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1 1 0!? Q.? A. Q. B. Q.? A.! Scheme 80! λ 81!? λ ( ) 82!? λ ( ) 83!? λ 4 3! λ

2 0 1 q : POSIX : : q jhc engine

3 golgo Df-pn Df-pn kogitsune Bottom-Up LR HaskEll Lens Traversal Iso Prism Real World Lens ? 166

4 3 q Web UI Web! /! CPU POSIX API!!!

5 Web 100 UML Web kernel UNIX kernel / kernel 10 ( ) kernel *1 OCaml kernel kernel kernel *2 UNIX kernel kernel kernel UNIX kernel POSIX *3 kernel *1 Haskell/OCaml OS *2 *3 : Copilot

6 1.2 5 kernel kernel *4 20 POSIX POSIX API kernel kernel ( 1.1 ) POSIX GCC Firefox Web 1.1: POSIX API OS kernel kernel POSIX *5 C kernel ( 1.2 ) 1.2: : kernel *4 *5

7 6 1 POSIX OCaml UNIX kernel 1.3!! *6 *6

8 47 lens Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire Web lens lens lens

9 b B A B B h A B h Nil = b (1) h(cons(a,as)) = a (h as) foldr h = ( b, ) (2) length = ( 0, ) where a n = 1 + n filter p = ( Nil, ) where a as p a = Cons(a,as) p a = as EMACS Haskell cata length filter!!

10 71 engine Haskell Haskell Haskell Haskell

11 106 4 (K5) (M5) (M1)-(M5) (K1)-(K5) (M1)-(M5) (K1)-(K5) Kleisli M C M Kleisli X C X Ob(C) f : X Y f : X M(Y ) X id X η X : X M(X) f : X Y g: Y Z g f µ Z M A (g) f X Y hom Hom(X, Y ) Hom ( X, M(Y ) ) 4.4: C M Kleisli C Haskell Hask M X M(Y ) * *10 Haskell

12 123 第5章 golgo 5.1 プロローグ 図 5.1: λカ娘三連敗! あううう また負けたでゲソ これで儂の 3 連勝 やはり置石が足らんかな そ そんなことないでゲソ 4 子も置いて負けたのはたまたまでゲソ! 次は勝つでゲソ!! まあその意気込みだけは買ってやるがな λカ娘は最近ある老人と囲碁を打つようになった (図 5.1) 囲碁に自信があったλカ娘である が この老人には 4 子のハンデ (段級位にして 4 段級差に相当) を付けてもらってもまるで勝てな かった あううう ああは言ったものの そう簡単に勝てる相手ではないことは良くわかるでゲソ 囲碁 はそう簡単に強くなれるゲームでは無いでゲソ 私も囲碁歴は 10 年近くて アマ三段はあると思 うでゲソが あの老人は何者でゲソか 特に読みの力が全然違うでゲソ うーん 仕方な いでゲソ こうなったら 自分で囲碁の探索プログラムを作ってそれを使ってカンニングする でゲソ! そう考えたλカ娘は 早速図書館で囲碁の探索に関する論文を探し始めた しばらくして 証明

13 133 kogitsune LLVM *1 ( ) *2 ( )! (4) : : : 6.1????!?! LR!? LR(k)! *1, ( ), ( ): 3 LLVM, MotiPizza (2012) *2

14 155 7 HaskEll import Control.Lens data Person = Person { _name :: String, _self :: Object, _endurance :: Int, _equipment :: Equipment } data Object = Object { _position :: Vector3, _velocity :: Vector3 } data Equipment = Equipment { _sword :: Object, _body :: ArmorType } data Vector3 = Vector3 { _x :: Float, _y :: Float, _z :: Float } makelenses Person makelenses Object makelenses Equipment makelenses Vector3

15 156 7 HaskEll Shaddai do zoom (equipment. sword) $ do velocity. x += 5 v <- use velocity position %= addv3 v self. velocity. z += Lens import Control.Applicative type LensLike f s a = (a -> f a) -> s -> f s lens :: Functor f => (s -> a) -> (s -> a -> s) -> LensLike f s a lens getter setter f s = fmap (setter s) (f (getter s)) _1 :: Functor f => LensLike f (a, b) a _1 f (a, b) = fmap (\a -> (a, b)) (f a) contains :: (Ord a, Functor f) => a -> LensLike f (Set.Set a) Bool contains a f s = fmap (\b -> if b then Set.insert a s else Set.delete a s) $ f (Set.elem a s) Lens LensLike f s a s a a s Lens type Getting r s a = LensLike (Const r) s a type Getter s a = Getting a s a -- (a -> Const a a) -> s -> Const a s view :: Getter s a -> s -> a view g = getconst. g Const Getter Const a s s a Lens Const Const a

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