Is there a shorthand for operations like `fromNewtype . f . toNewtype`?

A pattern that presents itself the more often the more type safety is being introduced via newtype is to project a value (or several values) to a newtype wrapper, do some operations, and then retract the projection. An ubiquitous example is that of Sum and Product monoids:

λ x + y = getSum $ Sum x `mappend` Sum y
λ 1 + 2
3

I imagine a collection of functions like withSum, withSum2, and so on, may be automagically rolled out for each newtype. Or maybe a parametrized Identity may be created, for use with ApplicativeDo. Or maybe there are some other approaches that I could not think of.

I wonder if there is some prior art or theory around this.

P.S. I am unhappy with coerce, for two reasons:

safety I thought it is not very safe. After being pointed that it is actually safe, I tried a few things and I could not do anything harmful, because it requires a type annotation when there is a possibility of ambiguity. For example:
```
λ newtype F = F Int deriving Show
λ newtype G = G Int deriving Show
λ coerce . (mappend (1 :: Sum Int)) . coerce $ F 1 :: G
G 2
λ coerce . (mappend (1 :: Product Int)) . coerce $ F 1 :: G
G 1
λ coerce . (mappend 1) . coerce $ F 1 :: G
...
    • Couldn't match representation of type ‘a0’ with that of ‘Int’
        arising from a use of ‘coerce’
...
```
But I would still not welcome coerce, because it is far too easy to strip a safety label and shoot someone, once the reaching for it becomes habitual. Imagine that, in a cryptographic application, there are two values: x :: Prime Int and x' :: Sum Int. I would much rather type getPrime and getSum every time I use them, than coerce everything and have one day made a catastrophic mistake.
usefulness coerce does not bring much to the table regarding a shorthand for certain operations. The leading example of my post, that I repeat here:
```
λ getSum $ Sum 1 `mappend` Sum 2
3
```
— Turns into something along the lines of this spiked monster:
```
λ coerce $ mappend @(Sum Integer) (coerce 1) (coerce 2) :: Integer
3
```
— Which is hardly of any benfit.

Solution

Your "spiked monster" example is better handled by putting the summands into a list and using the ala function available here, which has type:

ala :: (Coercible a b, Coercible a' b') 
    => (a -> b) 
    -> ((a -> b) -> c -> b')   
    -> c 
    -> a'

where

a is the unwrapped base type.
b is the newtype that wraps a.
a -> b is the newtype constructor.
((a -> b) -> c -> b') is a function that, knowing how to wrap values of the base type a, knows how to process a value of type c (almost always a container of as) and return a wrapped result b'. In practice this function is almost always foldMap.
a' the unwrapped final result. The unwrapping is handled by ala itself.

in your case, it would be something like:

ala Sum foldMap [1,2::Integer]

"ala" functions can be implemented through means other than coerce, for example using generics to handle the unwrapping, or even lenses.