functional-programming chapter; improve examples and explain iterate

[timothypratley]

your exercises for functional-programming chapter rely heavily on iterate, but that's not brought up in the chapter. Exercise for the author: how do you solve those problems without iterate? (Doable, in theory.) More seriously, it might be better to defer those exercises in favor of something more related to map, reduce, and/or filter.

Also, maybe have an exercise to just rewrite an existing super nested expression using a threading macro, since the topic was covered? Ex, when already given:

(defn count-i-before-e
  [s]
  (count (filter #(= % [\i \e]) (partition 2 1 (seq s)))))

Try: (count-i-before-e "sieve") and (count-i-before-e "seize") Now rewrite using thread-last macro (->>):

(defn count-i-before-e
  [s]
  (->> s
       seq
       (partition 2 1)
       (filter #(= % [\i \e]))
       count))

I think some work can go into exercises for map/reduce/filter to replace the ones using iterate, what do you think? I would need some time to think on what to come up with ideas for that.