Implement map using reduce (clojure)

map-via-reduce.clj

;;Excerpt "Clojure for the Brave and True" by Daniel Higginbotham:
;;"If you want an exercise that will really blow your hair back, try implementing map using reduce..."

;;This actually took me a really long time to come up with, have to keep thinking about how reduce expands to (fn (fn (fn...

;;Tried cons first, but couldn't figure it out - needed to think about the order arguments are applied in within the anonymous
;;function AND the order of arguments for reduce. That was more obvious after I tried using conj
(defn my-map-conj
  "map implemented in terms of reduce and conj"
  [f coll]
  (reduce #(conj %1 (f %2)) [] coll))

(defn my-map-cons
  "map implemented in terms of reduce and cons"
  [f sequence]
  (reduce #(cons (f %2) %1) '() (reverse sequence)))

The thing is, map takes many collections as arguments, not just a single one :).