separate into files, parser error messages

This commit is contained in:
hi 2025-08-07 09:23:50 +00:00
parent 68bc86c496
commit 0fa510e31a
5 changed files with 353 additions and 310 deletions

19
.gitignore vendored Normal file
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# binaries
*
# compilation intermediate files
*.hi
*.ho
# vim generates these
*.swp
*.swo
# include directories
!*/
# include files with an extension
!*.*
# special cases
!Makefile

77
Logic/Parse.hs Normal file
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module Logic.Parse where
import Control.Applicative (Applicative, Alternative(..))
import Data.Functor (Functor)
newtype Parser output = Parser
{ runParser :: Input -> Either ParseError (output, Input)
}
data Input = Input
{ inputPos :: Int
, inputSeq :: [Char]
} deriving (Eq, Show)
mkInput :: [Char] -> Input
mkInput = Input 0
data ParseError =
ParseError Int String
deriving (Show)
expected :: String -> Input -> ParseError
expected thing input = ParseError (inputPos input) $
"expected " <> thing <> ", found " <> show (take 20 $ inputSeq input)
eof :: Parser a -> Input -> Either ParseError a
eof p input = do
(result, rest) <- runParser p input
case inputSeq rest of
[] -> Right result
_ -> Left $ expected "end of input" rest
instance Functor Parser where
fmap :: (a -> b) -> Parser a -> Parser b
fmap f (Parser p) = Parser $ \input -> do
(result, rest) <- p input
return (f result, rest)
instance Applicative Parser where
pure :: a -> Parser a
pure result = Parser $ \input -> Right (result, input)
(Parser p1) <*> (Parser p2) =
Parser $ \input -> do
(f, rest) <- p1 input
(result, rest') <- p2 rest
return (f result, rest')
instance Alternative Parser where
empty :: Parser a
empty = Parser $ const empty
(Parser p1) <|> (Parser p2) =
Parser $ \input -> p1 input <|> p2 input
instance Alternative (Either ParseError) where
empty :: Either ParseError a
empty = Left $ ParseError 0 "this parser always fails"
(Right x) <|> _ = Right x
(Left _) <|> e = e
parseToken :: String -> Parser String
parseToken token = Parser parse
where
n = length token
parse input@(Input pos xs)
| token == take n xs = Right $ (token,) $ Input (pos + n) (drop n xs)
| otherwise = Left $ expected (show token) input
parseIf :: String -> (Char -> Bool) -> Parser Char
parseIf description check = Parser $ \input ->
case inputSeq input of
[] -> Left $ ParseError (inputPos input) "unexpected end of input"
(char:chars)
| check char -> Right $ (char,) $ Input (inputPos input + 1) chars
| otherwise -> Left $ expected description input

237
Logic/Statement.hs Normal file
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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
= Atom String
| Not Statement
| And Statement Statement
| Or Statement Statement
| Implies Statement 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
mkSet (Atom key) = singleton key
mkSet (Not s) = mkSet s
mkSet (And s1 s2) = union (mkSet s1) (mkSet s2)
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

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Main.hs
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import Control.Applicative (Applicative, Alternative(..)) module Main where
import Data.Char (isAlphaNum)
import Data.Functor (Functor)
import Data.List (intercalate)
import Data.Maybe (fromJust)
import qualified Data.Set as S
newtype Parser symbol output = Parser import Logic.Parse (eof, mkInput, ParseError(..))
{ runParser :: [symbol] -> Maybe (output, [symbol]) import Logic.Statement (stmt)
}
instance Functor (Parser s) where main :: IO ()
fmap :: (a -> b) -> Parser s a -> Parser s b main = do
fmap f (Parser p) = Parser line <- getLine
{ runParser = \xs -> do either fail print $ eof stmt $ mkInput line
(result, xs') <- p xs
return (f result, xs')
}
instance Applicative (Parser s) where
pure :: a -> Parser s a
pure result = Parser $ \xs -> Just (result, xs)
(Parser p1) <*> (Parser p2) =
Parser $ \xs -> do
(f, xs') <- p1 xs
(result, xs'') <- p2 xs'
return (f result, xs'')
instance Alternative (Parser s) where
empty :: Parser s a
empty = Parser $ const Nothing
(Parser p1) <|> (Parser p2) =
Parser $ \xs -> p1 xs <|> p2 xs
data Statement
= Atom String
| Not Statement
| And Statement Statement
| Or Statement Statement
| Implies Statement Statement
| Iff Statement Statement
deriving (Show, Eq)
parseToken :: String -> Parser Char String
parseToken token = Parser parse
where where
n = length token fail err@(ParseError pos message) =
parse xs putStrLn $
| token == take n xs = Just (token, drop n xs) "parse error at position "
| otherwise = Nothing <> show pos
<> ": "
parseWhile :: (Char -> Bool) -> Parser Char String <> message
parseWhile check = Parser parse
where
parse [] = Nothing
parse (token:rest)
| check token =
case parse rest of
Nothing -> Just ([token], rest)
Just (tokens, rest') -> Just (token:tokens, rest')
| otherwise = Nothing
parseBrackets :: Parser Char a -> Parser Char a
parseBrackets p = parseToken "(" *> p <* parseToken ")"
parseInfix :: String -> Parser Char a -> Parser Char a -> Parser Char (a, a)
parseInfix token p1 p2 = (,) <$> (p1 <* parseToken token) <*> p2
parseConnective :: String -> Parser Char a -> Parser Char a -> Parser Char (a, a)
parseConnective token p1 p2 = parseBrackets $ parseInfix token p1 p2
stmtAtom :: Parser Char Statement
stmtAtom = Atom <$> parse
where
parse = parseWhile $ \char -> isAlphaNum char || char == '_'
stmtNot :: Parser Char Statement
stmtNot = Not <$> (parseToken "!" *> stmt)
stmtAnd :: Parser Char Statement
stmtAnd = uncurry And <$> parseConnective "&" stmt stmt
stmtOr :: Parser Char Statement
stmtOr = uncurry Or <$> parseConnective "|" stmt stmt
stmtImplies :: Parser Char Statement
stmtImplies = uncurry Implies <$> parseConnective "->" stmt stmt
stmtIff :: Parser Char Statement
stmtIff = uncurry Iff <$> parseConnective "<->" stmt stmt
stmt :: Parser Char Statement
stmt = stmtAtom <|> stmtNot <|> stmtAnd <|> stmtOr <|> stmtImplies <|> stmtIff
{-
ghci> runParser stmt "(!a<->((!(p->q)&x)|y))"
Just (Iff (Not (Atom "a")) (Or (And (Not (Implies (Atom "p") (Atom "q"))) (Atom "x")) (Atom "y")),"")
-}
p :: Statement
p = fromJust $ fst <$> runParser stmt "((a->b)<->!c)"
q :: Statement
q = fromJust $ fst <$> runParser stmt "(!a<->((!(p->q)&x)|y))"
atoms :: Statement -> S.Set String
atoms (Atom key) = S.singleton key
atoms (Not s) = atoms s
atoms (And s1 s2) = S.union (atoms s1) (atoms s2)
atoms (Or s1 s2) = S.union (atoms s1) (atoms s2)
atoms (Implies s1 s2) = S.union (atoms s1) (atoms s2)
atoms (Iff s1 s2) = S.union (atoms s1) (atoms s2)
eval :: [(String, Bool)] -> Statement -> Maybe Bool
eval assignments = aux
where
aux (Atom key) = lookup key assignments
aux (Not s) = not <$> 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
atomsList = S.toList $ atoms s
values = [fromJust $ eval assignments s | assignments <- enumerate $ atomsList]
enumerate :: [a] -> [[(a, Bool)]]
enumerate keys = map reverse $ aux start
where
aux assignments = (assignments:) $
case next assignments of
Nothing -> []
Just (assignments') -> aux assignments'
start = [(key, False) | key <- keys]
next [] = Nothing
next ((k, False):rest) = Just $ (k, True):rest
next ((k, True):rest) = ((k, False):) <$> (next rest)
{-
ghci> bucket $ fromJust $ fst <$> runParser stmt "(p<->p)"
Tautology
ghci> bucket p
Contingent
ghci> bucket q
Contingent
ghci> bucket $ fromJust $ fst <$> runParser stmt "(p<->!p)"
Contradiction
ghci> bucket $ fromJust $ fst <$> runParser stmt "(p|!p)"
Tautology
ghci> bucket $ fromJust $ fst <$> runParser stmt "(p->p)"
Tautology
ghci> bucket $ fromJust $ fst <$> runParser stmt "(p&!p)"
Contradiction
ghci> bucket $ fromJust $ fst <$> runParser stmt "(!(p->q)&!p)"
Contradiction
ghci> bucket $ fromJust $ fst <$> runParser stmt "(p|(p->q))"
Tautology
ghci> bucket $ fromJust $ fst <$> runParser stmt "((p->q)->(!p->r))"
Contingent
ghci> bucket $ fromJust $ fst <$> runParser stmt "(!(a&b)<->(!a|!b))"
Tautology
ghci> bucket $ fromJust $ fst <$> runParser stmt "(!(a|b)<->(!a&!b))"
Tautology
-}
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 -> Maybe [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 atomsList) 'c' <>
"||" <>
cellsSpec <>
"}\n"
close = "\\end{tabular}\n\n"
serial :: [Cell]
serial = serializeCells Latex s
atomsList :: [String]
atomsList = S.toAscList $ atoms s
header :: String
header =
intercalate " & " (map dollars atomsList) <>
" & " <>
intercalate " & " (map dollars $ map fromCell serial) <>
" \\\\\n"
dollars :: String -> String
dollars string = "$" <> string <> "$"
body :: String
body = concat $ map line $ enumerate atomsList
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]) $
fromJust $ serializeLatexTruthTableRow assignments s

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Makefile Normal file
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main: dirty clean
dirty:
ghc Main.hs -o logic
clean:
find | grep -E '\.(hi|o)' | xargs rm --