Generate natural transformations

[treeowl]

I want something like

data NT :: (Type -> Type) -> (Type -> Type) -> Type
appNT :: NT f g -> f a -> g a

and some way to generate arbitrary values of type NT f g. Any idea how this might be done?

[LightAndLight]

The first thing I'd try is a mechanical translation of https://github.com/qfpl/hedgehog-fn/blob/master/src/Hedgehog/Function/Internal.hs to work over objects of kind `* -> *`. The `Gen` type might present a difficulty if impredicativity (i.e. `Gen (forall x. T x)`) doesn't work, in which case `Gen1 :: (Type -> Type) -> Type` would also need to be written.

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On Tue, 27 Jul 2021, 4:49 am David Feuer, ***@***.***> wrote: I want something like data NT :: (Type -> Type) -> (Type -> Type) -> TypeappNT :: NT f g -> f a -> g a and some way to generate arbitrary values of type NT f g. Any idea how this might be done? — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#7>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AATLFOPBJLOEELNZOWHRN7LTZWU2HANCNFSM5BAVRWIQ> .

[treeowl]

The mechanism needs to be quite different, I think. I'm thinking specifically of containers of various sorts. There needs to be a Gen variant with a method that takes a list of values of the parameter type it can use to build the result. It doesn't/can't generate any of those on its own

[LightAndLight]

Does that mean something like: `fn1 :: (...) => (forall a. Gen a -> Gen (g a)) -> Gen x -> Gen (Fn1 f g x)`? (a la `Hedgehog.Function.fn`)

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On Tue, 27 Jul 2021, 8:22 am David Feuer, ***@***.***> wrote: The mechanism needs to be quite different, I think. I'm thinking specifically of containers of various sorts. There needs to be a Gen variant with a method that takes a list of values of the parameter type it can use to build the result. It doesn't/can't generate any of those on its own — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#7 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AATLFONFKHNYRULHFPBNJBLTZXN3RANCNFSM5BAVRWIQ> .