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

Symmetry of equality

Transitivity of equality

Type-safe cast, using propositional equality

Generalized form of type-safe cast using propositional equality

Apply one equality to another, respectively

Extract equality of the arguments from an equality of a applied types

Extract equality of type constructors from an equality of applied types

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.

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.