: b] Source # enumFromTo :: (a :~: b) -> (a :~: b) -> [a :~: b] Source # enumFromThenTo :: (a :~: b) -> (a :~: b) -> (a :~: b) -> [a :~: b] Source # | |
Eq (a :~: b) Source # | |
(a ~ b, Data a) => Data (a :~: b) Source # | Since: base-4.7.0.0 |
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) Source # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (a :~: b) Source # toConstr :: (a :~: b) -> Constr Source # dataTypeOf :: (a :~: b) -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (a :~: b)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (a :~: b)) Source # gmapT :: (forall b0. Data b0 => b0 -> b0) -> (a :~: b) -> a :~: b Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> (a :~: b) -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> (a :~: b) -> r Source # gmapQ :: (forall d. Data d => d -> u) -> (a :~: b) -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> (a :~: b) -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> (a :~: b) -> m (a :~: b) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> (a :~: b) -> m (a :~: b) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> (a :~: b) -> m (a :~: b) Source # | |
Ord (a :~: b) Source # | |
Defined in Data.Type.Equality | |
a ~ b => Read (a :~: b) Source # | Since: base-4.7.0.0 |
Show (a :~: b) Source # | |
class a ~# b => (a :: k0) ~~ (b :: k1) Source #
Lifted, heterogeneous equality. By lifted, we mean that it
can be bogus (deferred type error). By heterogeneous, the two
types a
and b
might have different kinds. Because ~~
can
appear unexpectedly in error messages to users who do not care
about the difference between heterogeneous equality ~~
and
homogeneous equality ~
, this is printed as ~
unless
-fprint-equality-relations
is set.
data (a :: k1) :~~: (b :: k2) where infix 4 Source #
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
Instances
Category ((:~~:) :: k -> k -> *) Source # | Since: base-4.10.0.0 |
TestEquality ((:~~:) a :: k -> *) Source # | Since: base-4.10.0.0 |
Defined in Data.Type.Equality | |
TestCoercion ((:~~:) a :: k -> *) Source # | Since: base-4.10.0.0 |
Defined in Data.Type.Coercion | |
a ~~ b => Bounded (a :~~: b) Source # | Since: base-4.10.0.0 |
a ~~ b => Enum (a :~~: b) Source # | Since: base-4.10.0.0 |
Defined in Data.Type.Equality Methods succ :: (a :~~: b) -> a :~~: b Source # pred :: (a :~~: b) -> a :~~: b Source # toEnum :: Int -> a :~~: b Source # fromEnum :: (a :~~: b) -> Int Source # enumFrom :: (a :~~: b) -> [a :~~: b] Source # enumFromThen :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] Source # enumFromTo :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] Source # enumFromThenTo :: (a :~~: b) -> (a :~~: b) -> (a :~~: b) -> [a :~~: b] Source # | |
Eq (a :~~: b) Source # | Since: base-4.10.0.0 |
(Typeable i, Typeable j, Typeable a, Typeable b, a ~~ b) => Data (a :~~: b) Source # | Since: base-4.10.0.0 |
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) Source # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (a :~~: b) Source # toConstr :: (a :~~: b) -> Constr Source # dataTypeOf :: (a :~~: b) -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (a :~~: b)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (a :~~: b)) Source # gmapT :: (forall b0. Data b0 => b0 -> b0) -> (a :~~: b) -> a :~~: b Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> (a :~~: b) -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> (a :~~: b) -> r Source # gmapQ :: (forall d. Data d => d -> u) -> (a :~~: b) -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> (a :~~: b) -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> (a :~~: b) -> m (a :~~: b) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> (a :~~: b) -> m (a :~~: b) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> (a :~~: b) -> m (a :~~: b) Source # | |
Ord (a :~~: b) Source # | Since: base-4.10.0.0 |
Defined in Data.Type.Equality Methods compare :: (a :~~: b) -> (a :~~: b) -> Ordering Source # (<) :: (a :~~: b) -> (a :~~: b) -> Bool Source # (<=) :: (a :~~: b) -> (a :~~: b) -> Bool Source # (>) :: (a :~~: b) -> (a :~~: b) -> Bool Source # (>=) :: (a :~~: b) -> (a :~~: b) -> Bool Source # | |
a ~~ b => Read (a :~~: b) Source # | Since: base-4.10.0.0 |
Show (a :~~: b) Source # | Since: base-4.10.0.0 |
Working with equality
gcastWith :: (a :~: b) -> (a ~ b => r) -> r Source #
Generalized form of type-safe cast using propositional equality
inner :: (f a :~: g b) -> a :~: b Source #
Extract equality of the arguments from an equality of applied types
outer :: (f a :~: g b) -> f :~: g Source #
Extract equality of type constructors from an equality of applied types
Inferring equality from other types
class TestEquality 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
Methods
testEquality :: f a -> f b -> Maybe (a :~: b) Source #
Conditionally prove the equality of a
and b
.
Instances
TestEquality (TypeRep :: k -> *) Source # | |
Defined in Data.Typeable.Internal | |
TestEquality ((:~:) a :: k -> *) Source # | Since: base-4.7.0.0 |
Defined in Data.Type.Equality | |
TestEquality ((:~~:) a :: k -> *) Source # | Since: base-4.10.0.0 |
Defined in Data.Type.Equality |