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MP in Clojure

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Why not try MP (monadic programming) in Clojure?

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MP in Clojure

  1. 1. MP in Clojure ~ herding cats with clj ~
  2. 2. Self-introduction /laʒenɔʁɛ̃k/ カマイルカlagénorhynque (defprofile lagénorhynque :name "Kent OHASHI" :languages [Clojure Haskell Python Scala English français Deutsch русский] :interests [programming language-learning mathematics] :contributing [github.com/japan-clojurians/clojure-site-ja])
  3. 3. Clojure × MP
  4. 4. Contents 1. What is MP? 2. Why MP in Clojure? 3. How MP in Clojure? 4. Examples
  5. 5. What is MP?
  6. 6. programming with monads cf. FP = functional programming MP = monadic programming
  7. 7. de nition of Monad in Haskell GHC.Base#Monad class Applicative m => Monad m where (>>=) :: forall a b. m a -> (a -> m b) -> m b (>>) :: forall a b. m a -> m b -> m b m >> k = m >>= _ -> k {-# INLINE (>>) #-} return :: a -> m a return = pure fail :: String -> m a fail s = errorWithoutStackTrace s
  8. 8. monads in Haskell 型クラス Monad のインスタンス >>= : m a -> (a -> m b) -> m b return : a -> m a モナド則( )を満たす シンプルで合成可能な構造 → 様々な形で利⽤可能 do 記法というシンタックスシュガー monad laws
  9. 9. e.g. ※ #渋⾕ java なので⼀応 Java の例から^_^; java.util.Optional jshell> Optional<Integer> a = Optional.of(2) a ==> Optional[2] jshell> Optional<Integer> b = Optional.of(3) b ==> Optional[3] jshell> a.flatMap( x -> // with `flatMap` & `map` ...> b.map( y -> ...> x * y ...> ) ...> ) $3 ==> Optional[6]
  10. 10. e.g. scala.Option scala> val a = Some(2) a: Some[Int] = Some(2) scala> val b = Some(3) b: Some[Int] = Some(3) scala> a.flatMap { x => // with `flatMap` & `map` | b.map { y => | x * y | } | } res0: Option[Int] = Some(6) scala> for { // with `for` expression | x <- a | y <- b | } yield x * y res1: Option[Int] = Some(6)
  11. 11. e.g. Prelude.Maybe > a = Just 2 > b = Just 3 > :{ -- with `>>=` & `return` | a >>= x -> | b >>= y -> | return $ x * y | :} Just 6 > :{ -- with `do` notation | do | x <- a | y <- b | return $ x * y | :} Just 6
  12. 12. e.g. cats.monad.maybe user=> (require '[cats.core :as m] #_=> '[cats.monad.maybe :as maybe]) nil user=> (def a (maybe/just 2)) #'user/a user=> (def b (maybe/just 3)) #'user/b user=> (m/>>= a (fn [x] ; with `>>=` & `return` #_=> (m/>>= b (fn [y] #_=> (m/return (* x y)))))) #<Just 6> user=> (m/mlet [x a ; with `mlet` macro #_=> y b] #_=> (m/return (* x y))) #<Just 6>
  13. 13. Why MP in Clojure?
  14. 14. MP in Clojure Clojureでは モナドは必須の機能ではないが…… 静的型付け&純粋関数型の⾔語ではないが…… シンプルで汎⽤的なDSL構築フレームワーク Haskellなどで有⽤なアイディアが活かせる ⇒ Clojureでも MP してみよう (*> ᴗ •*)ゞ
  15. 15. How MP in Clojure?
  16. 16. MP libraries in Clojure clojure/algo.monads Macros for defining monads, and definition of the most common monads funcool/cats Category Theory and Algebraic abstractions for Clojure and ClojureScript.
  17. 17. how to support MP in Clojure feature algo.monads cats Monad type class plain Map data protocol do notation macro macro context inference (n/a) protocol
  18. 18. anatomy of algo.monads user=> (require '[clojure.algo.monads :as m]) nil user=> (m/domonad m/maybe-m #_=> [x 2 #_=> y 3] #_=> (* x y)) 6
  19. 19. macroexpand-1 clojure.algo.monads/with-monad ? user=> (macroexpand-1 #_=> '(m/domonad m/maybe-m #_=> [x 2 #_=> y 3] #_=> (* x y))) (clojure.algo.monads/with-monad m/maybe-m (m-bind 2 (fn [x] (m-bind 3 (fn [y] (m-result (* x y)))))))
  20. 20. macroexpand-1 once more clojure.algo.monads/maybe-m ? user=> (macroexpand-1 *1) (clojure.core/let [name__3075__auto__ m/maybe-m m-bind (:m-bind name__3075__auto__) m-result (:m-result name__3075__auto__) m-zero (:m-zero name__3075__auto__) m-plus (:m-plus name__3075__auto__)] (clojure.tools.macro/with-symbol-macros (m-bind 2 (fn [x] (m-bind 3 (fn [y] (m-result (* x y))))))))
  21. 21. clojure.algo.monads/maybe-m just a keyword-function Map user=> clojure.algo.monads/maybe-m {:m-zero nil, :m-plus #object[clojure.algo.monads$fn__3167$m_plus_maybe__3172 0x77a7 :m-result #object[clojure.algo.monads$fn__3167$m_result_maybe__3168 0x :m-bind #object[clojure.algo.monads$fn__3167$m_bind_maybe__3170 0x142d user=> (class clojure.algo.monads/maybe-m) clojure.lang.PersistentArrayMap
  22. 22. strategy in algo.monads 1. :m-bind, :m-result をkey、対応する関数を valueとしたMapを⽤意 2. マクロによってMapから取り出した関数 m-bind, m-result の組み合わせに変換
  23. 23. anatomy of cats user=> (require '[cats.core :as m] #_=> '[cats.monad.maybe :as maybe]) nil user=> (m/mlet [x (maybe/just 2) #_=> y (maybe/just 3)] #_=> (m/return (* x y))) #<Just 6>
  24. 24. macroexpand-1 cats.core/bind ? without explicit monad context? user=> (macroexpand-1 #_=> '(m/mlet [x (maybe/just 2) #_=> y (maybe/just 3)] #_=> (m/return (* x y)))) (cats.core/bind (maybe/just 2) (clojure.core/fn [x] (cats.core/bind (maybe/just 3) (clojure.core/fn [y] (do (m/return (* x y)))))))
  25. 25. cats.core/bind cats.context/infer ? can infer monad context? user=> (source cats.core/bind) (defn bind ;; (docstring here) [mv f] (let [ctx (ctx/infer mv)] (p/-mbind ctx mv (fn [v] (ctx/with-context ctx (f v)))))) nil
  26. 26. cats.context/infer cats.protocols/Contextual ? user=> (source cats.context/infer) (defn infer ;; (docstring here) ;; (0-arity pattern here) ([v] (cond ; blank lines omitted (not (nil? *context*)) *context* (satisfies? p/Contextual v) (p/-get-context v) :else (throw-illegal-argument (str "No context is set and it can not be automatically " "resolved from provided value"))))) nil
  27. 27. cats.protocols/Contextual -get-context method user=> (source cats.protocols/Contextual) (defprotocol Contextual "Abstraction that establishes a concrete type as a member of a contex A great example is the Maybe monad type Just. It implements this abstraction to establish that Just is part of the Maybe monad." (-get-context [_] "Get the context associated with the type.")) nil
  28. 28. cats.core/bind (again) cats.protocols/-mbind ? user=> (source cats.core/bind) (defn bind ;; (docstring here) [mv f] (let [ctx (ctx/infer mv)] (p/-mbind ctx mv (fn [v] (ctx/with-context ctx (f v)))))) nil
  29. 29. cats.protocols/Monad -mreturn & -mbind methods user=> (source cats.protocols/Monad)) (defprotocol Monad "The Monad abstraction." (-mreturn [m v]) (-mbind [m mv f])) nil
  30. 30. cats.core/bind ( nally) cats.context/with-context ? user=> (source cats.core/bind) (defn bind ;; (docstring here) [mv f] (let [ctx (ctx/infer mv)] (p/-mbind ctx mv (fn [v] (ctx/with-context ctx (f v)))))) nil
  31. 31. cats.context/with-context dynamic Var *context* user=> (source cats.context/with-context) (defmacro with-context "Set current context to specific monad." [ctx & body] `(do (when-not (context? ~ctx) (throw-illegal-argument "The provided context does not implements Context.")) (binding [*context* ~ctx] ~@body))) nil user=> (source cats.context/*context*) (def ^:dynamic *context* nil) nil
  32. 32. strategy in cats 1. Monad プロトコル(-mreturn, -mbind)を実装した コンテキストオブジェクトを⽤意 2. Monad 値は Contextual プロトコルによってコン テキストオブジェクトを取り出せる 3. マクロで関数 bind, return の組み合わせに変換 4. bind は第1引数の Monad 値からコンテキストオブ ジェクトを取り出す(コンテキストの推論) 5. with-context で⼀度推論したコンテキストオブ ジェクトを動的スコープで再利⽤
  33. 33. Examples
  34. 34. example code repositories cf. lagenorhynque/mp-in-clojure lagenorhynque/mp-in-haskell
  35. 35. using monads: safe RPN calculator from Learn You a Haskell for Great Good! 10.1 Reverse Polish Notation Calculator 14.6 Making a Safe RPN Calculator
  36. 36. RPN: reverse Polish notation ↓ with parentheses ↓ evaluate 8 6 1 - * 2 + ((8 (6 1 -) *) 2 +) 42
  37. 37. without monads naïve implementation (defn- folding-function [[x y & ys :as xs] s] (cond (and x y (= s "*")) (conj ys (* y x)) (and x y (= s "+")) (conj ys (+ y x)) (and x y (= s "-")) (conj ys (- y x)) :else (conj xs (Double/parseDouble s)))) (defn solve-rpn [s] (as-> s v (str/split v #"s+") (reduce folding-function () v) (first v)))
  38. 38. ;; valid RPN user=> (solve-rpn "8 6 1 - * 2 +") 42.0 ;; unsupported operator user=> (solve-rpn "8 6 1 - * 2 /") NumberFormatException For input string: "/" sun.misc.FloatingDecimal.r ;; invalid number user=> (solve-rpn "8 6 1 - * a +") NumberFormatException For input string: "a" sun.misc.FloatingDecimal.r ;; invalid RPN user=> (solve-rpn "8 6 1 - * 2") 2.0
  39. 39. with Maybe monad valid ⇒ just x ; invalid ⇒ nothing lift-m for lifting conj function (defn- read-maybe [s] (try (maybe/just (Double/parseDouble s)) (catch NumberFormatException _ (maybe/nothing)))) (defn- folding-function' [[x y & ys :as xs] s] (cond (and x y (= s "*")) (maybe/just (conj ys (* y x))) (and x y (= s "+")) (maybe/just (conj ys (+ y x))) (and x y (= s "-")) (maybe/just (conj ys (- y x))) :else ((m/lift-m 1 #(conj xs %)) (read-maybe s))))
  40. 40. reduce with monadic function using foldm length of result sequence ≠ 1 ⇒ nothing MonadZero cf. MonadPlus, Alternative (defn solve-rpn' [s] (m/mlet [result (m/foldm folding-function' () (str/split s #"s+")) :when (= (count result) 1)] (m/return (first result))))
  41. 41. ;; valid RPN user=> (solve-rpn' "8 6 1 - * 2 +") #<Just 42.0> ;; unsupported operator user=> (solve-rpn' "8 6 1 - * 2 /") #<Nothing> ;; invalid number user=> (solve-rpn' "8 6 1 - * a +") #<Nothing> ;; invalid RPN user=> (solve-rpn' "8 6 1 - * 2") #<Nothing>
  42. 42. making monads: probability distribution from Learn You a Haskell for Great Good! 14.8 Making Monads
  43. 43. probability distribution e.g. 6-sided die n p 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6
  44. 44. implementing Prob monad define the data type Prob (deftype Prob [v] p/Contextual (-get-context [_] context) p/Extract (-extract [_] v) p/Printable (-repr [_] (str "#<Prob " (pr-str v) ">")) Object (equals [this obj] (= (.v this) (.v obj))))
  45. 45. define the context object for Prob (def context (reify ;; (other protocol implementations here) p/Monad (-mreturn [m v] (p/-pure m v)) (-mbind [_ mv f] (assert (prob? mv) (str "Context mismatch: " (p/-repr mv) " is not allowed to use with prob context.")) (->Prob (for [[x p] (p/-extract mv) [y q] (p/-extract (f x))] [y (* p q)]))) ;; (below omitted)
  46. 46. define factory/conversion functions (defn uniform [s] ; sequence (let [n (count s)] ; -> Prob value of uniform distribution (->> s (map (fn [x] [x (/ 1 n)])) ->Prob))) (defn prob->dist [prob] ; Prob value -> Map of distribution (letfn [(add-prob [d [x p]] (update d x (fnil #(+ % p) 0)))] (reduce add-prob {} (p/-extract prob))))
  47. 47. sum of 2 dice user=> (def die (range 1 (inc 6))) #'user/die user=> (def prob #_=> (m/mlet [d1 (uniform die) #_=> d2 (uniform die)] #_=> (m/return (+ d1 d2)))) #'user/prob user=> prob #<Prob ([2 1/36] [3 1/36] [4 1/36] [5 1/36] [6 1/36] [7 1/36] [3 1/36] user=> (prob->dist prob) {7 1/6, 4 1/12, 6 5/36, 3 1/18, 12 1/36, 2 1/36, 11 1/18, 9 1/9, 5 1/9, 10 1/12, 8 5/36}
  48. 48. Monty Hall problem user=> (def doors #{:a :b :c}) #'user/doors user=> (prob->dist #_=> (m/mlet [prize (uniform doors) #_=> choice (uniform doors)] #_=> (m/return (if (= choice prize) #_=> :win #_=> :lose)))) {:win 1/3, :lose 2/3}
  49. 49. user=> (prob->dist #_=> (m/mlet [prize (uniform doors) #_=> choice (uniform doors) #_=> opened (uniform (disj doors prize choice)) #_=> choice' (uniform (disj doors opened choice))] #_=> (m/return (if (= choice' prize) #_=> :win #_=> :lose)))) {:lose 1/3, :win 2/3}
  50. 50. Vive les S-expressions ! Long live S-expressions!
  51. 51. Further Reading / / clojure/algo.monads khinsen/monads-in-clojure funcool/cats 独習 Scalaz learning Scalaz 猫番 herding cats モナド (プログラミング) - Wikipedia
  52. 52. / 第14章 もうちょっとだけモナド / For a Few Monads More 10.1 逆ポーランド記法電卓 / 14.6 安全な逆ポーランド記法電卓を作ろう / Making a Safe RPN Calculator 14.8 モナドを作る / 『すごいHaskellたのしく学ぼう!』 Learn You a Haskell for Great Good! Reverse Polish Notation Calculator Making Monads
  53. 53. cf. Haskell の Monad とは⾔語内DSLのフレームワー クである Functor, Applicative, Monadのシンプルな定式化 継承によらないポリモーフィズム実現⼿法 思ったほど怖くない! Haskell on JVM 超⼊⾨ MP in Scala MP in Haskell Free Monads Getting Started

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