| 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 (~#) j k a b => (j ~~ k) a b
- 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
class (~#) j k a b => (j ~~ k) a b 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.
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 a 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 ((:~:) k a) # | |
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 k k1) a b # | |
| type (==) (k, k1) a b # | |
| type (==) (k, k1, k2) a b # | |
| type (==) (k, k1, k2, k3) a b # | |
| type (==) (k, k1, k2, k3, k4) a b # | |
| type (==) (k, k1, k2, k3, k4, k5) a b # | |
| type (==) (k, k1, k2, k3, k4, k5, k6) a b # | |
| type (==) (k, k1, k2, k3, k4, k5, k6, k7) a b # | |
| type (==) (k, k1, k2, k3, k4, k5, k6, k7, k8) a b # | |
| type (==) (k, k1, k2, k3, k4, k5, k6, k7, k8, k9) a b # | |
| type (==) (k, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10) a b # | |
| type (==) (k, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11) a b # | |
| type (==) (k, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12) a b # | |
| type (==) (k, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13) a b # | |
| type (==) (k, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14) a b # | |