MonadControlT is not the transitive closure of MonadControl

Prerequisites

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Description

The docstring of MonadControlT says that it's the transitive closure of MonadControl, but the types of MonadControl.restoreM and MonadControlT.restoreM are different. It's not clear to me why this is, and it's different from the relationship between MonadLiftT and MonadLift (whose fields are identical). I think this should either be clarified in the documentation or changed so that the types agree. I don't know what the intended behavior is here.

Context

I've been adding typeclasses for lawful MonadLift and MonadControl and was unable to implement

instance instLawfulMonadControlT.{u, v₁, v₂, v₃} (m : Type u → Type v₁) (n : Type u → Type v₂) (o : Type u → Type v₃)
  [Monad m] [Monad n] [Monad o] [LawfulMonad m] [LawfulMonad n] [LawfulMonad o]
  [MonadControl n o] [MonadControlT m n] [LawfulMonadControl n o] [LawfulMonadControlT m n]
    : LawfulMonadControlT m o

If the difference between the types of MonadControl.restoreM and MonadControlT.restoreM is intentional I would appreciate any suggestions on what the laws for MonadControlT should be.

I asked about this in a zulip thread.

Versions

[Output of #eval Lean.versionString]
4.3.0-rc1
[OS version]
Windows 11 Home, 10.0.22621 Build 22621

Impact

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Start by comparing the documented relationship and field types of MonadControl and MonadControlT, especially restoreM. Read the linked Zulip discussion for the unresolved intent, then determine whether the types should align or the documentation should explain the difference. Done means the intended behavior is decided and reflected consistently in the implementation or documentation.