I like that the function in your link is called preduce and not just reduce. Reduce has a standard definition, which doesn't require associativity. To eliminate

I like that the function in your link is called preduce and not just reduce. Reduce has a standard definition, which doesn't require associativity. To eliminate confusion, a function that does require associativity deserves a different name, just like here. And using these names, I would say that preduce seems much more useful to me than reduce.