| 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: 4.7.0.0
- data a :~: b where
- class (~#) k0 k1 a b => (k0 ~~ k1) (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
The equality types
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
Instances
| Category k ((:~:) k) # | Since: 4.7.0.0 |
| TestEquality k ((:~:) k a) # | Since: 4.7.0.0 |
| TestCoercion k ((:~:) k a) # | Since: 4.7.0.0 |
| (~) k a b => Bounded ((:~:) k a b) # | Since: 4.7.0.0 |
| (~) k a b => Enum ((:~:) k a b) # | Since: 4.7.0.0 |
| Eq ((:~:) k a b) # | |
| ((~) * a b, Data a) => Data ((:~:) * a b) # | Since: 4.7.0.0 |
| Ord ((:~:) k a b) # | |
| (~) k a b => Read ((:~:) k a b) # | Since: 4.7.0.0 |
| Show ((:~:) k a b) # | |
class (~#) k0 k1 a b => (k0 ~~ k1) (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 #
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: 4.10.0.0
Instances
| Category k ((:~~:) k k) # | Since: 4.10.0.0 |
| TestEquality k ((:~~:) k1 k a) # | Since: 4.10.0.0 |
| TestCoercion k ((:~~:) k1 k a) # | Since: 4.10.0.0 |
| (~~) k1 k2 a b => Bounded ((:~~:) k1 k2 a b) # | Since: 4.10.0.0 |
| (~~) k1 k2 a b => Enum ((:~~:) k1 k2 a b) # | Since: 4.10.0.0 |
| Eq ((:~~:) k1 k2 a b) # | Since: 4.10.0.0 |
| (Typeable * i2, Typeable * j2, Typeable i2 a, Typeable j2 b, (~~) i2 j2 a b) => Data ((:~~:) i2 j2 a b) # | Since: 4.10.0.0 |
| Ord ((:~~:) k1 k2 a b) # | Since: 4.10.0.0 |
| (~~) k1 k2 a b => Read ((:~~:) k1 k2 a b) # | Since: 4.10.0.0 |
| Show ((:~~:) k1 k2 a b) # | Since: 4.10.0.0 |
Working with equality
gcastWith :: (a :~: b) -> (a ~ b => r) -> r #
Generalized form of type-safe cast using propositional equality
inner :: (f a :~: g b) -> a :~: b #
Extract equality of the arguments from an equality of applied types
outer :: (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 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.
Minimal complete definition
Instances
| TestEquality k (TypeRep k) # | |
| TestEquality k ((:~:) k a) # | Since: 4.7.0.0 |
| TestEquality k ((:~~:) k1 k a) # | Since: 4.10.0.0 |
Boolean type-level equality
type family (a :: k) == (b :: k) :: Bool infix 4 #
A type family to compute Boolean equality. Instances are provided
only for open kinds, such as * and function kinds. Instances are
also provided for datatypes exported from base. A poly-kinded instance
is not provided, as a recursive definition for algebraic kinds is
generally more useful.
Instances
| type (==) Bool a b # | |
| type (==) Ordering a b # | |
| type (==) * a b # | |
| type (==) Nat a b # | |
| type (==) Symbol a b # | |
| type (==) () a b # | |
| type (==) [k] a b # | |
| type (==) (Maybe k) a b # | |
| type (==) (k1 -> k2) a b # | |
| type (==) (Either k1 k2) a b # | |
| type (==) (k1, k2) a b # | |
| type (==) (k1, k2, k3) a b # | |
| type (==) (k1, k2, k3, k4) a b # | |
| type (==) (k1, k2, k3, k4, k5) a b # | |
| type (==) (k1, k2, k3, k4, k5, k6) a b # | |
| type (==) (k1, k2, k3, k4, k5, k6, k7) a b # | |
| type (==) (k1, k2, k3, k4, k5, k6, k7, k8) a b # | |
| type (==) (k1, k2, k3, k4, k5, k6, k7, k8, k9) a b # | |
| type (==) (k1, k2, k3, k4, k5, k6, k7, k8, k9, k10) a b # | |
| type (==) (k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11) a b # | |
| type (==) (k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12) a b # | |
| type (==) (k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13) a b # | |
| type (==) (k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14) a b # | |
| type (==) (k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15) a b # | |