Or the visitor pattern, which is.... the map function.

One thing I will note from recent experience: programming for a long time with immutability cripples your ability to think about mutable things. I was writing up a streaming merge sort this week and it was a brutal nightmare because of all the state I had to deal with. Seems like a call to action to deal with a bit of mutable state every now and then. Everything is too pure these days. We're programmers, not mathematicians dammit.