| License | BSD-style (see the LICENSE file in the distribution) |
|---|---|
| Maintainer | [email protected] |
| Stability | experimental |
| Portability | not portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
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
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
| Category ((:~:) :: k -> k -> Type) | Since: base-4.7.0.0 |
| TestEquality ((:~:) a :: k -> Type) | Since: base-4.7.0.0 |
Defined in Data.Type.Equality | |
| TestCoercion ((:~:) a :: k -> Type) | Since: base-4.7.0.0 |
Defined in Data.Type.Coercion | |
| a ~ b => Bounded (a :~: b) | Since: base-4.7.0.0 |
| a ~ b => Enum (a :~: b) | Since: base-4.7.0.0 |
Defined in Data.Type.Equality Methodssucc :: (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) | Since: base-4.7.0.0 |
| (a ~ b, Data a) => Data (a :~: b) | Since: base-4.7.0.0 |
Defined in Data.Data Methodsgfoldl :: (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) | Since: base-4.7.0.0 |
Defined in Data.Type.Equality | |
| a ~ b => Read (a :~: b) | Since: base-4.7.0.0 |
| Show (a :~: b) | Since: base-4.7.0.0 |
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
| Category ((:~~:) :: k -> k -> Type) | Since: base-4.10.0.0 |
| TestEquality ((:~~:) a :: k -> Type) | Since: base-4.10.0.0 |
Defined in Data.Type.Equality | |
| TestCoercion ((:~~:) a :: k -> Type) | Since: base-4.10.0.0 |
Defined in Data.Type.Coercion | |
| a ~~ b => Bounded (a :~~: b) | Since: base-4.10.0.0 |
| a ~~ b => Enum (a :~~: b) | Since: base-4.10.0.0 |
Defined in Data.Type.Equality Methodssucc :: (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) | Since: base-4.10.0.0 |
| (Typeable i, Typeable j, Typeable a, Typeable b, a ~~ b) => Data (a :~~: b) | Since: base-4.10.0.0 |
Defined in Data.Data Methodsgfoldl :: (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) | Since: base-4.10.0.0 |
Defined in Data.Type.Equality Methodscompare :: (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) | Since: base-4.10.0.0 |
| Show (a :~~: b) | Since: base-4.10.0.0 |
sym :: (a :~: b) -> b :~: a Source
Symmetry of equality
trans :: (a :~: b) -> (b :~: c) -> a :~: c Source
Transitivity of equality
castWith :: (a :~: b) -> a -> b Source
Type-safe cast, using propositional equality
gcastWith :: (a :~: b) -> (a ~ b => r) -> r Source
Generalized form of type-safe cast using propositional equality
apply :: (f :~: g) -> (a :~: b) -> f a :~: g b Source
Apply one equality to another, respectively
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
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.
testEquality :: f a -> f b -> Maybe (a :~: b) Source
Conditionally prove the equality of a and b.
| TestEquality (TypeRep :: k -> Type) | |
Defined in Data.Typeable.Internal | |
| TestEquality ((:~:) a :: k -> Type) | Since: base-4.7.0.0 |
Defined in Data.Type.Equality | |
| TestEquality ((:~~:) a :: k -> Type) | Since: base-4.10.0.0 |
Defined in Data.Type.Equality | |
type family (a :: k) == (b :: k) :: Bool where ... infix 4 Source
A type family to compute Boolean equality.
© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.6.1/docs/html/libraries/base-4.12.0.0/Data-Type-Equality.html