cg (empty) → 0.0.9.0

raw patch · 11 files changed

+2292/−0 lines, 11 filesdep +basedep +bytestringdep +cerealsetup-changed

Dependencies added: base, bytestring, cereal, containers, deepseq, directory, filepath, hashable, mtl, parallel, parsec, process, split, text, unordered-containers, utf8-string, void

Files

• CG.hs +395/−0
• CG/Base.hs +260/−0
• CG/Parser.hs +82/−0
• CG/Parsing.hs +330/−0
• CG/Prover.hs +85/−0
• CG/Prover/Base.hs +226/−0
• CG/Prover/Ins.hs +32/−0
• CG/ToAgda.hs +176/−0
• LICENSE +674/−0
• Setup.hs +2/−0
• cg.cabal +30/−0

@@ -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}}"+  ]

@@ -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)

@@ -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."

@@ -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

@@ -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

@@ -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] }

@@ -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"

@@ -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'

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@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain

@@ -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