Created
September 19, 2021 04:56
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| module Mappers | |
| data Identity a = MkIdentity a | |
| Functor Identity where | |
| map f (MkIdentity x) = MkIdentity (f x) | |
| repapply : Nat -> (a -> a) -> (a -> a) | |
| repapply Z f = id | |
| repapply (S k) f = f . repapply k f | |
| mapND : Functor f => (n: Nat) -> (a -> b) -> (repapply n f $ a) -> (repapply n f $ b) | |
| mapND 0 g x = g x | |
| mapND 1 g x = map g x | |
| mapND (S k) g x = (map . mapND k) g x |
Ok! Maybe this is a nicer/smaller version:
module Mappers
repapply : Nat -> (a -> a) -> (a -> a)
repapply Z f = id
repapply (S k) f = f . repapply k f
mapND : Functor f => (n: Nat) -> (a -> b) -> (repapply n f $ a) -> (repapply n f $ b)
mapND 0 g = g
mapND (S k) g = (map . mapND k) g
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Ooh, whoops, I shouldn't have specified {f=Identity} there, I think you can specify whatever you want! It's just that the type checker can't guess it for you, so you have to manually specify the implicit "forall Functor f." part.