(def valid-name?
  "Returns truthy if argument is a non-namespaced symbol."
  (every-pred symbol? (complement namespace)))

(defn parse-arglist
  "Given an `arglist` (a vector of parameter names for a function method),
  returns a map of information about the method. May throw an exception if
  `arglist` cannot be parsed."
  [arglist]
  (assert (every? valid-name? arglist)
    "All parameter names must be non-namespaced symbols.")
  (let [variadic? (= (last (butlast arglist)) '&)
        fixed-args (cond->> arglist variadic? (drop-last 2))]
    {:fixed-args fixed-args
     :fixed-arity (count fixed-args)
     :rest-arg (when variadic? (last arglist))
     :variadic? variadic?}))

(defn arity-info
  "Given a seq of `arglists` (maps of information obtained via `parse-arglist`
  about methods of a particular function), returns a map of information about
  the function itself. May throw an exception if two or more `arglists` are
  mutually incompatible and therefore cannot coexist on the same function."
  [arglists]
  (assert (apply distinct? (map (juxt :fixed-arity :variadic?) arglists))
    "No two methods of a single function may share the same arity.")
  (let [max-fixed-arity (apply max (map :fixed-arity arglists))
        [variadic-arglist & more] (filter :variadic? arglists)]
    (assert (empty? more)
      "A function may have at most one variadic method.")
    (assert (= (:fixed-arity variadic-arglist) max-fixed-arity)
      (str "A variadic method may not take fewer parameters than a "
           "fixed-arity method of the same function."))
    {:arglists arglists
     :fixed-arities (set (map :fixed-arity arglists))
     :max-fixed-arity max-fixed-arity
     :variadic? (boolean variadic-arglist)}))

(defn valid-invoke-arity?
  "Returns truthy if it is acceptable to invoke `f` with `argc` arguments."
  [f argc]
  (or (contains? (:fixed-arities f) argc)
      (and (:variadic? f) (> argc (:max-fixed-arity f)))))

(defn take-when [pred [x & xs :as coll]]
  (if (pred x) [x xs] [nil coll]))