I'm unclear what you're suggesting here. Are you suggesting you couldn't write a POS in Haskell, say?
Can you implement it using functional code? Yes. Just make sure you wind up with partial states. And often times you are best off explicitly not using the RAI pattern for some of these. (I have rarely seen examples where they deal with this. Creating and reconciling transactions often have to be separate pieces of code. And the reconcile code cannot, necessarily, fallback to create a transaction if they get a "not found" fault.)