How to specify non-zippy applicatives like []?

[johannes-riecken]

I'm having trouble understanding how I'd specify the instances for data types that are free monads, where applicative operations result in cartesian products of their arguments. Examples would be the list type [] or also the main data type from algebraic-graphs, which is a bit more interesting for having multiple sums:

data Graph a = Empty | Vertex a | Overlay (Graph a) (Graph a) | Connect (Graph a) (Graph a)

This data type is isomorphic to

type Graph' = FreeT
    {- f -} (Product Identity Identity)
    {- m -} (FreeT
        {- f -} (Product Identity Identity)
        {- m -} (MaybeT Identity))

and has an equivalent Applicative instance.

[Icelandjack]

You might be interested in https://www.reddit.com/r/haskell/comments/wyg656/can_the_free_monad_be_deconstructed_as_the_sum_of/, it's likely not possible without adding new features to the library