Data.Eq.Type

Leibnizian equality. Injectivity in the presence of type families is provided by a generalization of a trick by Oleg Kiselyv posted here:

http://www.haskell.org/pipermail/haskell-cafe/2010-May/077177.html

Documentation

data a := b

Constructors

Refl

Fields

subst :: forall c. c a -> c b

Instances

Category :=

refl :: a := a

trans :: (a := b) -> (b := c) -> a := c

symm :: (a := b) -> b := a

coerce :: (a := b) -> a -> b

lift :: (a := b) -> f a := f b

lift2 :: (a := b) -> f a c := f b c

lift2' :: (a := b) -> (c := d) -> f a c := f b d

lift3 :: (a := b) -> f a c d := f b c d

lift3' :: (a := b) -> (c := d) -> (e := f) -> g a c e := g b d f

lower :: (f a := f b) -> a := b

lower2 :: (f a c := f b c) -> a := b

lower3 :: (f a c d := f b c d) -> a := b