1007 Finite Automata.ipynb

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   "source": [
    "# 유한 오토마타 Haskell로 작성해보기\n",
    "\n",
    "책 110p 예제"
   ]
  },
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    "type NFA = (Int, [(Int,String,Int)], [Int])\n",
    "{- (max state, transitaions, final states)\n",
    "\n",
    "assume start state is 0\n",
    "-}"
   ]
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   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
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   "source": [
    "import IHaskell.Display.Graphviz\n",
    "import Data.List\n",
    "\n",
    "toDot :: NFA -> String\n",
    "toDot (n, ds, fs) =\n",
    "    \"digraph { rankdir=LR; node [shape=circle]; start [shape=none] ; start -> 0; \"\n",
    "  ++ concat [show f++\" [shape=doublecircle]; \" | f<-fs ]\n",
    "  ++ concatMap showLabels ds\n",
    "  ++\"}\"\n",
    "  where\n",
    "  -- pqss = groupBy (\\(p,_,q) (p',_,q') -> p==p' && q==q') ds\n",
    "  -- pqs = [(p,as,q)| pqs<-pqss, let (p,_,q)=head pqs, let (_,as,_)=unzip3 pqs]\n",
    "  showLabels (p,\"\",q) = show p++\" -> \"++show q++\"[label=\\\"𝜀\\\",style=dotted]\"\n",
    "  showLabels (p, a,q) = show p++\" -> \"++show q++\"[label=\\\"\"++a++\"\\\"]\"\n",
    "  fillEpsilon \"\" = \"𝜀\"\n",
    "  fillEpsilon s  = s\n",
    "\n",
    "unwordsBy s = concat . intersperse s"
   ]
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  {
   "cell_type": "code",
   "execution_count": 3,
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   "source": [
    "data RE = Nul\n",
    "        | Eps\n",
    "        | A Char\n",
    "        | RE :+ RE\n",
    "        | RE :. RE\n",
    "        | Star RE\n",
    "        deriving Show\n",
    "\n",
    "infixr 6 :+\n",
    "infixr 7 :."
   ]
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   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "e = Eps\n",
    "a = A 'a'\n",
    "b = A 'b'"
   ]
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   "cell_type": "code",
   "execution_count": 5,
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   "source": [
    "mapNFA :: (Int -> Int) -> NFA -> NFA\n",
    "mapNFA f (m,ds,fs) = (f m, [(f p,a,f q) | (p,a,q)<-ds], map f fs)\n",
    "\n",
    "re2nfa :: RE -> NFA\n",
    "re2nfa Nul   = (0, [], [])\n",
    "re2nfa Eps   = (0, [], [0])\n",
    "re2nfa (A a) = (1, [(0,a:[],1)], [1])\n",
    "re2nfa (r1 :+ r2) = (m, es++ds1++ds2, [m])\n",
    "  where\n",
    "  m = m1 + m2 + 3\n",
    "  nfa1@(m1,_,_) = re2nfa r1\n",
    "  nfa2@(m2,_,_) = re2nfa r2\n",
    "  (_,ds1,fs1) = mapNFA (+1)      nfa1\n",
    "  (_,ds2,fs2) = mapNFA (+(m1+2)) nfa2\n",
    "  es = (0,\"\",1) : (0,\"\",m1+2) : [(f,\"\",m)| f<-fs1++fs2]\n",
    "re2nfa (r1 :. r2) = (m, es++ds1++ds2, fs2)\n",
    "  where\n",
    "  nfa1@(m1,ds1,fs1) = re2nfa r1\n",
    "  nfa2@(m2,_,_)     = re2nfa r2\n",
    "  (m,ds2,fs2) = mapNFA (+(m1+1)) nfa2\n",
    "  es = [(p,\"\",m1+1) | p<-fs1]\n",
    "re2nfa (Star r) = (m+1, es++ds, [m+1])\n",
    "  where\n",
    "  (m,ds,fs) = mapNFA (+1) $ re2nfa r\n",
    "  es = (0,\"\",m+1) : (m+1,\"\",0) : (0,\"\",1) : [(f,\"\",m+1) | f<-fs]"
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    "re2nfa Nul\n",
    "dot . toDot $ re2nfa Nul"
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    "re2nfa Eps\n",
    "dot . toDot $ re2nfa Eps"
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   "source": [
    "re2nfa $ a :+ b\n",
    "dot . toDot . re2nfa $ a :+ b"
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   "source": [
    "re2nfa $ Star (a :+ b)\n",
    "dot . toDot . re2nfa $ Star (a :+ b)"
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   "source": [
    "re2nfa $ Star (a :+ b) :. a :. b :. b\n",
    "dot . toDot . re2nfa $  Star (a :+ b) :. a :. b :. b"
   ]
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    "step :: NFA -> Int -> String -> [Int]\n",
    "step (_,ds,_) p a = [q | (p',a',q)<-ds, p==p', a==a']\n",
    "\n",
    "eStep :: NFA -> Int -> [Int]\n",
    "eStep nfa p = step nfa p \"\"\n",
    "\n",
    "eClosure :: NFA -> [Int] -> [Int]\n",
    "\n",
    "eClosure nfa ps | ps == ps' = ps'\n",
    "                | otherwise = eClosure nfa ps'\n",
    "  where\n",
    "  ps' = sort . nub $ concatMap (eStep nfa) ps `union` ps"
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   "execution_count": 45,
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    "nfa1 = re2nfa $ Star (a :+ b) :. a :. b :. b"
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    "nfa2 = re2nfa $ Star (a :+ b)\n",
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    "deEpsilon :: NFA -> NFA\n",
    "deEpsilon nfa@(m,ds,fs) = (m,ds',fs)\n",
    "  where\n",
    "  as = [ a | d@(_,a,_)<-ds, a/=\"\" ]\n",
    "  ds' = nub $ do p <- [0..m]\n",
    "                 a <- as\n",
    "                 p' <- eClosure nfa [p]\n",
    "                 q <- step nfa p' a\n",
    "                 q' <- eClosure nfa [q]\n",
    "                 return (p,a,q')"
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   "source": [
    "nfa2' = deEpsilon nfa2\n",
    "dot $ toDot nfa2'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
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   "source": [
    "toDot' :: NFA -> String\n",
    "toDot' (n, ds, fs) =\n",
    "    \"digraph { rankdir=LR; node [shape=circle]; start [shape=none] ; start -> 0; \"\n",
    "  ++ concat [show f++\" [shape=doublecircle]; \" | f<-fs ]\n",
    "  ++ concatMap showLabels pqs\n",
    "  ++\"}\"\n",
    "  where\n",
    "  pqss = groupBy (\\(p,_,q) (p',_,q') -> p==p' && q==q') ds\n",
    "  pqs = [(p,as,q)| pqs<-pqss, let (p,_,q)=head pqs, let (_,as,_)=unzip3 pqs]\n",
    "  showLabels (p,as,q) = show p++\" -> \"++show q++\"[label=\\\"\"++concat(intersperse \",\" as)++\"\\\"]\"\n",
    "  fillEpsilon \"\" = \"𝜀\"\n",
    "  fillEpsilon s  = s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
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   "source": [
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   "cell_type": "code",
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   "outputs": [],
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