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... Inspired by;
... "The Different Aspects of Monads and Mixins" by Bruno C. d. S. Oliveira
(.module:
  [library
   [lux "*"
    [abstract
     [hash {"+" [Hash]}]
     [monad {"+" [do]}]]
    [control
     ["." state {"+" [State]}]]
    [data
     ["." product]
     [collection
      ["." dictionary {"+" [Dictionary]}]]]]]
  ["." // "_"
   ["#" mixin {"+" [Mixin Recursive]}]])

(def: .public memoization
  (All (_ i o)
    (Mixin i (State (Dictionary i o) o)))
  (function (_ delegate recur)
    (function (_ input)
      (do {! state.monad}
        [memory state.get]
        (case (dictionary.value input memory)
          (#.Some output)
          (in output)

          #.None
          (do !
            [output (delegate input)
             _ (state.update (dictionary.has input output))]
            (in output)))))))

(type: .public (Memo i o)
  (Recursive i (State (Dictionary i o) o)))

(def: .public (open memo)
  (All (_ i o)
    (:let [Memory (Dictionary i o)]
      (-> (Memo i o) (-> [Memory i] [Memory o]))))
  (let [memo (//.fixed (//.mixed ..memoization (//.of_recursive memo)))]
    (function (_ [memory input])
      (|> input memo (state.result memory)))))

(def: .public (closed hash memo)
  (All (_ i o)
    (-> (Hash i) (Memo i o) (-> i o)))
  (let [memo (//.fixed (//.mixed ..memoization (//.of_recursive memo)))
        empty (dictionary.empty hash)]
    (|>> memo (state.result empty) product.right)))

(def: .public (none hash memo)
  (All (_ i o)
    (-> (Hash i) (Memo i o) (-> i o)))
  (let [memo (//.fixed (//.of_recursive memo))
        empty (dictionary.empty hash)]
    (|>> memo (state.result empty) product.right)))