License | BSD-style (see the LICENSE file in the distribution) |
---|---|

Maintainer | libraries@haskell.org |

Stability | experimental |

Portability | not portable |

Safe Haskell | None |

Language | Haskell2010 |

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 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

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

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 k ((:~:) k a) |

type family a == b :: 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.

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 (==) (k -> k1) 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/7.10.3/docs/html/libraries/base-4.8.2.0/Data-Type-Equality.html