Add with_inverse(f, x)?

[oschulz]

Maybe we should add an interface y, inverse_f = with_inverse(f, x), to support use cases that can't generate an inverse function without x (like a generic flatten-to-real-vector function, see JuliaGaussianProcesses/ParameterHandling.jl#43).

The default implementation would simply be

with_inverse(f, x) = f(x), inverse(f)

so it wouldn't make InverseFunctions noticeably heavier.

[devmotion]

I think it would be good to see some concrete implementations for ParameterHandling and one or two other packages first. This would make it easier to evaluate its usefulness and potential problems.

[oschulz]

I think it would be good to see some concrete implementations for ParameterHandling and one or two other packages first.

You mean implement a with_inverse-equivalent internally there, first?

[devmotion]

Yes, or implement with_inverse in a branch in these packages. Just to figure any problems and requirements of these concrete implementations and differences between different packages.

[oschulz]

Oh, sure, makes sense.

[aplavin]

Looks like this functionality is already present in Accessors.
With the same notation as the OP:

with_inverse(f, x) = f(x), y -> set(x, f, y)

f = @optic exp(_.field[2])  # just an example f
y, inverse_f = with_inverse(f, x)

Of course, defining this with_inverse function isn't actually needed, one would just use set(...) as needed.
set is also not as ambiguous as with_inverse: different meanings could potentially be assigned to the latter, see eg #25 (comment).

[oschulz]

Thanks @aplavin - I guess we should close this for now, then, until use cases come up that really can't separate forward and inverse calculation without significant overhead.