split Logic.Statement into files, simpler serialization

Logic/Statement.hs

@@ -1,11 +1,5 @@
 module Logic.Statement where
 
-import Logic.Parse
-
-import Control.Applicative (Alternative((<|>), some))
-import Data.Char (isAlphaNum)
-import Data.List (intercalate)
-import Data.Either (fromRight)
 import Data.Set (singleton, union, toAscList)
 
 data Statement
@@ -17,47 +11,6 @@ data Statement
   | Iff Statement Statement
   deriving (Show, Eq)
 
-stmtAtom :: Parser Statement
-stmtAtom = Atom <$> parse
-  where
-    parse = some $ parseIf "statement variable" $ \char -> isAlphaNum char || char == '_'
-
-stmtNot :: Parser Statement
-stmtNot = Not <$> (parseToken "!" *> stmt)
-
-stmtBinary :: Parser Statement
-stmtBinary = parseToken "(" *> body <* parseToken ")"
-  where
-    body = (\s1 f s2 -> f s1 s2) <$> stmt <*> parseConnective <*> stmt
-
-    parseConnective =
-      fmap (const And) (parseToken "&")
-      <|> fmap (const Or) (parseToken "|")
-      <|> fmap (const Implies) (parseToken "->")
-      <|> fmap (const Iff) (parseToken "<->")
-      <|> fail
-
-    fail = Parser $ \input -> Left $ expected "connective" input
-
-stmt :: Parser Statement
-stmt = Parser $ \input ->
-  let
-    parser =
-      case inputSeq input of
-        [] -> fail
-        ('!':_) -> stmtNot
-        ('(':_) -> stmtBinary
-        _ -> stmtAtom <|> fail
-  in runParser parser input
-  where
-    fail = Parser $ \input -> Left $ expected "statement" input
-
-p :: Statement
-p = fromRight undefined $ eof stmt $ mkInput "((a->b)<->!c)"
-
-q :: Statement
-q = fromRight undefined $ eof stmt $ mkInput "(!a<->((!(p->q)&x)|y))"
-
 atoms :: Statement -> [String]
 atoms = toAscList . mkSet
   where
@@ -67,171 +20,3 @@ atoms = toAscList . mkSet
     mkSet (Or s1 s2)      = union (mkSet s1) (mkSet s2)
     mkSet (Implies s1 s2) = union (mkSet s1) (mkSet s2)
     mkSet (Iff s1 s2)     = union (mkSet s1) (mkSet s2)
-
-eval :: [(String, Bool)] -> Statement -> Either String Bool
-eval assignments = aux
-  where
-    aux (Atom key)      = maybe (Left key) Right $ lookup key assignments
-    aux (Not s)         = not <$> aux s
-    aux (And s1 s2)     = (&&) <$> aux s1 <*> aux s2
-    aux (Or s1 s2)      = (||) <$> aux s1 <*> aux s2
-    aux (Implies s1 s2) = not <$> ((&&) <$> aux s1 <*> (not <$> aux s2))
-    aux (Iff s1 s2)     = (==) <$> aux s1 <*> aux s2
-
-data Bucket
-  = Tautology
-  | Contradiction
-  | Contingent
-  deriving (Eq, Show)
-
-bucket :: Statement -> Bucket
-bucket s
-  | and values = Tautology
-  | all not values = Contradiction
-  | otherwise = Contingent
-  where
-    values = [fromRight undefined $ eval assignments s | assignments <- enumerate $ atoms s]
-
-enumerate :: [a] -> [[(a, Bool)]]
-enumerate keys = map reverse $ aux start
-  where
-    aux assignments = (assignments:) $
-      case next assignments of
-        Nothing -> []
-        Just (assignments') -> aux assignments'
-
-    start = map (, False) keys
-
-    next [] = Nothing
-    next ((key, False):rest) = Just $ (key, True):rest
-    next ((key, True):rest) = ((key, False):) <$> (next rest)
-
-data SerializeFormat
-  = Ascii
-  | Latex
-  deriving (Show, Eq)
-
-data Cell
-  = Main String
-  | NotMain String
-  deriving (Show, Eq)
-
-fromCell :: Cell -> String
-fromCell (Main x) = x
-fromCell (NotMain x) = x
-
-fromCellLatex :: Cell -> String
-fromCellLatex (Main x) = "\\textbf " <> x
-fromCellLatex (NotMain x) = x
-
-isMain :: Cell -> Bool
-isMain (Main _) = True
-isMain _ = False
-
-serializeCells :: SerializeFormat -> Statement -> [Cell]
-serializeCells = aux Main
-  where
-    aux mkCell Ascii = ascii mkCell
-    aux mkCell Latex = latex mkCell
-
-    ascii' = ascii NotMain
-    latex' = latex NotMain
-
-    ascii mkCell (Atom key)      = [mkCell key]
-    ascii mkCell (Not s)         = [mkCell "!"] ++ ascii' s
-    ascii mkCell (And s1 s2)     = connective (mkCell "&") (ascii' s1) (ascii' s2)
-    ascii mkCell (Or s1 s2)      = connective (mkCell "|") (ascii' s1) (ascii' s2)
-    ascii mkCell (Implies s1 s2) = connective (mkCell "->") (ascii' s1) (ascii' s2)
-    ascii mkCell (Iff s1 s2)     = connective (mkCell "<->") (ascii' s1) (ascii' s2)
-
-    latex mkCell (Atom key)      = [mkCell key]
-    latex mkCell (Not s)         = [mkCell "\\neg "] ++ latex' s
-    latex mkCell (And s1 s2)     = connective (mkCell "\\land ") (latex' s1) (latex' s2)
-    latex mkCell (Or s1 s2)      = connective (mkCell "\\lor ") (latex' s1) (latex' s2)
-    latex mkCell (Implies s1 s2) = connective (mkCell "\\to ") (latex' s1) (latex' s2)
-    latex mkCell (Iff s1 s2)     = connective (mkCell "\\leftrightarrow ") (latex' s1) (latex' s2)
-
-    connective middle s1 s2 = [NotMain "("] ++ s1 ++ [middle] ++ s2 ++ [NotMain ")"]
-
-serialize :: SerializeFormat -> Statement -> String
-serialize fmt s = concat $ map fromCell $ serializeCells fmt s
-
-latexTruthTableMainColumnIndex :: Statement -> Int
-latexTruthTableMainColumnIndex s =
-  fst $ head $ filter (\(i, cell) -> isMain cell) $ zip [0..] $ serializeCells Latex s
-
-serializeLatexTruthTableRow :: [(String, Bool)] -> Statement -> Either String [String]
-serializeLatexTruthTableRow ass s = map fromCellLatex <$> latexRow Main ass s
-  where
-    latexRow mkCell ass (Atom key)      = list <$> mkCell <$> toInt <$> eval ass (Atom key)
-    latexRow mkCell ass (Not s)         = (list <$> mkCell <$> toInt <$> not <$> eval ass s) <> latexRow NotMain ass s
-    latexRow mkCell ass (And s1 s2)     = latexRowBinaryConnective (&&) mkCell ass s1 s2
-    latexRow mkCell ass (Or s1 s2)      = latexRowBinaryConnective (||) mkCell ass s1 s2
-    latexRow mkCell ass (Implies s1 s2) = latexRowBinaryConnective implies mkCell ass s1 s2
-    latexRow mkCell ass (Iff s1 s2)     = latexRowBinaryConnective (==) mkCell ass s1 s2
-
-    latexRowBinaryConnective op mkCell ass s1 s2 =
-      (
-        \subrow1 subrow2 result ->
-          [NotMain " "] ++ subrow1 ++ [mkCell $ toInt result] ++ subrow2 ++ [NotMain " "]
-      ) <$>
-      latexRow NotMain ass s1 <*> latexRow NotMain ass s2 <*>
-      (op <$> eval ass s1 <*> eval ass s2)
-
-    toInt :: Bool -> String
-    toInt False = "0"
-    toInt True = "1"
-
-    list :: a -> [a]
-    list x = [x]
-
-    implies :: Bool -> Bool -> Bool
-    implies b1 b2 = not b1 || b2
-
-truthtable :: Statement -> String
-truthtable s = open <> header <> "\\hline\n" <> body <> close
-  where
-    mainIndex = latexTruthTableMainColumnIndex s
-
-    cellsSpec
-      | mainIndex == 0 && length serial <= 1 = "c"
-      | mainIndex == 0 = "c|" <> replicate (length serial - 1) 'c'
-      | mainIndex == length serial - 1 = replicate (length serial - 1) 'c' <> "|c"
-      | otherwise = replicate mainIndex 'c' <> "|c|" <> replicate (length serial - mainIndex - 1) 'c'
-
-    open =
-      "\\begin{tabular}{" <>
-      replicate (length $ atoms s) 'c' <>
-      "||" <>
-      cellsSpec <>
-      "}\n"
-
-    close = "\\end{tabular}\n\n"
-
-    serial :: [Cell]
-    serial = serializeCells Latex s
-
-    header :: String
-    header =
-      intercalate " & " (map dollars $ atoms s) <>
-      " & " <>
-      intercalate " & " (map dollars $ map fromCell serial) <>
-      " \\\\\n"
-
-    dollars :: String -> String
-    dollars string = "$" <> string <> "$"
-
-    body :: String
-    body = concat $ map line $ enumerate $ atoms s
-
-    line assignments =
-      intercalate " & " (bools assignments) <>
-      " &" <>
-      intercalate "&" (cells assignments) <>
-      "\\\\\n"
-
-    bools assignments = [if bool then "1" else "0" | (key, bool) <- assignments]
-
-    cells assignments =
-      (\xs -> [if x /= " " then " " <> x <> " " else " " | x <- xs]) $
-      fromRight undefined $ serializeLatexTruthTableRow assignments s

Logic/Statement/Eval.hs

@@ -0,0 +1,47 @@
+module Logic.Statement.Eval where
+
+import Logic.Statement (Statement(..), atoms)
+
+import Data.List (intercalate)
+import Data.Either (fromRight)
+
+data Bucket
+  = Tautology
+  | Contradiction
+  | Contingent
+  deriving (Eq, Show)
+
+bucket :: Statement -> Bucket
+bucket s
+  | and values = Tautology
+  | all not values = Contradiction
+  | otherwise = Contingent
+  where
+    values = [fromRight undefined $ eval assignments s | assignments <- enumerate $ atoms s]
+
+eval :: [(String, Bool)] -> Statement -> Either String Bool
+eval assignments = aux
+  where
+    aux (Atom key)      = maybe (Left key) Right $ lookup key assignments
+    aux (Not s)         = not <$> aux s
+    aux (And s1 s2)     = (&&) <$> aux s1 <*> aux s2
+    aux (Or s1 s2)      = (||) <$> aux s1 <*> aux s2
+    aux (Implies s1 s2) = not <$> ((&&) <$> aux s1 <*> (not <$> aux s2))
+    aux (Iff s1 s2)     = (==) <$> aux s1 <*> aux s2
+
+enumerate :: [a] -> [[(a, Bool)]]
+enumerate keys = map reverse $ aux start
+  where
+    aux assignments = (assignments:) $
+      case next assignments of
+        Nothing -> []
+        Just (assignments') -> aux assignments'
+
+    start = map (, False) keys
+
+    next [] = Nothing
+    next ((key, False):rest) = Just $ (key, True):rest
+    next ((key, True):rest) = ((key, False):) <$> (next rest)
+
+implies :: Bool -> Bool -> Bool
+implies b1 b2 = not b1 || b2

Logic/Statement/Parse.hs

@@ -0,0 +1,49 @@
+module Logic.Statement.Parse where
+
+import Logic.Parse
+  ( Parser(..)
+  , Input(..)
+  , ParseError
+  , expected
+  , parseToken
+  , parseIf
+  )
+import Logic.Statement (Statement(..))
+
+import Control.Applicative (Alternative((<|>), some))
+import Data.Char (isAlphaNum)
+
+stmtAtom :: Parser Statement
+stmtAtom = Atom <$> parse
+  where
+    parse = some $ parseIf "statement variable" $ \char -> isAlphaNum char || char == '_'
+
+stmtNot :: Parser Statement
+stmtNot = Not <$> (parseToken "!" *> stmt)
+
+stmtBinary :: Parser Statement
+stmtBinary = parseToken "(" *> body <* parseToken ")"
+  where
+    body = (\s1 f s2 -> f s1 s2) <$> stmt <*> parseConnective <*> stmt
+
+    parseConnective =
+      fmap (const And) (parseToken "&")
+      <|> fmap (const Or) (parseToken "|")
+      <|> fmap (const Implies) (parseToken "->")
+      <|> fmap (const Iff) (parseToken "<->")
+      <|> fail
+
+    fail = Parser $ \input -> Left $ expected "connective" input
+
+stmt :: Parser Statement
+stmt = Parser $ \input ->
+  let
+    parser =
+      case inputSeq input of
+        [] -> fail
+        ('!':_) -> stmtNot
+        ('(':_) -> stmtBinary
+        _ -> stmtAtom <|> fail
+  in runParser parser input
+  where
+    fail = Parser $ \input -> Left $ expected "statement" input

Logic/Statement/Serialize.hs

@@ -0,0 +1,173 @@
+module Logic.Statement.Serialize where
+
+import Logic.Statement (Statement(..), atoms)
+import Logic.Statement.Eval (enumerate, eval, implies)
+
+import Data.List (intercalate)
+import Data.Either (fromRight)
+
+data TokenString = TokenString
+  { tsCanEval :: CanEval
+  , tsLevel :: Int
+  , tsString :: String
+  } deriving (Show, Eq)
+
+data CanEval
+  = Filler
+  | CanEval
+  deriving (Show, Eq)
+
+data TokenValue = TokenValue
+  { tvLevel :: Int
+  , tvValue :: Value
+  } deriving (Show, Eq)
+
+data Value
+  = NoValue
+  | Value Bool
+  deriving (Show, Eq)
+
+data SerializeFormat
+  = Plain
+  | Latex
+--  | PrefixPlain
+  deriving (Show, Eq)
+
+serialize :: SerializeFormat -> Statement -> String
+serialize fmt s = concat $ map tsString $ serializeStrings fmt s
+
+serializeStrings :: SerializeFormat -> Statement -> [TokenString]
+serializeStrings fmt = aux 0
+  where
+    aux :: Int -> Statement -> [TokenString]
+    aux =
+      case fmt of
+        Plain -> serializeStringsPlain
+        Latex -> serializeStringsLatex
+
+-- Internal function
+serializeStringsPlain :: Int -> Statement -> [TokenString]
+serializeStringsPlain level = aux
+  where
+    f = serializeStringsPlain
+    level' = level + 1
+
+    aux (Atom key)      = [TokenString CanEval level key]
+    aux (Not s)         = [TokenString CanEval level "!"] ++ f level' s
+    aux (And s1 s2)     = connective level "&"   (f level' s1) (f level' s2)
+    aux (Or s1 s2)      = connective level "|"   (f level' s1) (f level' s2)
+    aux (Implies s1 s2) = connective level "->"  (f level' s1) (f level' s2)
+    aux (Iff s1 s2)     = connective level "<->" (f level' s1) (f level' s2)
+
+-- Internal function
+serializeStringsLatex :: Int -> Statement -> [TokenString]
+serializeStringsLatex level = aux
+  where
+    f = serializeStringsLatex
+    level' = level + 1
+
+    aux (Atom key)      = [TokenString CanEval level key]
+    aux (Not s)         = [TokenString CanEval level "\\neg "] ++ f level' s
+    aux (And s1 s2)     = connective level "\\land "           (f level' s1) (f level' s2)
+    aux (Or s1 s2)      = connective level "\\lor "            (f level' s1) (f level' s2)
+    aux (Implies s1 s2) = connective level "\\to "             (f level' s1) (f level' s2)
+    aux (Iff s1 s2)     = connective level "\\leftrightarrow " (f level' s1) (f level' s2)
+
+-- Internal function
+connective :: Int -> String -> [TokenString] -> [TokenString] -> [TokenString]
+connective level middle tokens1 tokens2 =
+  [TokenString Filler level "("]
+  ++ tokens1
+  ++ [TokenString CanEval level middle]
+  ++ tokens2
+  ++ [TokenString Filler level ")"]
+
+-- Using infix convention with brackets
+serializeValues :: [(String, Bool)] -> Statement -> Either String [TokenValue]
+serializeValues ass = fmap snd . aux 0
+  where
+    aux :: Int -> Statement -> Either String (Bool, [TokenValue])
+    aux level s@(Atom key) = do
+      bool <- eval ass s
+      return (bool, [TokenValue level $ Value bool])
+    aux level (Not s) = do
+      (bool, tokens) <- aux (level + 1) s
+      return (not bool, [TokenValue level $ Value $ not bool] ++ tokens)
+    aux level (And s1 s2)     = connective level (&&) s1 s2
+    aux level (Or s1 s2)      = connective level (||) s1 s2
+    aux level (Implies s1 s2) = connective level implies s1 s2
+    aux level (Iff s1 s2)     = connective level (==) s1 s2
+
+    connective
+      :: Int
+      -> (Bool -> Bool -> Bool)
+      -> Statement
+      -> Statement
+      -> Either String (Bool, [TokenValue])
+    connective level f s1 s2 = do
+      (bool1, tokens1) <- aux (level + 1) s1
+      (bool2, tokens2) <- aux (level + 1) s2
+      let bracket = [TokenValue level NoValue]
+      let bool = f bool1 bool2
+      return (bool, bracket ++ tokens1 ++ [TokenValue level $ Value bool] ++ tokens2 ++ bracket)
+
+serializeLatexTruthTable :: Statement -> String
+serializeLatexTruthTable s = open <> header <> "\\hline\n" <> body <> close
+  where
+    open :: String
+    open = "\\begin{tabular}{" <> replicate (length $ atoms s) 'c' <> "||" <> spec <> "}\n"
+
+    close :: String
+    close = "\\end{tabular}\n"
+
+    spec :: String
+    spec
+      | length serial == 0 = undefined
+      | length serial == 1 = "c"
+      | isMain (head serial) = "c|" <> replicate (length serial - 1) 'c'
+      | isMain (serial !! (length serial - 1)) = replicate (length serial - 1) 'c' <> "|c"
+      | otherwise = concat $ map (\token -> if isMain token then "|c|" else "c") serial
+
+    isMain :: TokenString -> Bool
+    isMain (TokenString CanEval level string) = level == 0
+    isMain _ = False
+
+    serial :: [TokenString]
+    serial = serializeStrings Latex s
+
+    header :: String
+    header =
+      intercalate " & " (map dollars $ atoms s) <>
+      " & " <>
+      intercalate " & " (map dollars $ map tsString serial) <>
+      " \\\\\n"
+
+    dollars :: String -> String
+    dollars string = "$" <> string <> "$"
+
+    body :: String
+    body = concat $ map line $ enumerate $ atoms s
+
+    line :: [(String, Bool)] -> String
+    line ass =
+      intercalate " & " (bools ass) <>
+      " & " <>
+      intercalate " & " (cells ass) <>
+      "\\\\\n"
+
+    bools :: [(String, Bool)] -> [String]
+    bools ass = [if bool then "1" else "0" | (key, bool) <- ass]
+
+    cells :: [(String, Bool)] -> [String]
+    cells ass = map cell $ fromRight undefined $ serializeValues ass s
+
+    cell :: TokenValue -> String
+    cell (TokenValue level value) =
+      case value of
+        NoValue -> ""
+        Value bool -> mkBold level $ if bool then "1" else "0"
+
+    mkBold :: Int -> String -> String
+    mkBold level string
+      | level == 0 = "\\textbf " <> string
+      | otherwise = string

Main.hs

@@ -1,12 +1,17 @@
 module Main where
 
 import Logic.Parse (eof, mkInput, ParseError(..))
-import Logic.Statement (stmt)
+import Logic.Statement.Parse (stmt)
+import Logic.Statement.Serialize (serializeLatexTruthTable)
 
 main :: IO ()
 main = do
   line <- getLine
-  either fail print $ eof stmt $ mkInput line
+  case eof stmt $ mkInput line of
+    Left err -> fail err
+    Right statement -> do
+      putStrLn $ show statement
+      putStr $ serializeLatexTruthTable statement
   where
     fail err@(ParseError pos message) =
       putStrLn $