Data.Type.Equality
Data.Type.Equality
License | BSD-style (see the LICENSE file in the distribution) |
---|---|
Maintainer | libraries@haskell.org |
Stability | experimental |
Portability | not portable |
Safe Haskell | Trustworthy |
Language | Haskell2010 |
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
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: 4.7.0.0
Instances
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
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 a 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 k ((:~:) k a) | |
Boolean type-level equality
type family (a :: k) == (b :: k) :: Bool infix 4 Source
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 | |
© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.0.1/docs/html/libraries/base-4.9.0.0/Data-Type-Equality.html