| Safe Haskell | Trustworthy |
|---|---|
| Language | Haskell2010 |
Data.Type.Equality.Compat
Synopsis
- data (a :: k) :~: (b :: k) where
- class a ~# b => (a :: k0) ~~ (b :: k1)
- data (a :: k1) :~~: (b :: k2) where
- sym :: forall {k} (a :: k) (b :: k). (a :~: b) -> b :~: a
- trans :: forall {k} (a :: k) (b :: k) (c :: k). (a :~: b) -> (b :~: c) -> a :~: c
- castWith :: (a :~: b) -> a -> b
- gcastWith :: forall {k} (a :: k) (b :: k) r. (a :~: b) -> (a ~ b => r) -> r
- apply :: forall {k1} {k2} (f :: k1 -> k2) (g :: k1 -> k2) (a :: k1) (b :: k1). (f :~: g) -> (a :~: b) -> f a :~: g b
- inner :: forall {k1} {k2} (f :: k1 -> k2) (a :: k1) (g :: k1 -> k2) (b :: k1). (f a :~: g b) -> a :~: b
- outer :: forall {k1} {k2} (f :: k1 -> k2) (a :: k1) (g :: k1 -> k2) (b :: k1). (f a :~: g b) -> f :~: g
- class TestEquality (f :: k -> Type) where
- testEquality :: forall (a :: k) (b :: k). f a -> f b -> Maybe (a :~: b)
- type family (a :: k) == (b :: k) :: Bool where ...
The equality types
data (a :: k) :~: (b :: k) where infix 4 #
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
| TestCoercion ((:~:) a :: k -> Type) | Since: base-4.7.0.0 |
Defined in Data.Type.Coercion | |
| TestEquality ((:~:) a :: k -> Type) | Since: base-4.7.0.0 |
Defined in Data.Type.Equality | |
| 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 Methods succ :: (a :~: b) -> a :~: b # pred :: (a :~: b) -> 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-4.7.0.0 |
| Show (a :~: b) | Since: base-4.7.0.0 |
| Eq (a :~: b) | Since: base-4.7.0.0 |
| Ord (a :~: b) | Since: base-4.7.0.0 |
Defined in Data.Type.Equality | |
class a ~# b => (a :: k0) ~~ (b :: k1) infix 4 #
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.
In 0.7.0, the fixity was set to infix 4 to match the fixity of :~~:.
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
Instances
| TestCoercion ((:~~:) a :: k -> Type) | Since: base-4.10.0.0 |
Defined in Data.Type.Coercion | |
| TestEquality ((:~~:) a :: k -> Type) | Since: base-4.10.0.0 |
Defined in Data.Type.Equality | |
| 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 Methods succ :: (a :~~: b) -> a :~~: b # pred :: (a :~~: b) -> 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 |
| Show (a :~~: b) | Since: base-4.10.0.0 |
| Eq (a :~~: b) | Since: base-4.10.0.0 |
| Ord (a :~~: b) | Since: base-4.10.0.0 |
Working with equality
trans :: forall {k} (a :: k) (b :: k) (c :: k). (a :~: b) -> (b :~: c) -> a :~: c #
Transitivity of equality
gcastWith :: forall {k} (a :: k) (b :: k) r. (a :~: b) -> (a ~ b => r) -> r #
Generalized form of type-safe cast using propositional equality
apply :: forall {k1} {k2} (f :: k1 -> k2) (g :: k1 -> k2) (a :: k1) (b :: k1). (f :~: g) -> (a :~: b) -> f a :~: g b #
Apply one equality to another, respectively
inner :: forall {k1} {k2} (f :: k1 -> k2) (a :: k1) (g :: k1 -> k2) (b :: k1). (f a :~: g b) -> a :~: b #
Extract equality of the arguments from an equality of applied types
outer :: forall {k1} {k2} (f :: k1 -> k2) (a :: k1) (g :: k1 -> k2) (b :: k1). (f a :~: g b) -> f :~: g #
Extract equality of type constructors from an equality of applied types
Inferring equality from other types
class TestEquality (f :: k -> Type) where #
This class contains types where you can learn the equality of two types from information contained in terms.
The result should be Just Refl if and only if the types applied to f are
equal:
testEquality (x :: f a) (y :: f b) = Just Refl ⟺ a = b
Typically, only singleton types should inhabit this class. In that case type argument equality coincides with term equality:
testEquality (x :: f a) (y :: f b) = Just Refl ⟺ a = b ⟺ x = y
isJust (testEquality x y) = x == y
Singleton types are not required, however, and so the latter two would-be laws are not in fact valid in general.
Methods
testEquality :: forall (a :: k) (b :: k). f a -> f b -> Maybe (a :~: b) #
Conditionally prove the equality of a and b.
Instances
| 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 | |
| TestEquality f => TestEquality (Compose f g :: k2 -> Type) | The deduction (via generativity) that if Since: base-4.14.0.0 |
Defined in Data.Functor.Compose | |