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(walk/postwalk
  #(do (print (str % " ")) %)
  [:add 1 [:mul "x" 2]])

:add 1 :mul x 2 [:mul "x" 2] [:add 1 [:mul "x" 2]]

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(defn print-expr [expr]
  (walk/postwalk
    (fn algebra [e]
      (cond
        (cst? e) (str e)
        (sym? e) e
        (add? e) (str "(+ " (string/join " " (rest e)) ")")
        (mul? e) (str "(* " (string/join " " (rest e)) ")")
        :else e))
    expr))

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(def expr
  (add
    (cst 1) (cst 2)
    (mul (cst 0) (sym "x") (sym "y"))
    (mul (cst 1) (sym "y") (cst 2))
    (add (cst 0) (sym "x"))))

(print-expr expr)
=> "(+ 1 2 (* 0 x y) (* 1 y 2) (+ 0 y))"

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(defn evaluate [env e]
  (walk/postwalk
    (fn [e]
      (cond
        (sym? e) (get env e)
        (add? e) (reduce + (rest e))
        (mul? e) (reduce * (rest e))
        :else e))
    e))

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(defn dependencies [e]
  (walk/postwalk
    (fn [e]
      (cond
        (cst? e) #{}
        (sym? e) #{e}
        (op? e) (apply set/union (rands e))
        :else e))
    e))

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(defn optimize-add [e]
  (if (add? e)
    (optimize-op e + 0)
    e))

(defn optimize-mul [e]
  (if (mul? e)
    (if (some #{(cst 0)} e)
      (cst 0)
      (optimize-op e * 1))

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(defn- make-op
  [rator rands]
  (if (< 1 (count rands))
    (into [rator] rands)
    (first rands)))

(defn- optimize-op
  [[rator & rands] binary-op neutral]
  (let [{csts true vars false} (group-by cst? rands)
        sum-cst (reduce binary-op neutral csts)]

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(defn optimize [e]
  (walk/postwalk
    (comp optimize-mul optimize-add)
    e))

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(defn replace-var
  [env x]
  (if (string? x) (get env x x) x))

(defn partial-eval
  [env e]
  (walk/postwalk
    (comp optimize-mul optimize-add #(replace-var env %))
    e))

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(ns arithmetic
  (:require
    [clojure.string :as string]
    [clojure.set :as set]
    [clojure.walk :as walk]
    ))