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If we consider the staged power function, we observe a fundamental difficulty of writing programs polymorphic in their stage.

staticPower_s :: Syntax r => Int -> r Int -> r Int                              
staticPower_s n k = if n == 0                                                   
                                     then pure 1                                               
                                     else ([ k * (staticPower_s (n - 1) k) ])  

Notice that the conditional and scrutinee are both statically evaluated using the non-overloaded versions of if and ap.

However, we could also use the overloaded variants and then instantiate them to Identity. The hope being that this would provide a more uniform treatment.

staticPower_s :: Syntax r => Int -> r Int -> r Int                              
staticPower_s n k = runIdentity $ _if (pure (==) <*> pure n <*> pure 0)                                                   
                                         (pure (pure 1)                                               
                                         (pure ([ k * (staticPower_s (n - 1) k) ])) 

The type of the _if :: Identity Bool -> Identity (r Int) -> Identity (r Int) -> Identity (r Int)

At the moment any application is desugared to the _ap combinator. This seems like a good idea
but in practice it doesn't work very well as you end up writing pure (+) n (pure 1).

The "obvious" solution which is very hairy is to also automatically lift variables by wrapping them with pure.
The results of this can be seen on the https://github.com/mpickering/lift-plugin/tree/wrap branch. The problem here is that when you observe a variable x, how do we decide whether we want to lift it or not? If x :: r a then it is already lifted but what about x :: IO a, is that lifted? The implementation got very out of hand anyway with a very ad-hoc type checker plugin.

So, the solution here is to overload neither ap or pure and use idiom brackets when we want to overload either. The idiom bracket overloading is provided by Oleg's plugin which we just run at the start.
This is the only way which we overload ap and pure now at the expense of a slightly more verbose program.

Hi Matt!

I've just last night released Parsley onto hackage, and I was hoping to release my updated fork of the lift-plugin (along with the idioms-plugin, if Oleg is happy) together into a Parsley-specific bundle. Firstly, would you be ok with that (obviously fully acknowledged), and, if so, can you put the BSD-3-Clause License onto this repo so it's legal for me to do it?