-
-
Save japesinator/e2f066112c920872124b to your computer and use it in GitHub Desktop.
Problems with Isos
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
class Profunctor (p : Type -> Type -> Type) where | |
dimap : (a -> b) -> (c -> d) -> p b c -> p a d | |
dimap f g = lmap f . rmap g | |
lmap : (a -> b) -> p b c -> p a c | |
lmap = flip dimap id | |
rmap : (a -> b) -> p c a -> p c b | |
rmap = dimap id | |
Iso : Profunctor p => Type -> Type -> Type -> Type -> Type | |
Iso {p} s t a b = p a b -> p s t | |
specialize : Profunctor q => ({p : _} -> Profunctor p => p a b -> p s t) -> q a b -> q s t | |
specialize f x = f x | |
record Forgotten r a b where | |
constructor Forget | |
runForget : a -> r | |
forwards : Profunctor p => Iso {p} s t a b -> s -> a | |
forwards {a} {b} {s} {t} i = runForget . fi $ Forget id where | |
fi : Forgotten a a b -> Forgotten a s t | |
fi = specialize i | |
record Tagged a b where | |
constructor Tag | |
runTagged : b | |
backwards : Profunctor p => Iso {p} s t a b -> b -> t | |
backwards {a} {b} {s} {t} i = runTagged . bi . Tag where | |
bi : Tagged a b -> Tagged s t | |
bi = specialize i | |
from : Profunctor p => Iso {p} s t a b -> Iso {p} b a t s | |
from i = dimap (backwards i) (forwards i) |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment