Combining pure and impure fragments

[mpickering]

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)