diff --git a/CG.hs b/CG.hs new file mode 100644 --- /dev/null +++ b/CG.hs @@ -0,0 +1,395 @@ +{-# LANGUAGE OverloadedStrings, ViewPatterns, FlexibleContexts, PartialTypeSignatures, TupleSections, RecordWildCards, ScopedTypeVariables #-} +module Main where + + +import Prelude hiding (lex) +import Control.Exception (IOException, handle) +import Control.Monad (forM,forM_,when,unless) +import Data.List (stripPrefix) +import Data.List.Split (splitOn) +import Data.Map (Map) +import Data.Maybe (fromMaybe,maybe) +import qualified Data.Text as T +import qualified Data.Text.IO as T +import Data.Void (Void) +import System.Console.GetOpt (OptDescr(..),ArgDescr(..),ArgOrder(..),usageInfo,getOpt) +import System.Directory (renameFile,doesFileExist,getDirectoryContents,createDirectoryIfMissing) +import System.Environment (getProgName,getArgs,getEnv) +import System.Exit (ExitCode(..), exitSuccess, exitFailure) +import System.FilePath (takeBaseName,dropExtension,(),(<.>),(-<.>)) +import System.IO +import System.Process +import qualified Text.Parsec as P (parse) +import Text.Printf (printf) + +import CG.Prover +import CG.Parser +import CG.Base hiding (Term) +import CG.Parsing +import CG.ToAgda + + +descInstalled :: FilePath -> IO () +descInstalled dir = do + let + readDesc :: FilePath -> IO (Maybe String) + readDesc f = + handle (\(e :: IOException) -> return Nothing) + (stripPrefix "-- " . T.unpack <$> withFile f ReadMode T.hGetLine) + + filesAndDirectories <- getDirectoryContents dir + forM_ filesAndDirectories $ \fileOrDirectory -> do + isFile <- doesFileExist (dir fileOrDirectory) + when isFile $ do + mbDesc <- readDesc (dir fileOrDirectory) + case mbDesc of + Nothing -> return () + Just desc -> do + putStrLn (printf "%s%-32s %s" (replicate 19 ' ') fileOrDirectory desc) + + + +main :: IO () +main = do + + args <- getArgs + + let (actions, _, _) = getOpt Permute options args + opts <- foldl (>>=) (return defaultOptions) actions + let Options { optTasks = tasks + , optLexicon = mbLexicon + , optSystem = sys@System{..} + , optOutput = out + , optGoal = g + , optDepth = d + , optVerbose = verbose + } = opts + + let + mbHandles :: IO (Maybe Handle, Maybe Handle) + mbHandles = + if verbose then return (Nothing, Nothing) + else do f <- openFile "/dev/null" AppendMode; return (Just f, Just f) + + -- run a command + runCommand :: String -> [String] -> Maybe FilePath -> IO () + runCommand cmd args dir = do + putStrLn (showCommandForUser cmd args) + (mbOut,mbErr) <- mbHandles + p <- runProcess cmd args dir Nothing Nothing mbOut mbErr + e <- waitForProcess p + case e of + ExitSuccess -> return () + ExitFailure r -> error ("Error in `"++cmd++"' (exit "++show r++")") + + -- use the given lexicon, otherwise read the default lexicon + givenOrDefaultLexicon :: IO (Map String (Term ConId Void)) + givenOrDefaultLexicon = case mbLexicon of + Just lx -> return lx + Nothing -> do hPutStrLn stderr "Reading default lexicon..."; readLexicon "default" + + + when (null tasks) + (putStrLn "Usage: For basic information, try the `--help' option.") + + let + runTask :: Task -> IO [Result] + runTask (Solve str) = case P.parse judgement "" str of + Left e -> error (show e) + Right g -> return $ map (uncurry Solved) (solve sys d [g]) + runTask (Parse sent expr) = do + lx <- givenOrDefaultLexicon + return (map (uncurry $ Parsed sent expr) (parse sys d lx sent g)) + + proofs <- concat <$> mapM runTask tasks + + let + generateAgda :: Maybe FilePath -> IO [FilePath] + generateAgda Nothing = writeAgdaFile stdout "Main" sys proofs g + generateAgda (Just fn) = withFile fn WriteMode (\h -> writeAgdaFile h (takeBaseName fn) sys proofs g) + + generateLaTeX :: Maybe FilePath -> IO [FilePath] + generateLaTeX targetDir = do + home <- fromMaybe "." <$> getCgHome + + let mainFile = home "Main.agda" + createDirectoryIfMissing True home + fileList <- withFile mainFile WriteMode (\h -> writeAgdaFile h "Main" sys proofs g) + + agdaInclude <- map ("-i"++) . (home:) . splitOn ":" <$> getEnv "AGDA_PATH" + let args = "--compile" : "--compile-dir" : home : agdaInclude ++ [mainFile] + + runCommand "agda" args (Just home) + runCommand (dropExtension mainFile) [] targetDir + + return fileList + + generatePNG :: Maybe FilePath -> IO [FilePath] + generatePNG mbDir = do + + let targetDir = fromMaybe "." mbDir + home <- fromMaybe "." <$> getCgHome + latexFiles <- generateLaTeX (Just home) + + forM_ latexFiles $ \latexFile -> do + + putStrLn ("Processing `"++latexFile++"'...") + + contents <- readFile (home latexFile <.> "tex") + writeFile (home latexFile <.> "standalone_tex") . unlines $ + [ "\\documentclass[preview,border={10pt 10pt 50pt 10pt}]{standalone}" + , preamble + , "\\begin{document}" + , contents + , "\\end{document}" + ] + + let args1 = ["-shell-escape" + ,"-output-directory",home + ,latexFile <.> "standalone_tex"] + runCommand "pdflatex" args1 (Just home) + + let args2 = ["-density","300" + ,home latexFile <.> "pdf" + ,"-quality","90" + ,home latexFile <.> "png"] + runCommand "convert" args2 (Just home) + + renameFile (home latexFile <.> "png") (targetDir latexFile <.> "png") + + return latexFiles + + case out of + StdOut -> mapM_ printResult proofs + AgdaFile fn -> do maybe (return ()) checkFile fn; generateAgda fn; return () + LaTeX mb -> do generateLaTeX mb >>= mapM_ (putStrLn . (<.> "tex")) + PNG mb -> do generatePNG mb >>= mapM_ (putStrLn . (<.> "png")) + + +-- * Command-Line Options + +data Task + = Solve String + | Parse String [String] + +data Output + = StdOut -- ^ Print proofs to the standard output. + | AgdaFile (Maybe FilePath) -- ^ Convert proofs to an Agda program and print it. + | LaTeX (Maybe FilePath) -- ^ Convert proofs to LaTeX files. + | PNG (Maybe FilePath) -- ^ Convert proofs to PNG files. + +data Options = Options + { optTasks :: [Task] + , optLexicon :: Maybe (Map String (Term ConId Void)) + , optSystem :: System ConId + , optOutput :: Output + , optGoal :: Term ConId Void + , optDepth :: Int + , optVerbose :: Bool + } + +defaultOptions :: Options +defaultOptions = Options + { optTasks = [] + , optLexicon = Nothing + , optSystem = error "System must be specified." + , optOutput = StdOut + , optGoal = Con (NegAtom "s") [] + , optDepth = 5 + , optVerbose = False + } + +options :: [ OptDescr (Options -> IO Options) ] +options = + [ Option [] ["solve"] + (ReqArg (\arg opt -> return opt { optTasks = optTasks opt ++ [Solve arg] }) "SEQUENT") + "Search for proof of a sequent." + + , Option [] ["parse"] + (ReqArg (\arg opt -> return opt { optTasks = optTasks opt ++ [Parse arg []] }) "SENTENCE") + "Parse the given sentence." + + , Option [] ["to","or"] + (ReqArg addExpected "EXPRESSION") + "Generate check if the previous test results in this expression." + + , Option "s" ["system"] + (ReqArg (\arg opt -> do sys <- readSystem arg; return opt { optSystem = sys }) "SYSTEM_FILE") + "Type-logical system (see below)." + + , Option "d" ["depth"] + (ReqArg (\arg opt -> return opt { optDepth = read arg }) "SEARCH_DEPTH") + "Set the search depth. For systems marked as `infinite' only. Defaults to `5'." + + , Option "l" ["lexicon"] + (ReqArg (\arg opt -> do lex <- readLexicon arg; return opt { optLexicon = Just lex }) "LEXICON_FILE") + "Lexicon used in parsing. Defaults to `$CGTOOL_HOME/lex/default'." + + , Option "g" ["goal"] + (ReqArg (\arg opt -> do g <- parseGoal arg; return opt { optGoal = g }) "GOAL_FORMULA") + "Goal formula for parsing. Defaults to `s⁻'." + + , Option [] ["to-agda"] + (OptArg (\arg opt -> do return opt { optOutput = AgdaFile arg }) "AGDA_FILE") + "Produce an Agda module, and write it to the given file (or stdout)." + + , Option [] ["to-latex"] + (OptArg (\arg opt -> do return opt { optOutput = LaTeX arg }) "DIRECTORY") + "Produce a TeX file for each proof, and write it to DIRECTORY." + + , Option [] ["to-png"] + (OptArg (\arg opt -> do return opt { optOutput = PNG arg }) "DIRECTORY") + "Produce a PNG file for each proof, and write it to DIRECTORY." + + , Option "v" ["verbose"] + (NoArg (\opt -> return opt { optVerbose = True })) + "Verbose output." + + , Option "h" ["help"] + (NoArg (\_ -> do + prg <- getProgName + hPutStrLn stderr (usageInfo prg options) + mbCgHome <- getCgHome + case mbCgHome of + Nothing -> do + putStrLn "Warning: `$CGTOOL_HOME' is not set." + exitFailure + Just cgHome -> do + hPutStrLn stderr (printf "\nAvailable systems (in `%s')\n" (cgHome "sys")) + descInstalled (cgHome "sys") + hPutStrLn stderr (printf "\nAvailable lexicons (in `%s')\n" (cgHome "lex")) + descInstalled (cgHome "lex") + exitSuccess + )) + "Show help." + ] + + + +-- * Helper functions + +compileAgda :: FilePath -> FilePath -> IO ExitCode +compileAgda dir mainFile = do + agdaInclude <- map ("-i"++) . (dir:) . splitOn ":" <$> getEnv "AGDA_PATH" + let args = "--compile" : "--compile-dir" : dir : agdaInclude ++ [mainFile] + (ext,out,err) <- readProcessWithExitCode "agda" args "" + case ext of + ExitSuccess -> return ExitSuccess + _ -> do hPutStrLn stdout out; hPutStrLn stderr err; return ext + +-- |Check if a given file exists, and if so ask for a confirmation +-- for overwriting the file. +checkFile :: FilePath -> IO () +checkFile fn = do + fileExists <- doesFileExist fn + unless fileExists $ do + hSetBuffering stdout NoBuffering + putStr (fn ++ " exists. Overwrite? (y/n) ") + hSetBuffering stdin NoBuffering + hSetEcho stdin False + hFlushInput stdin + answer <- yorn + when (answer == 'Y') exitSuccess + where + hFlushInput hdl = do + r <- hReady hdl + when r (hGetChar hdl >> hFlushInput hdl) + + yorn = do + c <- getChar + if c == 'Y' || c == 'N' then return c + else if c == 'y' then return 'Y' + else if c == 'n' then return 'N' + else yorn + + +-- |Print results. +printResult :: Result -> IO () +printResult (Solved g p) = do print g; print p +printResult (Parsed s _ g p) = do putStrLn s; print g; print p + + +-- |Add an expected result to the most recent @Parse@ task. +addExpected :: String -> Options -> IO Options +addExpected expr opt@Options{..} = do + progName <- getProgName + + when (null optTasks) $ + do putStrLn ("Usage: "++progName++"--parse SENTENCE --to " + ++"EXPRESSION [--or EXPRESSION]"); exitFailure + + let lastTask = last optTasks + + unless (isParse lastTask) $ + do putStrLn ("Usage: "++progName++"--parse SENTENCE --to " + ++"EXPRESSION [--or EXPRESSION]"); exitFailure + + let (Parse sent exprs) = lastTask + return opt { optTasks = init optTasks ++ [Parse sent (exprs ++ [expr])]} + + +-- |Check if given Task is a parse-task with no expected result. +isParse :: Task -> Bool +isParse (Parse _ _) = True +isParse _ = False + + +-- preamble.tex +preamble :: String +preamble = unlines + [ "\\usepackage{adjustbox}%" + , "\\usepackage[labelformat=empty]{caption}%" + , "\\usepackage{amssymb}%" + , "\\usepackage{amsmath}%" + , "\\usepackage{bussproofs}%" + , "\\usepackage[usenames,dvipsnames]{color}%" + , "\\usepackage{etoolbox}%" + , "\\usepackage{mdframed}%" + , "\\usepackage{pict2e}%" + , "\\usepackage{picture}%" + , "\\usepackage{scalerel}%" + , "\\usepackage{stmaryrd}%" + , "\\usepackage{textgreek}%" + , "\\usepackage{ucs}%" + , "\\usepackage[utf8x]{inputenc}%" + , "\\usepackage{xifthen}%" + , "" + , "\\EnableBpAbbreviations%" + , "" + , "\\makeatletter" + , "\\newcommand{\\pictslash}[2]{%" + , " \\vcenter{%" + , " \\sbox0{$\\m@th#1\\varobslash$}\\dimen0=.55\\wd0" + , " \\hbox to\\wd 0{%" + , " \\hfil\\pictslash@aux#2\\hfil" + , " }%" + , " }%" + , "}" + , "\\newcommand{\\pictslash@aux}[2]{%" + , " \\begin{picture}(\\dimen0,\\dimen0)" + , " \\roundcap" + , " \\linethickness{.15ex}" + , " \\put(0,#1\\dimen0){\\line(1,#2){\\dimen0}}" + , " \\end{picture}%" + , "}" + , "\\makeatother" + , "" + , "\\newcommand{\\varslash}{%" + , " \\mathbin{\\mathpalette\\pictslash{{0}{1}}}%" + , "}" + , "\\newcommand{\\varbslash}{%" + , " \\mathbin{\\mathpalette\\pictslash{{1}{-1}}}%" + , "}" + , "\\newcommand{\\focus}[1]{%" + , " \\adjustbox{padding=.4em .15ex .1em .15ex,bgcolor=Cyan}{%" + , " \\ensuremath{\\color{white}\\rule[-4pt]{0pt}{14pt}#1}" + , " }%" + , "}" + , "" + , "\\newcommand{\\varbox}[1][]{\\ifthenelse{\\isempty{#1}}{\\Box}{\\,[\\,#1\\,]\\,}}" + , "\\newcommand{\\vardia}[1][]{\\ifthenelse{\\isempty{#1}}{\\Diamond}{\\,\\langle\\,#1\\,\\rangle\\,}}" + , "\\newcommand{\\varpref}[1]{{}_{#1}}" + , "\\newcommand{\\varsuff}[1]{{}^{#1}}" + , "\\newcommand{\\vardown}[1]{\\,\\cdot\\,#1\\,\\cdot\\,}" + , "\\renewcommand{\\fCenter}{\\mathbin{\\vdash}}" + ] diff --git a/CG/Base.hs b/CG/Base.hs new file mode 100644 --- /dev/null +++ b/CG/Base.hs @@ -0,0 +1,260 @@ +{-# LANGUAGE DeriveGeneric, TypeSynonymInstances, FlexibleInstances, + FlexibleContexts, RecordWildCards, UndecidableInstances #-} +module CG.Base (ConId(..) + ,nullary,unary,binary + ,unaryLogical,unaryStructural + ,binaryLogical,binaryStructural + ,sequents + ,toLogical,toStructural + ,ASCII(..),Result(..) + ,module X + ) where + + +import CG.Prover as X +import Control.DeepSeq (NFData) +import Data.Hashable (Hashable) +import Data.Serialize (Serialize) +import Data.Void (Void) +import GHC.Generics (Generic) + + +-- * Operators + +data ConId + + -- atomic formulas + = PosAtom String + | NegAtom String + + -- mediator between logical and structural formulas + | Down + + -- logical operators + | FProd | FImpR | FImpL + | FPlus | FSubL | FSubR + | F0L | F0R | FBox + | F1L | F1R | FDia + + -- structural operators + | SProd | SImpR | SImpL + | SPlus | SSubL | SSubR + | S0L | S0R | SBox + | S1L | S1R | SDia + | Comma + + -- hollow product and slashes + | HProd | HImpR | HImpL + + -- sequents + | JAlgebr | JStruct + | JFocusL | JFocusR + + deriving (Eq,Ord,Show,Generic) + + +instance Hashable ConId +instance NFData ConId +instance Serialize ConId + + +-- * Groupings of operators. + +unaryLogical :: [ConId] +unaryLogical = [F0L, F0R, FBox, F1L, F1R, FDia, HProd, HImpR, HImpL] + +unaryStructural :: [ConId] +unaryStructural = [S0L, S0R, SBox, S1L, S1R, SDia] + +binaryLogical :: [ConId] +binaryLogical = [FProd, FImpR, FImpL, FPlus, FSubL, FSubR] + +binaryStructural :: [ConId] +binaryStructural = [SProd, SImpR, SImpL, SPlus, SSubL, SSubR, Comma] + +sequents :: [ConId] +sequents = [JAlgebr, JStruct, JFocusL, JFocusL] + + +-- |Convert structural operators to their logical equivalents. +toLogical :: ConId -> ConId +toLogical SProd = FProd +toLogical SImpR = FImpR +toLogical SImpL = FImpL +toLogical SPlus = FPlus +toLogical SSubL = FSubL +toLogical SSubR = FSubR +toLogical S0L = F0L +toLogical S0R = F0R +toLogical SBox = FBox +toLogical S1L = F1L +toLogical S1R = F1R +toLogical SDia = FDia +toLogical c = c + + +-- |Convert logical operators to their structural equivalents. +toStructural :: ConId -> ConId +toStructural FProd = SProd +toStructural FImpR = SImpR +toStructural FImpL = SImpL +toStructural FPlus = SPlus +toStructural FSubL = SSubL +toStructural FSubR = SSubR +toStructural F0L = S0L +toStructural F0R = S0R +toStructural FBox = SBox +toStructural F1L = S1L +toStructural F1R = S1R +toStructural FDia = SDia +toStructural c = c + + +-- * Utility constructors + +nullary :: ConId -> Term ConId v +nullary c = Con c [] + +unary :: ConId -> Term ConId v -> Term ConId v +unary c x = Con c [x] + +binary :: ConId -> Term ConId v -> Term ConId v -> Term ConId v +binary c x y = Con c [x,y] + + +-- * Guards + +instance Guardable ConId where + + isAtomic (Con (PosAtom _) _) = True + isAtomic (Con (NegAtom _) _) = True + isAtomic _ = False + + isPositive (Var _) = True + isPositive (Con (PosAtom _) _) = True + isPositive (Con (NegAtom _) _) = False + isPositive (Con FProd _) = True + isPositive (Con FSubL _) = True + isPositive (Con FSubR _) = True + isPositive (Con HProd _) = True + isPositive (Con F1L _) = True + isPositive (Con F1R _) = True + isPositive (Con FDia _) = True + isPositive _ = False + + isNegative (Var _) = True + isNegative (Con (PosAtom _) _) = False + isNegative (Con (NegAtom _) _) = True + isNegative (Con FPlus _) = True + isNegative (Con FImpR _) = True + isNegative (Con FImpL _) = True + isNegative (Con HImpR _) = True + isNegative (Con HImpL _) = True + isNegative (Con F0L _) = True + isNegative (Con F0R _) = True + isNegative (Con FBox _) = True + isNegative _ = False + + + +-- * Printing + +instance ToString ConId where + toString (PosAtom x) = x + toString (NegAtom x) = x ++ "⁻" + toString F0L = "₀"; toString F0R = "⁰"; toString FBox = "□" + toString F1L = "₁"; toString F1R = "¹"; toString FDia = "◇" + toString FProd = "⊗"; toString FImpR = "⇒"; toString FImpL = "⇐" + toString SProd = "⊗"; toString SImpR = "⇒"; toString SImpL = "⇐" + toString HProd = "∘"; toString HImpR = "⇨"; toString HImpL = "⇦" + toString FPlus = "⊕"; toString FSubL = "⇚"; toString FSubR = "⇛" + toString SPlus = "⊕"; toString SSubL = "⇚"; toString SSubR = "⇛" + toString S0L = "₀"; toString S0R = "⁰"; toString SBox = "[]" + toString S1L = "₁"; toString S1R = "¹"; toString SDia = "⟨⟩" + toString JAlgebr = "⊢"; toString JStruct = "⊢" + toString JFocusL = "⊢"; toString JFocusR = "⊢" + toString Down = "·"; toString Comma = "," + +instance Operator ConId where + + prec (PosAtom _) = 0 + prec (NegAtom _) = 0 + prec F0L = 9; prec F0R = 9; prec FBox = 9 + prec F1L = 9; prec F1R = 9; prec FDia = 9 + prec FProd = 8; prec FImpR = 7; prec FImpL = 7 + prec FPlus = 8; prec FSubL = 7; prec FSubR = 7 + prec HProd = 8; prec HImpR = 7; prec HImpL = 7 + prec S0L = 6; prec S0R = 6; prec SBox = 0 + prec S1L = 6; prec S1R = 6; prec SDia = 0 + prec SProd = 5; prec SImpR = 4; prec SImpL = 4 + prec SPlus = 5; prec SSubL = 4; prec SSubR = 4 + prec JAlgebr = 0; prec JStruct = 0 + prec JFocusL = 0; prec JFocusR = 0 + prec Down = 0; prec Comma = 3 + + template (PosAtom x) _ = showString x . showChar ' ' + template (NegAtom x) _ = showString x . showString "⁻ " + template F0L [x] = showString "₀ " . x + template F0R [x] = x . showString "⁰ " + template FBox [x] = showString "□ " . x + template F1L [x] = showString "₁ " . x + template F1R [x] = x . showString "¹ " + template FDia [x] = showString "◇ " . x + template FProd [x,y] = x . showString "⊗ " . y + template FImpR [x,y] = x . showString "⇒ " . y + template FImpL [x,y] = x . showString "⇐ " . y + template SProd [x,y] = x . showString "⊗ " . y + template SImpR [x,y] = x . showString "⇒ " . y + template SImpL [x,y] = x . showString "⇐ " . y + template HProd [x,y] = x . showString "∘ " . y + template HImpR [x,y] = x . showString "⇨ " . y + template HImpL [x,y] = x . showString "⇦ " . y + template FPlus [x,y] = x . showString "⊕ " . y + template FSubL [x,y] = x . showString "⇚ " . y + template FSubR [x,y] = x . showString "⇛ " . y + template SPlus [x,y] = x . showString "⊕ " . y + template SSubL [x,y] = x . showString "⇚ " . y + template SSubR [x,y] = x . showString "⇛ " . y + template S0L [x] = showString "₀ " . x + template S0R [x] = x . showString "⁰ " + template SBox [x] = showString "[ " . x . showString "]" + template S1L [x] = showString "₁ " . x + template S1R [x] = x . showString "¹ " + template SDia [x] = showString "⟨ " . x . showString "⟩" + template JAlgebr [x,y] = x . showString "⊢ " . y + template JStruct [x,y] = x . showString "⊢ " . y + template JFocusL [x,y] = showString "[ " . x . showString "]⊢ " . y + template JFocusR [x,y] = x . showString "⊢[ " . y . showString "] " + template Down [x] = showString "· " . x . showString "· " + template Comma [x,y] = x . showString ", " . y + + +-- * ASCII printing + +newtype ASCII a = ASCII a + +instance ToString (ASCII ConId) where + toString (ASCII (PosAtom x)) = x + toString (ASCII (NegAtom x)) = x ++ "'" + toString (ASCII F0L) = "0" ; toString (ASCII F0R) = "0" ; toString (ASCII FBox) = "[]" + toString (ASCII F1L) = "1" ; toString (ASCII F1R) = "1" ; toString (ASCII FDia) = "<>" + toString (ASCII FProd) = "*" ; toString (ASCII FImpR) = "->"; toString (ASCII FImpL) = "<-" + toString (ASCII SProd) = "*" ; toString (ASCII SImpR) = "->"; toString (ASCII SImpL) = "<-" + toString (ASCII HProd) = "o" ; toString (ASCII HImpR) = "-o"; toString (ASCII HImpL) = "o-" + toString (ASCII FPlus) = "+" ; toString (ASCII FSubL) = "<="; toString (ASCII FSubR) = "=>" + toString (ASCII SPlus) = "+" ; toString (ASCII SSubL) = "<="; toString (ASCII SSubR) = "=>" + toString (ASCII S0L) = "0" ; toString (ASCII S0R) = "0" ; toString (ASCII SBox) = "[]" + toString (ASCII S1L) = "1" ; toString (ASCII S1R) = "1" ; toString (ASCII SDia) = "<>" + toString (ASCII JAlgebr) = "|-"; toString (ASCII JStruct) = "|-" + toString (ASCII JFocusL) = "|-"; toString (ASCII JFocusR) = "|-" + toString (ASCII Down) = "." ; toString (ASCII Comma) = "," + + +-- * Proofs + +type Proof = Term RuleId Void + +data Result + = Solved (Term ConId Void) Proof + | Parsed String [String] (Term ConId Void) Proof + deriving (Show) diff --git a/CG/Parser.hs b/CG/Parser.hs new file mode 100644 --- /dev/null +++ b/CG/Parser.hs @@ -0,0 +1,82 @@ +{-# LANGUAGE TupleSections, RecordWildCards #-} +module CG.Parser (parse) where + + +import Prelude hiding (lex) +import CG.Base +import Control.Arrow (first) +import Control.Parallel.Strategies +import Data.List (nub) +import Data.Map (Map) +import qualified Data.Map as M +import Data.Void (Void) + + + +-- * Parsing + +-- |Create all possible structures from a list of formulas, joining +-- them with the binary structural connective @·⊗·@, and then find +-- all proofs for each of these structures, returning a list of +-- structures paired with their proofs. +-- Note: the resulting list may contain pairs for structures for +-- which no proofs were found. +parse :: System ConId -- ^ Inference system + -> Int -- ^ Search depth + -> Map String (Term ConId Void) -- ^ Lexicon + -> String -- ^ Sentence + -> Term ConId Void -- ^ Goal formula + -> [(Term ConId Void,Term RuleId Void)] +parse sys@System{..} d lex sent g = + solve sys d judgements `using` parList rdeepseq + where + -- read the entries from the lexicon, wrapping them in a + -- down constructor if the logic is structural + entries = lookupAll lex (words sent) + entries' + | structural = map (unary Down) entries + | otherwise = entries + + -- construct the left-hand sides using the @brackets@ function + leftHandSides = brackets (unary <$> unaryOp) (binary (unsafeBinaryOp sys)) entries' + + -- construct all possible judgements by combining them with + -- the sequent and the goal formula + sequent = if structural then JFocusR else JAlgebr + judgements = map (flip (binary sequent) g) leftHandSides + + + +-- |Look up all words in a given list of words in a lexicon. +lookupAll :: Map String (Term ConId Void) -- ^ Lexicon + -> [String] -- ^ Sentence + -> [Term ConId Void] +lookupAll _ [ ] = [] +lookupAll lex (w:ws) = case M.lookup w lex of + Just tm -> tm : lookupAll lex ws + Nothing -> error ("Cannot find `"++w++"' in the lexicon.") + + + +-- |Generate all binary trees with n nodes, formed by applications of +-- a given binary operator, with at most one application of a given +-- unary operator at every node. +brackets :: (Eq a) => Maybe (a -> a) -> (a -> a -> a) -> [a] -> [a] +brackets mbPre op = nub . brack where + + brack [ ] = [ ] + brack [x] = [x] + brack lst = maybe (go id) (\pre -> go id ++ go pre) mbPre + where + go f = [ f (l `op` r) | (ls,rs) <- split lst, l <- brack ls, r <- brack rs ] + + split [_] = [] + split (x:xs) = ([x],xs) : map (first (x:)) (split xs) + + +-- |Retrieve the single binary connective from the system, or throw an error. +unsafeBinaryOp :: System c -> c +unsafeBinaryOp System{..} = case binaryOp of + [ ] -> error "Must set at least one binary operator to parse." + [ f ] -> f + (_:_) -> error "Parsing with multiple binary operators is not implemented." diff --git a/CG/Parsing.hs b/CG/Parsing.hs new file mode 100644 --- /dev/null +++ b/CG/Parsing.hs @@ -0,0 +1,330 @@ +{-# LANGUAGE RecordWildCards, RankNTypes, TupleSections, ScopedTypeVariables #-} +module CG.Parsing (readSystem + ,readLexicon + ,parseGoal + ,formula + ,structure + ,judgement + ,getCgHome + )where + + +import CG.Base +import Control.Exception (IOException, handle) +import Data.Char (isSpace) +import Data.List (nub,isPrefixOf) +import Data.Void (Void) +import Data.Map (Map) +import qualified Data.Map as M +import Text.Parsec hiding (option) +import Text.Parsec.Expr +import Text.Parsec.Error (setErrorPos) +import Text.Parsec.String (Parser) +import Text.Parsec.Language (LanguageDef,haskellStyle) +import Text.Parsec.Token (TokenParser,GenTokenParser(..),GenLanguageDef(..),makeTokenParser) +import System.Directory (doesFileExist) +import System.Environment (getEnv) +import System.FilePath (()) + + +-- * Variable Parsing + +class VarParser v where + formulaVar :: Parser v + structureVar :: Parser v + +instance VarParser Void where + formulaVar = oneOf "ABCD" *> unexpected "Variables {A,B,C,D} are not allowed." + structureVar = oneOf "XYZW" *> unexpected "Variables {X,Y,Z,W} are not allowed." + +instance VarParser Char where + formulaVar = lexeme cg (oneOf "ABCD") "formula variable" + structureVar = lexeme cg (oneOf "XYZW") "structure variable" + + +-- * Language Definition + +cgDef :: LanguageDef st +cgDef = haskellStyle + { identStart = identLetter cgDef + , identLetter = satisfy (\c -> not (isSpace c || c `elem` "()")) + , opStart = opLetter cgDef + , opLetter = oneOf "()" + , reservedNames = let + + reservedNames = ["where","and","atomic","positive","negative"] + reservedOpNames = nub (map toString operators ++ map (toString . ASCII) operators) + operators = concat [unaryLogical ,unaryStructural + ,binaryLogical,binaryStructural + ,sequents, [Down]] + + in reservedNames ++ reservedOpNames + } + +cg :: TokenParser st +cg = makeTokenParser cgDef + + +-- * Term Parsing + +con :: ConId -> Parser () +con c = reserved (toString c) <|> reserved (toString (ASCII c)) + where + TokenParser{..} = cg + +con' :: ConId -> Parser () +con' c = do symbol (toString c) <|> symbol (toString (ASCII c)); return () + where + TokenParser{..} = cg + +infl c = Infix (con c *> return (binary c)) AssocLeft +infr c = Infix (con c *> return (binary c)) AssocRight +pref c = Prefix (con c *> return (unary c)) +post c = Postfix (con c *> return (unary c)) + + +atom :: Parser (Term ConId v) +atom = do + let TokenParser{..} = cg + x <- identifier + return . nullary $ + if last x `elem` "⁻'" + then NegAtom (init x) + else PosAtom x + + +formulaWithVar :: Parser (Term ConId Char) +formulaWithVar = formula + +formula :: VarParser v => Parser (Term ConId v) +formula = + buildExpressionParser table (parens formula <|> fvar <|> atom) + where + TokenParser{..} = cg + fvar = Var <$> formulaVar + table = + [ [ pref F0L , post F0R , pref FBox + , pref F1L , post F1R , pref FDia ] + , [ infl FSubL , infl FImpL , infl HImpL + , infr FSubR , infr FImpR , infr HImpR ] + , [ infr FProd , infl FPlus , infr HProd ] + ] + + +structureWithVar :: Parser (Term ConId Char) +structureWithVar = structure + +structure :: VarParser v => Parser (Term ConId v) +structure = + buildExpressionParser table (parens structure <|> sdia <|> sbox <|> svar <|> down) + where + TokenParser{..} = cg + + svar = Var <$> structureVar + down = unary Down <$> cdots formula "down operator" + sdia = unary SDia <$> (angles structure <|> rangles structure) + sbox = unary SBox <$> (brackets structure) + cdots = between (con Down) (con Down) + rangles = between (symbol "⟨") (symbol "⟩") + table = + [ [ pref S0L , post S0R , pref S1L , post S1R ] + , [ infl SSubL , infl SImpL , infr SSubR , infr SImpR ] + , [ infr SProd , infl SPlus ] + , [ infr Comma ] + ] + + +judgementWithVar :: Parser (Term ConId Char) +judgementWithVar = judgement + +judgement :: VarParser v => Parser (Term ConId v) +judgement = + spaces *> (try (try jstruct <|> (try jfocusl <|> jfocusr)) <|> jalgebr) + where + TokenParser{..} = cg + + jstruct = binary JStruct <$> structure <* con' JStruct <*> structure + jfocusl = binary JFocusL <$> brackets formula <* con' JFocusL <*> structure + jfocusr = binary JFocusR <$> structure <* con' JFocusL <*> brackets formula + jalgebr = binary JAlgebr <$> formula <* con' JAlgebr <*> formula + + +lexicon :: Parser (Map String (Term ConId Void)) +lexicon = whiteSpace >> M.fromList <$> many1 entry + where + TokenParser{..} = cg + entry = (,) <$> identifier <* symbol ":" <*> formula + + +guard' :: Parser (Term ConId Char -> Guard ConId) +guard' = + do reserved "where" + gs <- sepBy1 single (reserved "and") + if null gs + then unexpected "panic!" + else return (foldr1 and gs) + where + TokenParser{..} = cg + and f g x = f x `And` g x + single = predicate <*> formulaVar + predicate = choice + [ reserved "atomic" *> return atomic + , reserved "positive" *> return positive + , reserved "negative" *> return negative + ] + + +rule :: Parser (Rule ConId Int) +rule = do + n <- identifier + _ <- symbol ":" + js <- sepBy1 judgement sep + + let ps = init js + let c = last js + let rule = mkRule n ps c + + mb <- optionMaybe guard' + return $ + case mb of + Just mk -> rule { guard = mk c } + _ -> rule + + where + TokenParser{..} = cg + sep = symbol "→" <|> symbol "-->" + + +option :: Parser Option +option = do + symbol "set" + choice (map try + [ symbol "finite" *> return (IsFinite True) + , symbol "infinite" *> return (IsFinite False) + , symbol "algebraic" *> return (IsStructural False) + , symbol "structural" *> return (IsStructural True) + , symbol "agda_name" *> symbol "=" *> (AgdaName <$> many1 (satisfy (not . isSpace))) + , symbol "agda_module" *> symbol "=" *> (AgdaModule <$> many1 (satisfy (not . isSpace))) + , symbol "parse_with" *> symbol "=" *> (ParseWith <$> pParseWith) + ]) + "option" + where + TokenParser{..} = cg + pParseWith :: Parser [ParseWith] + pParseWith = many1 (useBinary <|> useUnary) + where + useOp opt = choice . map (\c -> con c >> return (opt c)) + useUnary = useOp UseUnary (unaryLogical ++ unaryStructural) + useBinary = useOp UseBinary (binaryLogical ++ binaryStructural) + + +-- * Options + +data Option + = IsFinite Bool + | IsStructural Bool + | ParseWith [ParseWith] + | AgdaName String + | AgdaModule String + deriving Show + +data ParseWith + = UseUnary ConId + | UseBinary ConId + deriving Show + + +-- |Handle options for proof systems. +runOptions :: [Option] -> System ConId +runOptions = postProcess . foldr runOption emptySystem + where + runOption (IsFinite b) s = s { finite = b } + runOption (IsStructural b) s = s { structural = b } + runOption (AgdaName n) s = s { agdaName = Just n } + runOption (AgdaModule n) s = s { agdaModule = Just n } + runOption (ParseWith x) s = foldr runPW s x + + runPW (UseUnary op) = addUnary op + runPW (UseBinary op) = addBinary op + + postProcess sys@System{..} + | structural = sys { unaryOp = fmap toStructural unaryOp + , binaryOp = fmap toStructural binaryOp } + | otherwise = sys + + +-- * Parsers + +parseGoal :: String -> IO (Term ConId Void) +parseGoal str = case parse formula "" str of + Left e -> fail ("Could not parse goal formula `"++show str++"'.\n"++show e) + Right x -> return x + +getCgHome :: IO (Maybe String) +getCgHome = + handle (\(e :: IOException) -> return Nothing) (Just <$> getEnv "CGTOOL_HOME") + +readLexicon :: FilePath -> IO (Map String (Term ConId Void)) +readLexicon lexiconFile = do + fileExist <- doesFileExist lexiconFile + if fileExist + then unsafeReadLexicon lexiconFile + else do mbHome <- getCgHome + case mbHome of + Just home -> do + let lexiconFile' = home "lex" lexiconFile + fileExist' <- doesFileExist lexiconFile' + if fileExist' + then unsafeReadLexicon lexiconFile' + else error ("No such lexicon `" ++ lexiconFile ++ "'") + Nothing -> error ("No such lexicon `" ++ lexiconFile ++ "'") + +unsafeReadLexicon :: FilePath -> IO (Map String (Term ConId Void)) +unsafeReadLexicon lexiconFile = do + lexiconContent <- readFile lexiconFile + case parse lexicon lexiconFile lexiconContent of + Left e -> fail ("Could not parse lexicon.\n"++show e) + Right l -> return l + +readSystem :: FilePath -> IO (System ConId) +readSystem systemFile = do + fileExist <- doesFileExist systemFile + if fileExist + then unsafeReadSystem systemFile + else do mbHome <- getCgHome + case mbHome of + Just home -> do + let systemFile' = home "sys" systemFile + fileExist' <- doesFileExist systemFile' + if fileExist' + then unsafeReadSystem systemFile' + else error ("No such system `" ++ systemFile ++ "'") + Nothing -> error ("No such system `" ++ systemFile ++ "'") + + +unsafeReadSystem :: FilePath -> IO (System ConId) +unsafeReadSystem systemFile = go <$> readFile systemFile + where + go contents = sys { rules = rules } + where + TokenParser{..} = cg + + (rawOpts,rawRules) + = span (isOption . snd) -- break at first non-option + $ filter (not . isComment . snd) -- filter out all comments + $ zip [1..] -- add line numbers + $ lines contents -- split lines + + opts = map (parseOrError option systemFile) rawOpts + rules = map (parseOrError rule systemFile) rawRules + sys = runOptions opts + + isOption ln = "set" `isPrefixOf` ln + isComment ln = case parse (whiteSpace *> eof) "" ln of + Left _ -> False + Right _ -> True + + parseOrError :: Parser a -> FilePath -> (Line, String) -> a + parseOrError p fn (n,str) = case parse p fn str of + Left e -> error (show (setErrorPos (setSourceLine (errorPos e) n) e)) + Right x -> x diff --git a/CG/Prover.hs b/CG/Prover.hs new file mode 100644 --- /dev/null +++ b/CG/Prover.hs @@ -0,0 +1,85 @@ +{-# LANGUAGE GADTs, FlexibleInstances, FlexibleContexts, MultiParamTypeClasses, + UndecidableInstances, DeriveGeneric, RecordWildCards, TupleSections #-} +module CG.Prover (module X,System(..),solve,findAll,findFirst) where + + +import CG.Prover.Base as X +import CG.Prover.Ins as X +import Data.Hashable (Hashable(..)) +import Data.HashSet as S (insert,member,empty) +import Data.Maybe (mapMaybe) +import Data.Void (Void) + + +-- |Search for proofs of the given goals using the given system, using +-- either breadth-first search (for finite systems) or depth-limited +-- interleaved breadth-first search (for infinite systems). +-- Note: this algorithm performs loop-checking under the assumption +-- that /unary/ rules may cause loops, and rules of other arities +-- make progress. +solve :: (Operator c, Guardable c, Hashable c, Ord c) => System c -> Int -> [Term c Void] -> [(Term c Void, Term String Void)] +solve System{..} depth goals + | finite = concatMap (\goal -> map (goal,) (findAll goal rules)) goals + | otherwise = findFirst depth goals rules + + +-- |Search for proofs of the given goal using the gives rules using +-- breadth-first search. +-- Note: this algorithm performs loop-checking under the assumption +-- that /unary/ rules may cause loops, and rules of other arities +-- make progress. +findAll :: (Operator c, Guardable c, Hashable c, Ord c) => Term c Void -> [Rule c Int] -> [Term String Void] +findAll goal rules = slv [(S.empty,[goal],head)] [] + where + slv [ ] [ ] = [] + slv [ ] acc = slv (reverse acc) [] + slv ((_ , [],prf):prfs) acc = prf [] : slv prfs acc + slv ((seen,g:gs,prf):prfs) acc + | S.member g seen = slv prfs acc + | otherwise = slv prfs (mapMaybe step rules ++ acc) + where + step (Rule n grd a ps c) = + if runGuard grd g + then do s <- runIns (ins g c) + let prf' = prf . build n a + let seen' | a == 1 = S.insert g seen + | otherwise = S.empty + ps' <- mapM (subst s) ps + return (seen', ps' ++ gs, prf') + else fail ("Cannot apply rule `"++n++"'") + + +-- |Search for proofs of the given goal using the gives rules using +-- depth-limited breadth-first search. +-- Note: this algorithm performs loop-checking under the assumption +-- that /unary/ rules may cause loops, and rules of other arities +-- make progress. +findFirst :: (Guardable c, Hashable c, Ord c) + => Int -- ^ Search Depth + -> [Term c Void] -- ^ Goal Terms + -> [Rule c Int] -- ^ Inference rules + -> [(Term c Void, Term String Void)] +findFirst d goals rules = slv (d + 1) (fmap (\g -> (S.empty,g,[g],head)) goals) [] + where + slv 0 _ _ = [] + slv _ [ ] [ ] = [] + slv d [ ] acc = slv (d - 1) (reverse acc) [] + slv _ ((_ ,o, [],prf):_ ) _ = [(o, prf [])] + slv d ((seen,o,g:gs,prf):prfs) acc + | S.member g seen = slv d prfs acc + | otherwise = slv d prfs (mapMaybe step rules ++ acc) + where + step (Rule n grd a ps c) = + if runGuard grd g + then do s <- runIns (ins g c) + let prf' = prf . build n a + let seen' | a == 1 = S.insert g seen + | otherwise = S.empty + ps' <- mapM (subst s) ps + return (seen', o, ps' ++ gs, prf') + else fail ("Cannot apply rule `"++n++"'") + + +-- |Build a proof by adding a new constructor. +build :: r -> Int -> [Term r Void] -> [Term r Void] +build n a ts = let (xs,ys) = splitAt a ts in Con n xs : ys diff --git a/CG/Prover/Base.hs b/CG/Prover/Base.hs new file mode 100644 --- /dev/null +++ b/CG/Prover/Base.hs @@ -0,0 +1,226 @@ +{-# LANGUAGE GADTs, RankNTypes, FlexibleInstances, FlexibleContexts, + UndecidableInstances, DeriveGeneric, DeriveFunctor, DeriveFoldable, + DeriveTraversable, StandaloneDeriving, RecordWildCards #-} +module CG.Prover.Base where + + +import Control.Monad.State (MonadState(..),evalState) +import Control.DeepSeq (NFData) +import Data.Char (ord) +import Data.Hashable (Hashable) +import Data.Serialize (Serialize) +import Data.IntMap as IM (IntMap,lookup,empty,insert) +import Data.List (intersperse) +import Data.Void (Void,absurd) +import Data.Void.Unsafe (unsafeVacuous) +import GHC.Generics (Generic) + + +-- * Special Show instance for String + +class ToString a where toString :: a -> String +instance ToString Bool where toString = (++" ") . show +instance ToString Int where toString = (++" ") . show +instance ToString Void where toString = absurd +instance ToString String where toString = (++" ") +instance ToString Char where toString = (:" ") + + +-- * Terms + +data Term c v where + Var :: ! v -> Term c v + Con :: ! c -> [Term c v] -> Term c v + deriving (Eq,Ord,Generic) + + +deriving instance Functor (Term c) +deriving instance Foldable (Term c) +deriving instance Traversable (Term c) +instance (Hashable c, Hashable v) => Hashable (Term c v) +instance (NFData c, NFData v) => NFData (Term c v) +instance (Serialize c, Serialize v) => Serialize (Term c v) + + +-- |A class which defines a printable operator. The @prec@ function +-- returns the precedence of the operator. The @template@ function +-- is a generalisation of the fixity, where the operator can be +-- anything that knows how to print itself. +class Operator a where + prec :: a -> Int + template :: a -> ([ShowS] -> ShowS) + + +instance Operator String where + prec _ = 0 + template x [] = showString x + template x xs = + showParen True (foldr (.) id (intersperse (showChar ' ') (showString x : xs))) + + +instance (Operator c, ToString v) => Show (Term c v) where + showsPrec _ (Var i) = + showString (toString i) + showsPrec p (Con x xs) + | p > 0 && q > 0 && p >= q = showString "( " . ret . showString ") " + | otherwise = ret + where + q = prec x + ret = template x (map (showsPrec q) xs) + + +-- * Guards + +class (Eq c) => Guardable c where + isAtomic :: Term c v -> Bool + isPositive :: Term c v -> Bool + isNegative :: Term c v -> Bool + + +data Guard c + = Any + | Atomic (Term c Bool) + | Positive (Term c Bool) + | Negative (Term c Bool) + | And (Guard c) (Guard c) + deriving (Eq,Ord,Show,Generic) + + +instance (Hashable c) => Hashable (Guard c) +instance (NFData c) => NFData (Guard c) +instance (Serialize c) => Serialize (Guard c) + + +-- |Construct a given primitive guard, together with its arguments, into a +-- guarding function. Used internally in @runGuard@. +mkGuard :: (Guardable c) + => (forall v'. Term c v' -> Bool) + -> Term c Bool + -> (forall v'. Term c v' -> Bool) +mkGuard _ _ (Var _) = True +mkGuard p (Var True) y = p y +mkGuard _ (Var _ ) _ = True +mkGuard p (Con x xs) (Con y ys) | x == y = and (zipWith (mkGuard p) xs ys) +mkGuard _ _ _ = False + + +-- |Run a guard, checking if the given Term has all the desired properties. +runGuard :: (Guardable c) => Guard c -> (forall v. Term c v -> Bool) +runGuard Any = const True +runGuard (Atomic c) = mkGuard isAtomic c +runGuard (Positive c) = mkGuard isPositive c +runGuard (Negative c) = mkGuard isNegative c +runGuard (gd `And` gd2) = \x -> runGuard gd x && runGuard gd2 x + + +-- |Smart constructors for guards. +atomic, positive, negative :: (Eq v) => v -> Term c v -> Guard c +atomic x = Atomic . fmap (==x) +positive x = Positive . fmap (==x) +negative x = Negative . fmap (==x) + + +-- * Rules + +type RuleId = String + +data Rule c v = Rule + { name :: ! RuleId + , guard :: ! (Guard c) + , arity :: ! Int + , premises :: ! [Term c v] + , conclusion :: ! (Term c v) + } + deriving (Eq,Ord,Generic) + + +deriving instance Functor (Rule c) +deriving instance Foldable (Rule c) +deriving instance Traversable (Rule c) +instance (Hashable c, Hashable v) => Hashable (Rule c v) +instance (NFData c, NFData v) => NFData (Rule c v) +instance (Serialize c, Serialize v) => Serialize (Rule c v) + + +-- |Construct a @Rule@ from a @RuleId@, a list of premises and a conclusion. +mkRule :: RuleId -> [Term c Char] -> Term c Char -> Rule c Int +mkRule n ps c = Rule n Any (length ps) ps' c' + where + (c' : ps') = evalState (mapM (mapM label) (c : ps)) (0, IM.empty) + + label x = + do (i, vm) <- get + case IM.lookup (ord x) vm of + Just j -> return j + _ -> do put (i + 1, IM.insert (ord x) i vm); return i + + + +instance (Show c, ToString v, Show (Term c v)) => Show (Rule c v) where + showsPrec _ (Rule n g _ ps c) = + (showString (n++" : ")) . + (foldr1 (.) (intersperse (showString "→ ") (map shows (ps ++ [c])))) + + +-- * Substitutions + +type VMap c v = IntMap (Term c v) + + +-- |Apply the given variable map to a given term. Note: the variable +-- map has to contain a term for every variable used in the given +-- term. The resulting term will be variable-free. +subst :: VMap c Void -> Term c Int -> Maybe (Term c Void) +subst s = app where + + app (Con x xs) = Con x <$> mapM app xs + app (Var i ) = IM.lookup i s + + +-- * Systems + +data System c = System + { finite :: Bool + , structural :: Bool + , rules :: [Rule c Int] + + -- options related to parsing + , unaryOp :: Maybe c + , binaryOp :: [c] + + -- options related to Agda generation + , agdaName :: Maybe String + , agdaModule :: Maybe String + } + deriving (Eq,Ord,Show,Generic) + + +instance (Hashable c) => Hashable (System c) +instance (NFData c) => NFData (System c) +instance (Serialize c) => Serialize (System c) + + +-- |The minimal system. All it is missing is a binary operator. +emptySystem :: System c +emptySystem = System + { finite = False + , structural = False + , rules = [] + + , unaryOp = Nothing + , binaryOp = [] + + , agdaName = Nothing + , agdaModule = Nothing + } + +addUnary :: c -> System c -> System c +addUnary op sys = case unaryOp sys of + Nothing -> sys { unaryOp = Just op } + Just _ -> error "Cannot parse using more than one unary operator." + +addBinary :: c -> System c -> System c +addBinary op sys@System{..} = sys { binaryOp = binaryOp ++ [op] } + +addRule :: Rule c Int -> System c -> System c +addRule rule sys@System{..} = sys { rules = rules ++ [rule] } diff --git a/CG/Prover/Ins.hs b/CG/Prover/Ins.hs new file mode 100644 --- /dev/null +++ b/CG/Prover/Ins.hs @@ -0,0 +1,32 @@ +module CG.Prover.Ins (Ins,runIns,ins) where + + +import Control.Monad.State (MonadState(..),StateT,execStateT,liftM,liftM2) +import Data.IntMap as IM (lookup,empty,insert) +import Data.Void (Void) +import CG.Prover.Base + + +type Ins c a = StateT (VMap c Void) Maybe a + + +runIns :: Ins c a -> Maybe (VMap c Void) +runIns x = execStateT x IM.empty + + +ins :: (Eq c) => Term c Void -> Term c Int -> Ins c (Term c Void) +ins (Con x xs) (Con y ys) | x == y = liftM (Con x) (insAll xs ys) +ins x@(Con _ _ ) (Var i ) = do vm <- get + case IM.lookup i vm of + Just y -> if x == y + then return x + else fail "cannot insantiate" + _ -> do put (IM.insert i x vm) + return x +ins _ _ = fail "cannot insantiate" + + +insAll :: (Eq c) => [Term c Void] -> [Term c Int] -> Ins c [Term c Void] +insAll [] [] = return [] +insAll (x:xs) (y:ys) = liftM2 (:) (ins x y) (insAll xs ys) +insAll _ _ = fail "cannot instantiate" diff --git a/CG/ToAgda.hs b/CG/ToAgda.hs new file mode 100644 --- /dev/null +++ b/CG/ToAgda.hs @@ -0,0 +1,176 @@ +{-# LANGUAGE RecordWildCards, FlexibleContexts #-} +module CG.ToAgda (Result(..),writeAgdaFile) where + + +import CG.Base +import Control.Monad.State (State,get,put,runState) +import Data.Char (isSpace,toUpper,toLower) +import Data.List (intersperse,intercalate) +import Data.Map (Map) +import qualified Data.Map as M +import Data.Maybe (fromMaybe) +import Data.Void (Void) +import System.IO +import Text.Printf (printf) + + + +toCtxt :: System c -> String -> String +toCtxt sys@System{..} sent + | structural = unwords (intersperse "," (words sent ++ ["∅"])) + | otherwise = unwords (intersperse "," (words sent)) + +toAgdaName :: System c -> String +toAgdaName System{..} = case agdaName of + Just n -> n + _ -> error "Must set agda_name to export to Agda." + +toAgdaModule :: System c -> String +toAgdaModule System{..} = case agdaModule of + Just n -> n + _ -> error "Must set agda_module to export to Agda." + +toBaseName :: Result -> String +toBaseName (Solved g _) = defaultName g +toBaseName (Parsed s _ _ _) = map toLower (sanitise s) + +sanitise [] = [] +sanitise (' ':' ': xs) = sanitise (' ':xs) +sanitise (' ' : xs) = '_' : sanitise xs +sanitise ('.' : xs) = sanitise xs +sanitise (':' : xs) = sanitise xs +sanitise ( c : xs) = toUpper c : sanitise xs + +sanitiseForLaTeX [] = [] +sanitiseForLaTeX ('_':xs) = '\\' : '_' : sanitiseForLaTeX xs +sanitiseForLaTeX ( c :xs) = c : sanitiseForLaTeX xs + +defaultName :: (Show v, ToString v) => Term ConId v -> String +defaultName = map repl . filter (not . isSpace) . show + where + repl '(' = '[' + repl ')' = ']' + repl c = c + +withType :: (Show v, ToString v) => Term ConId v -> String -> String +withType = printf "id {A = ⟦ %s ⟧ᵀ} (%s)" . show + +agdaList :: [String] -> String +agdaList = unwords . intersperse "\n ∷" . (++["[]"]) + +agdaList' :: [String] -> String +agdaList' = unwords . intersperse " ∷" . (++["[]"]) + +toAgdaDefn :: System c -> Term ConId Void -> Result -> State (Map String Int) String +toAgdaDefn sys goalType ret = case ret of + (Solved g p) -> + return $ unlines + [ baseName++" : "++dataTypeName++" "++show g + , baseName++" = "++show p + , "" + ] + (Parsed s e g p) -> do + n <- next s; let subn = sub n + return . unlines $ + [ synBaseName++subn++" : "++dataTypeName++" "++show g + , synBaseName++subn++" \n = "++show p + , semBaseName++subn++" : ⟦ "++show goalType++" ⟧ᵀ" + , semBaseName++subn++" \n = [ "++synBaseName++subn++" ]ᵀ ("++toCtxt sys s++")" + , "" + ] + ++ + (if null e then [] else + [ listBaseName++subn++" : List Term" + , listBaseName++subn++" \n = "++agdaList (map (\x -> "quoteTerm ("++withType goalType x++")") e) + , testBaseName++subn++" : Assert (quoteTerm "++semBaseName++subn++" ∈ "++listBaseName++subn++")" + , testBaseName++subn++" = _" + , "" + ]) + ++ + [""] + where + baseName = toBaseName ret + synBaseName = map toUpper baseName + semBaseName = map toLower baseName + listBaseName = "LIST_"++baseName + testBaseName = "TEST_"++baseName + dataTypeName = toAgdaName sys + + +-- |Return a valid Agda file given a sequence of proofs. +writeAgdaFile :: Handle -> String -> System c -> [Result] -> Term ConId Void -> IO [String] +writeAgdaFile h moduleName sys@System{..} prfs goalType = do + + let (proofDefn, nameMap) = + runState (mapM (toAgdaDefn sys goalType) prfs) M.empty + let nameList = toNameList nameMap + let fileList = map (\(i,s) -> map toLower (sanitise s) ++ "_" ++ show i) nameList + + mapM_ (hPutStrLn h) $ + [ "------------------------------------------------------------------------" + , "-- The Lambek Calculus in Agda" + , "------------------------------------------------------------------------" + , "" + , "open import Data.Colist using (fromList)" + , "open import Data.Bool using (Bool; true; false; _∧_; _∨_)" + , "open import Data.List using (List; _∷_; [])" + , "open import Data.String using (String)" + , "open import Data.Vec using (_∷_; [])" + , "open import Function using (id)" + , "open import IO using (IO; mapM′; run)" + , "open import Reflection using (Term)" + , "open import "++toAgdaModule sys + , "" + , "module "++moduleName++" where" + , "" + , unlines proofDefn + , "" + , "proofList : List Proof" + , "proofList\n = " ++ (agdaList (proofList structural nameList)) + , "" + , "main : _" + , "main = run (mapM′ writeProof (fromList proofList))" + ] + + return fileList + + +-- |Convert a given map of sentences to max IDs, to a list of names. +toNameList :: Map String Int -> [(Int, String)] +toNameList sentenceIds = + [(j,s) | (s,i) <- M.toList sentenceIds, j <- [0..i-1]] + + +-- |Return a single list which contains all proofs as LaTeX strings. +proofList :: Bool -> [(Int, String)] -> [String] +proofList structural nameList = do + (i,s) <- nameList + let + fileName = map toLower (sanitise s) ++ "_" ++ show i + termName = map toUpper (sanitise s) ++ sub i + sentence = sanitiseForLaTeX (toUpper (head s) : map toLower (tail s) ++ ".") + wordList = if structural + then agdaList' (map (show . sanitiseForLaTeX) (words s)) + else agdaList' [show (sanitiseForLaTeX (sanitise s))] + return $ + printf "proof %s %s (toLaTeX %s) (toLaTeXTerm (%s) (toTerm %s))" + (show fileName) (show sentence) termName wordList termName + + +-- |Compute the next number for this String. +next :: String -> State (Map String Int) Int +next s = do m <- get + let n = fromMaybe 0 (M.lookup s m) + put (M.insert s (n + 1) m) + return n + + +-- |Show a number in subscript. +sub :: Int -> String +sub = map toSub . show + where + toSub '0' = '₀'; toSub '5' = '₅' + toSub '1' = '₁'; toSub '6' = '₆' + toSub '2' = '₂'; toSub '7' = '₇' + toSub '3' = '₃'; toSub '8' = '₈' + toSub '4' = '₄'; toSub '9' = '₉' diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/cg.cabal b/cg.cabal new file mode 100644 --- /dev/null +++ b/cg.cabal @@ -0,0 +1,30 @@ +name: cg +version: 0.0.9.0 +synopsis: Parser for categorial grammars. +description: Parser for categorial grammars. +stability: experimental +license: GPL-3 +license-file: LICENSE +author: Pepijn Kokke +maintainer: pepijn.kokke@gmail.com +copyright: (c) 2015 Pepijn Kokke +category: Language +build-type: Simple +cabal-version: >=1.10 + +executable CG + main-is: CG.hs + other-extensions: RecordWildCards, TupleSections, OverloadedStrings, + ViewPatterns, FlexibleContexts, PartialTypeSignatures, + DeriveGeneric, TypeSynonymInstances, FlexibleInstances, + GADTs, MultiParamTypeClasses, UndecidableInstances, + RankNTypes + other-modules: CG.Prover.Base, CG.Prover.Ins, CG.Prover, + CG.Base, CG.Parsing, CG.Parser, CG.ToAgda + build-depends: base >=4.8 && <4.9, bytestring, utf8-string, parallel >=3.2 && <3.3, + containers >=0.5 && <0.6, directory >=1.2 && <1.3, + filepath >=1.4 && <1.5, parsec >=3.1 && <3.2, + deepseq >=1.4 && <1.5, hashable >=1.2 && <1.3, + unordered-containers >=0.2 && <0.3, mtl >=2.2 && <2.3, + void >=0.7 && <0.8, cereal >= 0.4 && < 0.5, split, process, text + default-language: Haskell2010