15.Answer

We can state the associative law in terms of join:

x.join.join == x.map(_.join).join

For Par, the join combinator means something like "make the outer thread wait for the inner one to finish." What this law is saying is that if you have threads starting threads three levels deep, then joining the inner threads and then the outer ones is the same as joining the outer threads and then the inner ones.

For Parser, the join combinator is running the outer parser to produce a Parser, then running the inner Parser on the remaining input. The associative law is saying, roughly, that only the order of nesting matters, since that's what affects the order in which the parsers are run.