0930 CEK machine with primitives.ipynb

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   "source": [
    ":!./install.sh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CEK 기계에 기본제공연산 추가\n",
    "CEK 기계는 80년대에 Friedman과 Felleisen이 SECD 기계(Landin 1964)를 더 말끔하게 정리한 것이다.\n",
    "\n",
    "여기서는 지난번 노트북에서 살펴본 CEK 기계에 기본제공연산(pritivmve operation)을 추가해 보자.\n",
    "강의 일정상 지나친 복잡함은 피하기 위해 정수값들에 대한 기본연산만을 고려하기로 하자.\n",
    "\n",
    "###### 참고자료\n",
    "* https://www.cs.bham.ac.uk/~hxt/2015/compilers/compiling-functional.pdf\n",
    "* https://en.wikipedia.org/wiki/SECD_machine\n",
    "* https://www.brics.dk/RS/03/33/\n",
    "* https://pages.cpsc.ucalgary.ca/~robin/FMCS/FMCS2014/Prashant_talk.pdf\n",
    "* https://github.com/kseo/secd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "type Nm = String\n",
    "\n",
    "data Exp = Var Nm         -- x\n",
    "         | App Exp Exp    -- e1 e2\n",
    "         | Lam Nm Exp     -- \\x.e\n",
    "         | Lit Int        -- n\n",
    "         | Prm Prim [Exp] -- f(x1,...,xn)\n",
    "         deriving Show\n",
    "\n",
    "data Prim = Suc | Add deriving Show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "type CEK = (Code,Env,Kont)\n",
    "\n",
    "data Code = OpE Exp\n",
    "          | OpV Value\n",
    "          | OpArg\n",
    "          | OpCall\n",
    "          deriving Show\n",
    "type Env  = [(Nm,Value)]\n",
    "type Kont = [Frame]\n",
    "\n",
    "data Value = Vint Int      -- n\n",
    "           | Clos Exp Env  -- < \\x.e, env >\n",
    "           deriving Show\n",
    "\n",
    "data Frame = FrV Value   -- (v O)\n",
    "           | FrE Exp Env -- (O e env)\n",
    "           | FrP Prim [Value] [Exp] Env -- (f [vi,..] O [ei,...] env)\n",
    "           deriving Show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "lookup' x env = case lookup x env of Just v  -> v\n",
    "                                     Nothing -> error(\"x is unknown\")\n",
    "\n",
    "-- 기본제공연산이 호출되었을 때 동작 정의\n",
    "callPrim Suc [Vint n] = Vint (n+1)\n",
    "callPrim Add [Vint n2, Vint n1] = Vint (n1+n2)\n",
    "\n",
    "step :: CEK -> Maybe CEK\n",
    "step (OpE(Var x),     env, k) = Just (OpV(lookup' x env), env, k)\n",
    "step (OpE(App e1 e2), env, k) = Just (OpE e1, env, FrE e2 env : k)\n",
    "step (OpE(e@Lam{}),   env, k) = Just (OpV(Clos e env), env, k)\n",
    "step (OpE(Lit n),     env, k) = Just (OpV(Vint n), env, k)\n",
    "-- step (OpE(Prm f es),  env, k) = Just (OpArg, env, FrP f [] es env : k) -- 기본제공연산식 처리 시작\n",
    "step (OpV v,  env1, FrE e2 env2 : k) = Just (OpE e2, env2, FrV v : k)\n",
    "step (OpV v,  env1, FrV(Clos (Lam x e) env2) : k) = Just (OpE e, (x,v) : env2, k)\n",
    "-- step (OpArg,  env1, FrP f vs (e2:es) env2 : k) = undefined -- 다음 인자값 계산\n",
    "-- step (OpV v,  env1, FrP f vs es env2 : k) = undefined -- 계산된 인자값 프레임에 추가\n",
    "-- step (OpArg,  env1, FrP f vs [] env2 : k) = undefined -- 다음 인자값 계산 시도하지만 더 이상 인자 없는 경우 처리\n",
    "-- step (OpCall, env1, FrP f vs [] env2 : k) = Just (OpV(callPrim f vs), env2, k) -- 모든 인자 계산 후 기본제공연산 호출\n",
    "step _ = Nothing"
   ]
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   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "{-# LANGUAGE FlexibleInstances #-}\n",
    "import IHaskell.Display\n",
    "import Data.List (intersperse)\n",
    "\n",
    "class TeX a where\n",
    "  toTeX :: a -> String\n",
    "\n",
    "instance TeX Exp where\n",
    "  toTeX (Var x) = x\n",
    "  toTeX (App e1 e2) = \"(\"++toTeX e1++\"\\\\;\"++toTeX e2++\")\" \n",
    "  toTeX (Lam x e) = \"(\\\\lambda{}\"++x++\".\"++toTeX e++\")\"\n",
    "  toTeX (Lit n) = show n\n",
    "  toTeX (Prm f es) = \"\\\\textsf{\"++show f++\"}\"++toTeX es\n",
    "\n",
    "instance TeX Code where\n",
    "  toTeX (OpE e) = toTeX e\n",
    "  toTeX (OpV v) = toTeX v\n",
    "  toTeX (OpArg) = \"\\\\texttt{arg}\"\n",
    "  toTeX (OpCall) = \"\\\\texttt{call}\"\n",
    "\n",
    "instance TeX Value where\n",
    "  toTeX (Vint n) = show n\n",
    "  toTeX (Clos e env) = \"\\\\langle{}\" ++ toTeX e ++ \",\" ++ revTeX env ++ \"\\\\rangle{}\"\n",
    "\n",
    "instance TeX Frame where\n",
    "  toTeX (FrV v) = \"(\"++toTeX v++\"\\\\,\\\\bigcirc{})\"\n",
    "  toTeX (FrE e env) = \"(\\\\bigcirc{}\\\\,\"++toTeX e++\"\\\\;\"++revTeX env++\")\"\n",
    "  toTeX (FrP f vs es env) = \"(\\\\textsf{\"++show f++\"}\"++revTeX vs++\"\\\\,\\\\bigcirc{}\\\\,\"++toTeX es++\"\\\\;\"++revTeX env++\")\"\n",
    "\n",
    "instance TeX (Nm,Value) where\n",
    "  toTeX (x,v) = x++\"\\\\mapsto{}\"++toTeX v\n",
    "\n",
    "instance TeX CEK where\n",
    "  toTeX (c,env,k) = \"\\\\big\\\\langle{}\"\n",
    "                 ++ toTeX c ++ \"\\\\;\\\\big|\\\\;\" ++ revTeX env ++ \"\\\\;\\\\big|\\\\;\" ++ toTeX k\n",
    "                 ++ \"\\\\big\\\\rangle{}\"\n",
    "\n",
    "instance TeX a => TeX (Maybe a) where\n",
    "  toTeX (Just x)= \"\\\\texttt{Just}(\"++toTeX x++\")\"\n",
    "  toTeX Nothing = \"\\\\texttt{Nothing}\"\n",
    "\n",
    "instance TeX a => TeX [a] where\n",
    "  toTeX xs = \"[\" ++ (concat . intersperse \",\" $ map toTeX xs) ++ \"]\"\n",
    "\n",
    "revTeX = toTeX . reverse\n",
    "\n",
    "newtype LaTeX a = LaTeX a\n",
    "\n",
    "htmlTeX a = html $ \"$\"++toTeX a++\"$\"\n",
    "\n",
    "instance TeX a => IHaskellDisplay (LaTeX a) where\n",
    "  display (LaTeX a) = return $ Display [htmlTeX a]"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "이전 예제는 그대로 잘 동작한다."
   ]
  },
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       "App (App (Lam \"x\" (Lam \"y\" (Var \"x\"))) (Lit 1)) (Lit 2)"
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       "<style>/* Styles used for the Hoogle display in the pager */\n",
       ".hoogle-doc {\n",
       "display: block;\n",
       "padding-bottom: 1.3em;\n",
       "padding-left: 0.4em;\n",
       "}\n",
       ".hoogle-code {\n",
       "display: block;\n",
       "font-family: monospace;\n",
       "white-space: pre;\n",
       "}\n",
       ".hoogle-text {\n",
       "display: block;\n",
       "}\n",
       ".hoogle-name {\n",
       "color: green;\n",
       "font-weight: bold;\n",
       "}\n",
       ".hoogle-head {\n",
       "font-weight: bold;\n",
       "}\n",
       ".hoogle-sub {\n",
       "display: block;\n",
       "margin-left: 0.4em;\n",
       "}\n",
       ".hoogle-package {\n",
       "font-weight: bold;\n",
       "font-style: italic;\n",
       "}\n",
       ".hoogle-module {\n",
       "font-weight: bold;\n",
       "}\n",
       ".hoogle-class {\n",
       "font-weight: bold;\n",
       "}\n",
       ".get-type {\n",
       "color: green;\n",
       "font-weight: bold;\n",
       "font-family: monospace;\n",
       "display: block;\n",
       "white-space: pre-wrap;\n",
       "}\n",
       ".show-type {\n",
       "color: green;\n",
       "font-weight: bold;\n",
       "font-family: monospace;\n",
       "margin-left: 1em;\n",
       "}\n",
       ".mono {\n",
       "font-family: monospace;\n",
       "display: block;\n",
       "}\n",
       ".err-msg {\n",
       "color: red;\n",
       "font-style: italic;\n",
       "font-family: monospace;\n",
       "white-space: pre;\n",
       "display: block;\n",
       "}\n",
       "#unshowable {\n",
       "color: red;\n",
       "font-weight: bold;\n",
       "}\n",
       ".err-msg.in.collapse {\n",
       "padding-top: 0.7em;\n",
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       ".highlight-code {\n",
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       ".suggestion-warning { \n",
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       "}\n",
       ".suggestion-error { \n",
       "font-weight: bold;\n",
       "color: red;\n",
       "}\n",
       ".suggestion-name {\n",
       "font-weight: bold;\n",
       "}\n",
       "</style>$(((\\lambda{}x.(\\lambda{}y.x))\\;1)\\;2)$"
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       "padding-left: 0.4em;\n",
       "}\n",
       ".hoogle-code {\n",
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       ".hoogle-head {\n",
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       ".hoogle-sub {\n",
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       ".hoogle-package {\n",
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       ".hoogle-module {\n",
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       ".hoogle-class {\n",
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       "white-space: pre-wrap;\n",
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       ".show-type {\n",
       "color: green;\n",
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       ".mono {\n",
       "font-family: monospace;\n",
       "display: block;\n",
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       ".err-msg {\n",
       "color: red;\n",
       "font-style: italic;\n",
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       "white-space: pre;\n",
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       "#unshowable {\n",
       "color: red;\n",
       "font-weight: bold;\n",
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       ".err-msg.in.collapse {\n",
       "padding-top: 0.7em;\n",
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       ".suggestion-warning { \n",
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       "color: red;\n",
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       ".suggestion-name {\n",
       "font-weight: bold;\n",
       "}\n",
       "</style>$\\textsf{Suc}[3]$"
      ]
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   ],
   "source": [
    "fst_1_2 = App (App (Lam \"x\" $ Lam \"y\" $ Var \"x\") (Lit 1)) (Lit 2)\n",
    "fst_1_2\n",
    "LaTeX fst_1_2\n",
    "LaTeX (Prm Suc[Lit 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
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    {
     "data": {
      "text/plain": [
       "Just (OpE (App (App (Lam \"x\" (Lam \"y\" (Var \"x\"))) (Lit 1)) (Lit 2)),[],[])\n",
       "Just (OpE (App (Lam \"x\" (Lam \"y\" (Var \"x\"))) (Lit 1)),[],[FrE (Lit 2) []])\n",
       "Just (OpE (Lam \"x\" (Lam \"y\" (Var \"x\"))),[],[FrE (Lit 1) [],FrE (Lit 2) []])\n",
       "Just (OpV (Clos (Lam \"x\" (Lam \"y\" (Var \"x\"))) []),[],[FrE (Lit 1) [],FrE (Lit 2) []])\n",
       "Just (OpE (Lit 1),[],[FrV (Clos (Lam \"x\" (Lam \"y\" (Var \"x\"))) []),FrE (Lit 2) []])\n",
       "Just (OpV (Vint 1),[],[FrV (Clos (Lam \"x\" (Lam \"y\" (Var \"x\"))) []),FrE (Lit 2) []])\n",
       "Just (OpE (Lam \"y\" (Var \"x\")),[(\"x\",Vint 1)],[FrE (Lit 2) []])\n",
       "Just (OpV (Clos (Lam \"y\" (Var \"x\")) [(\"x\",Vint 1)]),[(\"x\",Vint 1)],[FrE (Lit 2) []])\n",
       "Just (OpE (Lit 2),[],[FrV (Clos (Lam \"y\" (Var \"x\")) [(\"x\",Vint 1)])])\n",
       "Just (OpV (Vint 2),[],[FrV (Clos (Lam \"y\" (Var \"x\")) [(\"x\",Vint 1)])])\n",
       "Just (OpE (Var \"x\"),[(\"y\",Vint 2),(\"x\",Vint 1)],[])\n",
       "Just (OpV (Vint 1),[(\"y\",Vint 2),(\"x\",Vint 1)],[])"
      ]
     },
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    }
   ],
   "source": [
    "mapM_ print $ takeWhile isJust $ iterate (step =<<) (Just(OpE fst_1_2,[],[]))"
   ]
  },
  {
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       ".hoogle-doc {\n",
       "display: block;\n",
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       "padding-left: 0.4em;\n",
       "}\n",
       ".hoogle-code {\n",
       "display: block;\n",
       "font-family: monospace;\n",
       "white-space: pre;\n",
       "}\n",
       ".hoogle-text {\n",
       "display: block;\n",
       "}\n",
       ".hoogle-name {\n",
       "color: green;\n",
       "font-weight: bold;\n",
       "}\n",
       ".hoogle-head {\n",
       "font-weight: bold;\n",
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       "}\n",
       ".hoogle-package {\n",
       "font-weight: bold;\n",
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       "}\n",
       ".hoogle-module {\n",
       "font-weight: bold;\n",
       "}\n",
       ".hoogle-class {\n",
       "font-weight: bold;\n",
       "}\n",
       ".get-type {\n",
       "color: green;\n",
       "font-weight: bold;\n",
       "font-family: monospace;\n",
       "display: block;\n",
       "white-space: pre-wrap;\n",
       "}\n",
       ".show-type {\n",
       "color: green;\n",
       "font-weight: bold;\n",
       "font-family: monospace;\n",
       "margin-left: 1em;\n",
       "}\n",
       ".mono {\n",
       "font-family: monospace;\n",
       "display: block;\n",
       "}\n",
       ".err-msg {\n",
       "color: red;\n",
       "font-style: italic;\n",
       "font-family: monospace;\n",
       "white-space: pre;\n",
       "display: block;\n",
       "}\n",
       "#unshowable {\n",
       "color: red;\n",
       "font-weight: bold;\n",
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       ".err-msg.in.collapse {\n",
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       "</style>$\\texttt{Just}(\\big\\langle{}(((\\lambda{}x.(\\lambda{}y.x))\\;1)\\;2)\\;\\big|\\;[]\\;\\big|\\;[]\\big\\rangle{})$"
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       ".hoogle-module {\n",
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       ".show-type {\n",
       "color: green;\n",
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       "margin-left: 1em;\n",
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       ".mono {\n",
       "font-family: monospace;\n",
       "display: block;\n",
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       ".err-msg {\n",
       "color: red;\n",
       "font-style: italic;\n",
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       "#unshowable {\n",
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       ".err-msg.in.collapse {\n",
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       "color: red;\n",
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       ".suggestion-name {\n",
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       "</style>$\\texttt{Just}(\\big\\langle{}((\\lambda{}x.(\\lambda{}y.x))\\;1)\\;\\big|\\;[]\\;\\big|\\;[(\\bigcirc{}\\,2\\;[])]\\big\\rangle{})$"
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