I agree that your definition of free will allows free will and functionalism to co-exist. I think that having the ability to do what we won't do, however, is not very compatible with functionalism unless there is some ability for functionalism to somehow be "deactivated" allowing for manual control by a conscious entity.

That doesn't explain how free will and functionalism could be compatible. It could be argued that the memory function of the mind serves to provide input for future outputs (deciding to get ice cream due to the input of the memory of ice cream in the freezer). Also, why should free will be a survival mechanism? Wouldn't philosophical zombies that are "programmed" to react appropriately to their environment via natural selection be able to survive? Why is free will necessary?

I think that makes functionalism and free will very compatible if that is the case! Interesting!

Why should an inability to "observe" free will in action mean that it exists? I would also like to further argue that we are not able to anticipate the complex reactions within a brain due to our lack of knowledge. If every physical detail of the body was known (reaction mechanisms, incoming stimuli, etc.), would we be able to predict the future actions of a person? If not, then it may suggest that free will is something that operates beyond the physical world. Why should material things be able to decide how it reacts to the world? How can that be described in terms of functionalism?

@FrankHubeny Also, why should it be assumed that a theory that does not allow for free will should be falsified? Why assume free will does not exist?

@FrankHubeny Yes, from iep.utm.edu/functism/#H2 , "The functions in question are usually taken to be those that mediate between stimulus (and psychological) inputs and behavioral (and psychological) outputs. Hilary Putnam’s contribution was to model these functions using the contemporary idea of computing machines and programs, where the program of the machine fixes how it mediates between its inputs and standing states, on one hand, and outputs and other standing states, on the other."