(defn- minimum-required-dimensions
  "Find a list of minimum required dimensions for the schema.

  e.g. An array of array of strings might be '(2 0 3), meaning the string must
  have length three, there can be zero or more strings in an array, and there
  must be three or more arrays of strings in the array of arrays of strings.

  To simplify logic, we keep a dimension for the innermost type, even if it is
  an atomic type and doesn't make sense."
  [schema]
  (reduce
   (fn [as bs]
     (let [length (max (count as) (count bs))
           as     (concat as (repeat (- length (count as)) 0))
           bs     (concat bs (repeat (- length (count bs)) 0))]
       (map max as bs)))
   (list)
   (m/search schema
     {"minLength" (m/some ?n)}             (list ?n)
     {"type"      "array"}                 (list 0 0)
     {"items"     (m/some (m/cata ?dims))} (cons 0 ?dims)
     {"allOf"     (m/scan (m/cata ?dims))} ?dims
     _                                     (list 0))))