hoq (empty) → 0.1.0.0

raw patch · 36 files changed

+4911/−0 lines, 36 filesdep +BNFCdep +arraydep +basebuild-type:Customsetup-changed

Dependencies added: BNFC, array, base, mtl, prelude-extras, pretty, readline

Files

• LICENSE +339/−0
• README.md +4/−0
• Setup.hs +24/−0
• data/hoq.vim +36/−0
• dist/build/hoq/hoq-tmp/Syntax/BNFC/LexGrammar.hs +388/−0
• dist/build/hoq/hoq-tmp/Syntax/BNFC/ParGrammar.hs +1277/−0
• examples/basics.hoq +122/−0
• examples/circle.hoq +152/−0
• examples/hlevel.hoq +77/−0
• examples/lem.hoq +37/−0
• hoq.cabal +55/−0
• src/File/Load.hs +35/−0
• src/Main.hs +12/−0
• src/Normalization.hs +104/−0
• src/REPL.hs +53/−0
• src/Syntax/BNFC/LexGrammar.x +209/−0
• src/Syntax/BNFC/ParGrammar.y +215/−0
• src/Syntax/ErrorDoc.hs +93/−0
• src/Syntax/Expr.hs +43/−0
• src/Syntax/Grammar.cf +81/−0
• src/Syntax/Pattern.hs +14/−0
• src/Syntax/PrettyPrinter.hs +97/−0
• src/Syntax/Scope.hs +105/−0
• src/Syntax/Term.hs +200/−0
• src/TypeChecking/Context.hs +42/−0
• src/TypeChecking/Definitions.hs +62/−0
• src/TypeChecking/Definitions/Conditions.hs +140/−0
• src/TypeChecking/Definitions/Coverage.hs +89/−0
• src/TypeChecking/Definitions/DataTypes.hs +115/−0
• src/TypeChecking/Definitions/Functions.hs +53/−0
• src/TypeChecking/Definitions/Patterns.hs +79/−0
• src/TypeChecking/Definitions/Termination.hs +87/−0
• src/TypeChecking/Expressions.hs +306/−0
• src/TypeChecking/Monad.hs +50/−0
• src/TypeChecking/Monad/Scope.hs +59/−0
• src/TypeChecking/Monad/Warn.hs +57/−0

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@@ -0,0 +1,4 @@+hoq+===++A language based on homotopy type theory with an interval

@@ -0,0 +1,24 @@+import Distribution.Simple+import Control.Monad+import System.Directory+import System.Process+import System.Exit++main :: IO ()+main = do+    b <- doesFileExist "src/Syntax/BNFC/AbsGrammar.hs"+    unless b bnfc+    t1 <- getModificationTime $ "src/" ++ grammar+    t2 <- getModificationTime "src/Syntax/BNFC"+    if t1 > t2 then bnfc else defaultMain+  where+    grammar = "Syntax/Grammar.cf"+    bnfc = do+        dir <- getCurrentDirectory+        setCurrentDirectory "src"+        status <- system $ "bnfc -p Syntax.BNFC " ++ grammar+        setCurrentDirectory dir+        case status of+            ExitSuccess -> defaultMain+            _ -> return ()+        exitWith status

@@ -0,0 +1,36 @@+if version < 600+  syn clear+elseif exists("b:current_syntax")+  finish+endif++syn keyword hoqConstructor     left right path coe iso squeeze+syn keyword hoqType            data I Path with+syn match   hoqLineComment     "---*\([^-!#$%&\*\+./<=>\?@\\^|~].*\)\?$"+syn region  hoqBlockComment    start="{-"  end="-}" contains=hoqBlockComment+syn match   hoqNumber          "\<[0-9]\+\>"+syn match   hoqType            "\<Type[0-9]*\>"+" syn match   hoqDelimiter       "(\|)\|;\|_\|{\|}"+syn match   hoqOperator        "=\|:\|->\|\\\|@"++if version >= 508 || !exists("did_hoq_syntax_inits")+  if version < 508+    let did_hoq_syntax_inits = 1+    command -nargs=+ HiLink hi link <args>+  else+    command -nargs=+ HiLink hi def link <args>+  endif++  HiLink hoqConstructor    Keyword+  HiLink hoqLineComment    hoqComment+  HiLink hoqBlockComment   hoqComment+  HiLink hoqComment        Comment+  HiLink hoqNumber         Number+  HiLink hoqType           Type+  HiLink hoqDelimiter      Delimiter+  HiLink hoqOperator       Operator++  delcommand HiLink+endif++let b:current_syntax = "hoq"

@@ -0,0 +1,388 @@+{-# LANGUAGE CPP,MagicHash #-}+{-# LINE 3 "src/Syntax/BNFC/LexGrammar.x" #-}++{-# OPTIONS -fno-warn-incomplete-patterns #-}+{-# OPTIONS_GHC -w #-}+module Syntax.BNFC.LexGrammar where++++import qualified Data.Bits+import Data.Word (Word8)++#if __GLASGOW_HASKELL__ >= 603+#include "ghcconfig.h"+#elif defined(__GLASGOW_HASKELL__)+#include "config.h"+#endif+#if __GLASGOW_HASKELL__ >= 503+import Data.Array+import Data.Char (ord)+import Data.Array.Base (unsafeAt)+#else+import Array+import Char (ord)+#endif+#if __GLASGOW_HASKELL__ >= 503+import GHC.Exts+#else+import GlaExts+#endif+alex_base :: AlexAddr+alex_base = AlexA# "\xf8\xff\xff\xff\xd9\xff\xff\xff\x49\x00\x00\x00\x1c\x01\x00\x00\x9c\x01\x00\x00\x6f\x02\x00\x00\xef\x02\x00\x00\xef\x03\x00\x00\xb7\xff\xff\xff\x00\x00\x00\x00\xe0\x03\x00\x00\x00\x00\x00\x00\x8b\x00\x00\x00\x1d\x02\x00\x00\xe0\x04\x00\x00\xa0\x04\x00\x00\x00\x00\x00\x00\x96\x05\x00\x00\x69\x06\x00\x00\x00\x00\x00\x00\xfe\xff\xff\xff\xdf\xff\xff\xff\x00\x00\x00\x00\x42\x07\x00\x00\xa5\x07\x00\x00\x08\x08\x00\x00\x6b\x08\x00\x00\xce\x08\x00\x00\x31\x09\x00\x00\x94\x09\x00\x00\xf7\x09\x00\x00\x5a\x0a\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xbd\x0a\x00\x00\x20\x0b\x00\x00\x83\x0b\x00\x00\xe6\x0b\x00\x00\x49\x0c\x00\x00\xac\x0c\x00\x00\x0f\x0d\x00\x00\x72\x0d\x00\x00\xd5\x0d\x00\x00\x38\x0e\x00\x00\x9b\x0e\x00\x00\xfe\x0e\x00\x00\x61\x0f\x00\x00\xc4\x0f\x00\x00\x27\x10\x00\x00\x8a\x10\x00\x00\xed\x10\x00\x00\x50\x11\x00\x00\xb3\x11\x00\x00\x16\x12\x00\x00\x79\x12\x00\x00\xdc\x12\x00\x00\x3f\x13\x00\x00\xa2\x13\x00\x00\x05\x14\x00\x00\x68\x14\x00\x00\xcb\x14\x00\x00"#++alex_table :: AlexAddr+alex_table = AlexA# 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:: AlexAddr+alex_check = AlexA# 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:: AlexAddr+alex_deflt = AlexA# "\xff\xff\xff\xff\x05\x00\x05\x00\xff\xff\x05\x00\xff\xff\x05\x00\x05\x00\x0b\x00\x0b\x00\x10\x00\x10\x00\xff\xff\x11\x00\x11\x00\x11\x00\x11\x00\x05\x00\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"#++alex_accept = listArray (0::Int,61) [AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccSkip,AlexAccSkip,AlexAccSkip,AlexAccSkip,AlexAcc (alex_action_3),AlexAcc (alex_action_3),AlexAcc (alex_action_4),AlexAcc (alex_action_5),AlexAcc (alex_action_6),AlexAcc (alex_action_7),AlexAcc (alex_action_8),AlexAcc (alex_action_9),AlexAcc (alex_action_10),AlexAcc (alex_action_11),AlexAcc (alex_action_12),AlexAcc (alex_action_13),AlexAcc (alex_action_14),AlexAcc (alex_action_15),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16),AlexAcc (alex_action_16)]+{-# LINE 51 "src/Syntax/BNFC/LexGrammar.x" #-}+++tok f p s = f p s++share :: String -> String+share = id++data Tok =+   TS !String !Int    -- reserved words and symbols+ | TL !String         -- string literals+ | TI !String         -- integer literals+ | TV !String         -- identifiers+ | TD !String         -- double precision float literals+ | TC !String         -- character literals+ | T_U !String+ | T_I !String+ | T_PLeft !String+ | T_PRight !String+ | T_PPath !String+ | T_Ppath !String+ | T_PCoe !String+ | T_PIso !String+ | T_PSqueeze !String+ | T_PLam !String+ | T_PPar !String+ | T_Pus !String+ | T_PIdent !String++ deriving (Eq,Show,Ord)++data Token = +   PT  Posn Tok+ | Err Posn+  deriving (Eq,Show,Ord)++tokenPos (PT (Pn _ l _) _ :_) = "line " ++ show l+tokenPos (Err (Pn _ l _) :_) = "line " ++ show l+tokenPos _ = "end of file"++tokenPosn (PT p _) = p+tokenPosn (Err p) = p+tokenLineCol = posLineCol . tokenPosn+posLineCol (Pn _ l c) = (l,c)+mkPosToken t@(PT p _) = (posLineCol p, prToken t)++prToken t = case t of+  PT _ (TS s _) -> s+  PT _ (TL s)   -> s+  PT _ (TI s)   -> s+  PT _ (TV s)   -> s+  PT _ (TD s)   -> s+  PT _ (TC s)   -> s+  PT _ (T_U s) -> s+  PT _ (T_I s) -> s+  PT _ (T_PLeft s) -> s+  PT _ (T_PRight s) -> s+  PT _ (T_PPath s) -> s+  PT _ (T_Ppath s) -> s+  PT _ (T_PCoe s) -> s+  PT _ (T_PIso s) -> s+  PT _ (T_PSqueeze s) -> s+  PT _ (T_PLam s) -> s+  PT _ (T_PPar s) -> s+  PT _ (T_Pus s) -> s+  PT _ (T_PIdent s) -> s+++data BTree = N | B String Tok BTree BTree deriving (Show)++eitherResIdent :: (String -> Tok) -> String -> Tok+eitherResIdent tv s = treeFind resWords+  where+  treeFind N = tv s+  treeFind (B a t left right) | s < a  = treeFind left+                              | s > a  = treeFind right+                              | s == a = t++resWords = b "@" 6 (b ":" 3 (b "->" 2 (b ")" 1 N N) N) (b "=" 5 (b ";" 4 N N) N)) (b "{" 9 (b "with" 8 (b "data" 7 N N) N) (b "}" 11 (b "|" 10 N N) N))+   where b s n = let bs = id s+                  in B bs (TS bs n)++unescapeInitTail :: String -> String+unescapeInitTail = id . unesc . tail . id where+  unesc s = case s of+    '\\':c:cs | elem c ['\"', '\\', '\''] -> c : unesc cs+    '\\':'n':cs  -> '\n' : unesc cs+    '\\':'t':cs  -> '\t' : unesc cs+    '"':[]    -> []+    c:cs      -> c : unesc cs+    _         -> []++-------------------------------------------------------------------+-- Alex wrapper code.+-- A modified "posn" wrapper.+-------------------------------------------------------------------++data Posn = Pn !Int !Int !Int+      deriving (Eq, Show,Ord)++alexStartPos :: Posn+alexStartPos = Pn 0 1 1++alexMove :: Posn -> Char -> Posn+alexMove (Pn a l c) '\t' = Pn (a+1)  l     (((c+7) `div` 8)*8+1)+alexMove (Pn a l c) '\n' = Pn (a+1) (l+1)   1+alexMove (Pn a l c) _    = Pn (a+1)  l     (c+1)++type Byte = Word8++type AlexInput = (Posn,     -- current position,+                  Char,     -- previous char+                  [Byte],   -- pending bytes on the current char+                  String)   -- current input string++tokens :: String -> [Token]+tokens str = go (alexStartPos, '\n', [], str)+    where+      go :: AlexInput -> [Token]+      go inp@(pos, _, _, str) =+               case alexScan inp 0 of+                AlexEOF                   -> []+                AlexError (pos, _, _, _)  -> [Err pos]+                AlexSkip  inp' len        -> go inp'+                AlexToken inp' len act    -> act pos (take len str) : (go inp')++alexGetByte :: AlexInput -> Maybe (Byte,AlexInput)+alexGetByte (p, c, (b:bs), s) = Just (b, (p, c, bs, s))+alexGetByte (p, _, [], s) =+  case  s of+    []  -> Nothing+    (c:s) ->+             let p'     = alexMove p c+                 (b:bs) = utf8Encode c+              in p' `seq` Just (b, (p', c, bs, s))++alexInputPrevChar :: AlexInput -> Char+alexInputPrevChar (p, c, bs, s) = c++  -- | Encode a Haskell String to a list of Word8 values, in UTF8 format.+utf8Encode :: Char -> [Word8]+utf8Encode = map fromIntegral . go . ord+ where+  go oc+   | oc <= 0x7f       = [oc]++   | oc <= 0x7ff      = [ 0xc0 + (oc `Data.Bits.shiftR` 6)+                        , 0x80 + oc Data.Bits..&. 0x3f+                        ]++   | oc <= 0xffff     = [ 0xe0 + (oc `Data.Bits.shiftR` 12)+                        , 0x80 + ((oc `Data.Bits.shiftR` 6) Data.Bits..&. 0x3f)+                        , 0x80 + oc Data.Bits..&. 0x3f+                        ]+   | otherwise        = [ 0xf0 + (oc `Data.Bits.shiftR` 18)+                        , 0x80 + ((oc `Data.Bits.shiftR` 12) Data.Bits..&. 0x3f)+                        , 0x80 + ((oc `Data.Bits.shiftR` 6) Data.Bits..&. 0x3f)+                        , 0x80 + oc Data.Bits..&. 0x3f+                        ]++alex_action_3 =  tok (\p s -> PT p (eitherResIdent (TV . share) s)) +alex_action_4 =  tok (\p s -> PT p (eitherResIdent (T_U . share) s)) +alex_action_5 =  tok (\p s -> PT p (eitherResIdent (T_I . share) s)) +alex_action_6 =  tok (\p s -> PT p (eitherResIdent (T_PLeft . share) s)) +alex_action_7 =  tok (\p s -> PT p (eitherResIdent (T_PRight . share) s)) +alex_action_8 =  tok (\p s -> PT p (eitherResIdent (T_PPath . share) s)) +alex_action_9 =  tok (\p s -> PT p (eitherResIdent (T_Ppath . share) s)) +alex_action_10 =  tok (\p s -> PT p (eitherResIdent (T_PCoe . share) s)) +alex_action_11 =  tok (\p s -> PT p (eitherResIdent (T_PIso . share) s)) +alex_action_12 =  tok (\p s -> PT p (eitherResIdent (T_PSqueeze . share) s)) +alex_action_13 =  tok (\p s -> PT p (eitherResIdent (T_PLam . share) s)) +alex_action_14 =  tok (\p s -> PT p (eitherResIdent (T_PPar . share) s)) +alex_action_15 =  tok (\p s -> PT p (eitherResIdent (T_Pus . share) s)) +alex_action_16 =  tok (\p s -> PT p (eitherResIdent (T_PIdent . share) s)) +alex_action_17 =  tok (\p s -> PT p (eitherResIdent (TV . share) s)) +{-# LINE 1 "templates/GenericTemplate.hs" #-}+{-# LINE 1 "templates/GenericTemplate.hs" #-}+{-# LINE 1 "<command-line>" #-}+{-# LINE 1 "templates/GenericTemplate.hs" #-}+-- -----------------------------------------------------------------------------+-- ALEX TEMPLATE+--+-- This code is in the PUBLIC DOMAIN; you may copy it freely and use+-- it for any purpose whatsoever.++-- -----------------------------------------------------------------------------+-- INTERNALS and main scanner engine++{-# LINE 35 "templates/GenericTemplate.hs" #-}++{-# LINE 45 "templates/GenericTemplate.hs" #-}+++data AlexAddr = AlexA# Addr#++#if __GLASGOW_HASKELL__ < 503+uncheckedShiftL# = shiftL#+#endif++{-# INLINE alexIndexInt16OffAddr #-}+alexIndexInt16OffAddr (AlexA# arr) off =+#ifdef WORDS_BIGENDIAN+  narrow16Int# i+  where+        i    = word2Int# ((high `uncheckedShiftL#` 8#) `or#` low)+        high = int2Word# (ord# (indexCharOffAddr# arr (off' +# 1#)))+        low  = int2Word# (ord# (indexCharOffAddr# arr off'))+        off' = off *# 2#+#else+  indexInt16OffAddr# arr off+#endif++++++{-# INLINE alexIndexInt32OffAddr #-}+alexIndexInt32OffAddr (AlexA# arr) off = +#ifdef WORDS_BIGENDIAN+  narrow32Int# i+  where+   i    = word2Int# ((b3 `uncheckedShiftL#` 24#) `or#`+		     (b2 `uncheckedShiftL#` 16#) `or#`+		     (b1 `uncheckedShiftL#` 8#) `or#` b0)+   b3   = int2Word# (ord# (indexCharOffAddr# arr (off' +# 3#)))+   b2   = int2Word# (ord# (indexCharOffAddr# arr (off' +# 2#)))+   b1   = int2Word# (ord# (indexCharOffAddr# arr (off' +# 1#)))+   b0   = int2Word# (ord# (indexCharOffAddr# arr off'))+   off' = off *# 4#+#else+  indexInt32OffAddr# arr off+#endif++++++#if __GLASGOW_HASKELL__ < 503+quickIndex arr i = arr ! i+#else+-- GHC >= 503, unsafeAt is available from Data.Array.Base.+quickIndex = unsafeAt+#endif+++++-- -----------------------------------------------------------------------------+-- Main lexing routines++data AlexReturn a+  = AlexEOF+  | AlexError  !AlexInput+  | AlexSkip   !AlexInput !Int+  | AlexToken  !AlexInput !Int a++-- alexScan :: AlexInput -> StartCode -> AlexReturn a+alexScan input (I# (sc))+  = alexScanUser undefined input (I# (sc))++alexScanUser user input (I# (sc))+  = case alex_scan_tkn user input 0# input sc AlexNone of+	(AlexNone, input') ->+		case alexGetByte input of+			Nothing -> ++++				   AlexEOF+			Just _ ->++++				   AlexError input'++	(AlexLastSkip input'' len, _) ->++++		AlexSkip input'' len++	(AlexLastAcc k input''' len, _) ->++++		AlexToken input''' len k+++-- Push the input through the DFA, remembering the most recent accepting+-- state it encountered.++alex_scan_tkn user orig_input len input s last_acc =+  input `seq` -- strict in the input+  let +	new_acc = (check_accs (alex_accept `quickIndex` (I# (s))))+  in+  new_acc `seq`+  case alexGetByte input of+     Nothing -> (new_acc, input)+     Just (c, new_input) -> ++++      case fromIntegral c of { (I# (ord_c)) ->+        let+                base   = alexIndexInt32OffAddr alex_base s+                offset = (base +# ord_c)+                check  = alexIndexInt16OffAddr alex_check offset+		+                new_s = if (offset >=# 0#) && (check ==# ord_c)+			  then alexIndexInt16OffAddr alex_table offset+			  else alexIndexInt16OffAddr alex_deflt s+	in+        case new_s of+	    -1# -> (new_acc, input)+		-- on an error, we want to keep the input *before* the+		-- character that failed, not after.+    	    _ -> alex_scan_tkn user orig_input (if c < 0x80 || c >= 0xC0 then (len +# 1#) else len)+                                                -- note that the length is increased ONLY if this is the 1st byte in a char encoding)+			new_input new_s new_acc+      }+  where+	check_accs (AlexAccNone) = last_acc+	check_accs (AlexAcc a  ) = AlexLastAcc a input (I# (len))+	check_accs (AlexAccSkip) = AlexLastSkip  input (I# (len))+{-# LINE 191 "templates/GenericTemplate.hs" #-}++data AlexLastAcc a+  = AlexNone+  | AlexLastAcc a !AlexInput !Int+  | AlexLastSkip  !AlexInput !Int++instance Functor AlexLastAcc where+    fmap f AlexNone = AlexNone+    fmap f (AlexLastAcc x y z) = AlexLastAcc (f x) y z+    fmap f (AlexLastSkip x y) = AlexLastSkip x y++data AlexAcc a user+  = AlexAccNone+  | AlexAcc a+  | AlexAccSkip+{-# LINE 235 "templates/GenericTemplate.hs" #-}++-- used by wrappers+iUnbox (I# (i)) = i

@@ -0,0 +1,1277 @@+{-# OPTIONS_GHC -w #-}+{-# OPTIONS -fglasgow-exts -cpp #-}+{-# OPTIONS_GHC -fno-warn-incomplete-patterns -fno-warn-overlapping-patterns #-}+module Syntax.BNFC.ParGrammar where+import Syntax.BNFC.AbsGrammar+import Syntax.BNFC.LexGrammar+import Syntax.BNFC.ErrM+import qualified Data.Array as Happy_Data_Array+import qualified GHC.Exts as Happy_GHC_Exts++-- parser produced by Happy Version 1.18.10++newtype HappyAbsSyn  = HappyAbsSyn HappyAny+#if __GLASGOW_HASKELL__ >= 607+type HappyAny = Happy_GHC_Exts.Any+#else+type HappyAny = forall a . a+#endif+happyIn5 :: (U) -> (HappyAbsSyn )+happyIn5 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn5 #-}+happyOut5 :: (HappyAbsSyn ) -> (U)+happyOut5 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut5 #-}+happyIn6 :: (I) -> (HappyAbsSyn )+happyIn6 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn6 #-}+happyOut6 :: (HappyAbsSyn ) -> (I)+happyOut6 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut6 #-}+happyIn7 :: (PLeft) -> (HappyAbsSyn )+happyIn7 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn7 #-}+happyOut7 :: (HappyAbsSyn ) -> (PLeft)+happyOut7 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut7 #-}+happyIn8 :: (PRight) -> (HappyAbsSyn )+happyIn8 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn8 #-}+happyOut8 :: (HappyAbsSyn ) -> (PRight)+happyOut8 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut8 #-}+happyIn9 :: (PPath) -> (HappyAbsSyn )+happyIn9 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn9 #-}+happyOut9 :: (HappyAbsSyn ) -> (PPath)+happyOut9 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut9 #-}+happyIn10 :: (Ppath) -> (HappyAbsSyn )+happyIn10 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn10 #-}+happyOut10 :: (HappyAbsSyn ) -> (Ppath)+happyOut10 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut10 #-}+happyIn11 :: (PCoe) -> (HappyAbsSyn )+happyIn11 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn11 #-}+happyOut11 :: (HappyAbsSyn ) -> (PCoe)+happyOut11 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut11 #-}+happyIn12 :: (PIso) -> (HappyAbsSyn )+happyIn12 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn12 #-}+happyOut12 :: (HappyAbsSyn ) -> (PIso)+happyOut12 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut12 #-}+happyIn13 :: (PSqueeze) -> (HappyAbsSyn )+happyIn13 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn13 #-}+happyOut13 :: (HappyAbsSyn ) -> (PSqueeze)+happyOut13 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut13 #-}+happyIn14 :: (PLam) -> (HappyAbsSyn )+happyIn14 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn14 #-}+happyOut14 :: (HappyAbsSyn ) -> (PLam)+happyOut14 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut14 #-}+happyIn15 :: (PPar) -> (HappyAbsSyn )+happyIn15 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn15 #-}+happyOut15 :: (HappyAbsSyn ) -> (PPar)+happyOut15 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut15 #-}+happyIn16 :: (Pus) -> (HappyAbsSyn )+happyIn16 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn16 #-}+happyOut16 :: (HappyAbsSyn ) -> (Pus)+happyOut16 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut16 #-}+happyIn17 :: (PIdent) -> (HappyAbsSyn )+happyIn17 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn17 #-}+happyOut17 :: (HappyAbsSyn ) -> (PIdent)+happyOut17 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut17 #-}+happyIn18 :: (Defs) -> (HappyAbsSyn )+happyIn18 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn18 #-}+happyOut18 :: (HappyAbsSyn ) -> (Defs)+happyOut18 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut18 #-}+happyIn19 :: (Def) -> (HappyAbsSyn )+happyIn19 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn19 #-}+happyOut19 :: (HappyAbsSyn ) -> (Def)+happyOut19 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut19 #-}+happyIn20 :: ([Def]) -> (HappyAbsSyn )+happyIn20 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn20 #-}+happyOut20 :: (HappyAbsSyn ) -> ([Def])+happyOut20 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut20 #-}+happyIn21 :: (FunCase) -> (HappyAbsSyn )+happyIn21 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn21 #-}+happyOut21 :: (HappyAbsSyn ) -> (FunCase)+happyOut21 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut21 #-}+happyIn22 :: ([FunCase]) -> (HappyAbsSyn )+happyIn22 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn22 #-}+happyOut22 :: (HappyAbsSyn ) -> ([FunCase])+happyOut22 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut22 #-}+happyIn23 :: (Pattern) -> (HappyAbsSyn )+happyIn23 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn23 #-}+happyOut23 :: (HappyAbsSyn ) -> (Pattern)+happyOut23 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut23 #-}+happyIn24 :: (ParPat) -> (HappyAbsSyn )+happyIn24 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn24 #-}+happyOut24 :: (HappyAbsSyn ) -> (ParPat)+happyOut24 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut24 #-}+happyIn25 :: ([ParPat]) -> (HappyAbsSyn )+happyIn25 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn25 #-}+happyOut25 :: (HappyAbsSyn ) -> ([ParPat])+happyOut25 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut25 #-}+happyIn26 :: (Con) -> (HappyAbsSyn )+happyIn26 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn26 #-}+happyOut26 :: (HappyAbsSyn ) -> (Con)+happyOut26 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut26 #-}+happyIn27 :: ([Con]) -> (HappyAbsSyn )+happyIn27 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn27 #-}+happyOut27 :: (HappyAbsSyn ) -> ([Con])+happyOut27 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut27 #-}+happyIn28 :: (ConTele) -> (HappyAbsSyn )+happyIn28 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn28 #-}+happyOut28 :: (HappyAbsSyn ) -> (ConTele)+happyOut28 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut28 #-}+happyIn29 :: ([ConTele]) -> (HappyAbsSyn )+happyIn29 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn29 #-}+happyOut29 :: (HappyAbsSyn ) -> ([ConTele])+happyOut29 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut29 #-}+happyIn30 :: (DataTele) -> (HappyAbsSyn )+happyIn30 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn30 #-}+happyOut30 :: (HappyAbsSyn ) -> (DataTele)+happyOut30 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut30 #-}+happyIn31 :: ([DataTele]) -> (HappyAbsSyn )+happyIn31 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn31 #-}+happyOut31 :: (HappyAbsSyn ) -> ([DataTele])+happyOut31 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut31 #-}+happyIn32 :: (PiTele) -> (HappyAbsSyn )+happyIn32 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn32 #-}+happyOut32 :: (HappyAbsSyn ) -> (PiTele)+happyOut32 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut32 #-}+happyIn33 :: ([PiTele]) -> (HappyAbsSyn )+happyIn33 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn33 #-}+happyOut33 :: (HappyAbsSyn ) -> ([PiTele])+happyOut33 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut33 #-}+happyIn34 :: (Expr) -> (HappyAbsSyn )+happyIn34 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn34 #-}+happyOut34 :: (HappyAbsSyn ) -> (Expr)+happyOut34 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut34 #-}+happyIn35 :: (Expr) -> (HappyAbsSyn )+happyIn35 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn35 #-}+happyOut35 :: (HappyAbsSyn ) -> (Expr)+happyOut35 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut35 #-}+happyIn36 :: (Expr) -> (HappyAbsSyn )+happyIn36 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn36 #-}+happyOut36 :: (HappyAbsSyn ) -> (Expr)+happyOut36 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut36 #-}+happyIn37 :: (Expr) -> (HappyAbsSyn )+happyIn37 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn37 #-}+happyOut37 :: (HappyAbsSyn ) -> (Expr)+happyOut37 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut37 #-}+happyIn38 :: (Expr) -> (HappyAbsSyn )+happyIn38 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn38 #-}+happyOut38 :: (HappyAbsSyn ) -> (Expr)+happyOut38 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut38 #-}+happyIn39 :: (Expr) -> (HappyAbsSyn )+happyIn39 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn39 #-}+happyOut39 :: (HappyAbsSyn ) -> (Expr)+happyOut39 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut39 #-}+happyIn40 :: (Arg) -> (HappyAbsSyn )+happyIn40 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn40 #-}+happyOut40 :: (HappyAbsSyn ) -> (Arg)+happyOut40 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut40 #-}+happyIn41 :: ([Arg]) -> (HappyAbsSyn )+happyIn41 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyIn41 #-}+happyOut41 :: (HappyAbsSyn ) -> ([Arg])+happyOut41 x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOut41 #-}+happyInTok :: (Token) -> (HappyAbsSyn )+happyInTok x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyInTok #-}+happyOutTok :: (HappyAbsSyn ) -> (Token)+happyOutTok x = Happy_GHC_Exts.unsafeCoerce# x+{-# INLINE happyOutTok #-}+++happyActOffsets :: HappyAddr+happyActOffsets = HappyA# "\x36\x01\xbb\x01\xab\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x72\x00\xbb\x01\x00\x00\x00\x00\x9f\x01\xb2\x01\x85\x01\x00\x00\xaf\x01\x82\x00\xc8\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xad\x01\x78\x01\x82\x01\x00\x00\x00\x00\x7d\x01\x6c\x01\x00\x00\xbb\x01\x36\x01\x67\x01\xbb\x01\xbb\x01\x00\x00\xc8\x01\xc8\x01\xc8\x01\xc8\x01\xbb\x01\x00\x00\x25\x00\x40\x00\x4b\x01\xbb\x01\x00\x00\x00\x00\xbb\x01\x49\x01\x00\x00\x00\x00\xc8\x01\x3e\x01\x1c\x01\x00\x00\x00\x00\x00\x00\x6d\x01\x00\x00\x00\x00\x00\x00\x00\x00\x2b\x01\xbb\x01\x00\x00\x04\x01\x00\x00\x1a\x01\x00\x00\x19\x01\x00\x00\x00\x00\x00\x00\x00\x00\x06\x01\xe4\x00\xe8\x00\xbb\x01\xe1\x00\xd1\x00\xc8\x01\xbb\x01\x00\x00\x00\x00\x00\x00\xd1\x00\xde\x00\x00\x00\xb7\x00\xaf\x00\xb4\x00\x24\x00\xbb\x01\x00\x00\xa0\x00\x00\x00\xad\x00\x00\x00\x00\x00"#++happyGotoOffsets :: HappyAddr+happyGotoOffsets = HappyA# "\xd5\x01\x03\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x9c\x01\xf6\x00\x00\x00\x00\x00\x57\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x96\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x69\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x4d\x00\x3c\x00\xd2\x00\xda\x01\xa3\x01\xc5\x00\xa1\x00\x00\x00\x58\x01\x89\x01\x34\x01\x27\x01\x94\x00\x00\x00\x00\x00\x98\x01\x00\x00\x70\x00\x00\x00\x00\x00\x63\x00\x00\x00\x00\x00\x00\x00\x96\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x3f\x01\x00\x00\x00\x00\x00\x00\x00\x00\x6a\x01\x3f\x00\x00\x00\x9d\x01\x38\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x03\x00\x00\x00\x00\x00\x00\x00\x32\x00\x00\x00\x6b\x01\x65\x01\x0e\x00\x00\x00\x00\x00\x00\x00\xdf\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x01\x00\x00\x00\xb1\x01\x00\x00\x00\x00\x00\x00\x00\x00"#++happyDefActions :: HappyAddr+happyDefActions = HappyA# "\xe9\xff\x00\x00\x00\x00\xfd\xff\xc1\xff\xc0\xff\xbf\xff\xbe\xff\xbd\xff\xbc\xff\xbb\xff\xba\xff\xb9\xff\x00\x00\x00\x00\xb6\xff\xb7\xff\xcf\xff\x00\x00\x00\x00\xcc\xff\xc9\xff\xc7\xff\xc5\xff\xc3\xff\xc2\xff\xfc\xff\xfb\xff\xfa\xff\xf9\xff\xf8\xff\xf7\xff\xf6\xff\xf5\xff\xf4\xff\xf3\xff\xf2\xff\xf1\xff\xdc\xff\x00\x00\xe8\xff\xf0\xff\xee\xff\xed\xff\x00\x00\xd2\xff\x00\x00\xe9\xff\xe2\xff\x00\x00\x00\x00\xc4\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xce\xff\x00\x00\xb5\xff\x00\x00\x00\x00\xb4\xff\xb8\xff\x00\x00\x00\x00\xca\xff\xcb\xff\xc6\xff\xc8\xff\x00\x00\xef\xff\xe0\xff\xdf\xff\x00\x00\xdb\xff\xe1\xff\xe7\xff\xe6\xff\xea\xff\x00\x00\xd1\xff\x00\x00\xdc\xff\x00\x00\xde\xff\x00\x00\xcd\xff\xd0\xff\xdd\xff\xd5\xff\xd9\xff\xec\xff\x00\x00\x00\x00\x00\x00\x00\x00\xda\xff\x00\x00\xd4\xff\xd6\xff\xd8\xff\xe5\xff\x00\x00\xd3\xff\xe4\xff\x00\x00\x00\x00\x00\x00\x00\x00\xeb\xff\xe5\xff\xe3\xff\x00\x00\xd7\xff"#++happyCheck :: HappyAddr+happyCheck = HappyA# 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:: HappyAddr+happyTable = HappyA# 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= Happy_Data_Array.array (2, 75) [+	(2 , happyReduce_2),+	(3 , happyReduce_3),+	(4 , happyReduce_4),+	(5 , happyReduce_5),+	(6 , happyReduce_6),+	(7 , happyReduce_7),+	(8 , happyReduce_8),+	(9 , happyReduce_9),+	(10 , happyReduce_10),+	(11 , happyReduce_11),+	(12 , happyReduce_12),+	(13 , happyReduce_13),+	(14 , happyReduce_14),+	(15 , happyReduce_15),+	(16 , happyReduce_16),+	(17 , happyReduce_17),+	(18 , happyReduce_18),+	(19 , happyReduce_19),+	(20 , happyReduce_20),+	(21 , happyReduce_21),+	(22 , happyReduce_22),+	(23 , happyReduce_23),+	(24 , happyReduce_24),+	(25 , happyReduce_25),+	(26 , happyReduce_26),+	(27 , happyReduce_27),+	(28 , happyReduce_28),+	(29 , happyReduce_29),+	(30 , happyReduce_30),+	(31 , happyReduce_31),+	(32 , happyReduce_32),+	(33 , happyReduce_33),+	(34 , happyReduce_34),+	(35 , happyReduce_35),+	(36 , happyReduce_36),+	(37 , happyReduce_37),+	(38 , happyReduce_38),+	(39 , happyReduce_39),+	(40 , happyReduce_40),+	(41 , happyReduce_41),+	(42 , happyReduce_42),+	(43 , happyReduce_43),+	(44 , happyReduce_44),+	(45 , happyReduce_45),+	(46 , happyReduce_46),+	(47 , happyReduce_47),+	(48 , happyReduce_48),+	(49 , happyReduce_49),+	(50 , happyReduce_50),+	(51 , happyReduce_51),+	(52 , happyReduce_52),+	(53 , happyReduce_53),+	(54 , happyReduce_54),+	(55 , happyReduce_55),+	(56 , happyReduce_56),+	(57 , happyReduce_57),+	(58 , happyReduce_58),+	(59 , happyReduce_59),+	(60 , happyReduce_60),+	(61 , happyReduce_61),+	(62 , happyReduce_62),+	(63 , happyReduce_63),+	(64 , happyReduce_64),+	(65 , happyReduce_65),+	(66 , happyReduce_66),+	(67 , happyReduce_67),+	(68 , happyReduce_68),+	(69 , happyReduce_69),+	(70 , happyReduce_70),+	(71 , happyReduce_71),+	(72 , happyReduce_72),+	(73 , happyReduce_73),+	(74 , happyReduce_74),+	(75 , happyReduce_75)+	]++happy_n_terms = 27 :: Int+happy_n_nonterms = 37 :: Int++happyReduce_2 = happySpecReduce_1  0# happyReduction_2+happyReduction_2 happy_x_1+	 =  case happyOutTok happy_x_1 of { happy_var_1 -> +	happyIn5+		 (U (mkPosToken happy_var_1)+	)}++happyReduce_3 = happySpecReduce_1  1# happyReduction_3+happyReduction_3 happy_x_1+	 =  case happyOutTok happy_x_1 of { happy_var_1 -> +	happyIn6+		 (I (mkPosToken happy_var_1)+	)}++happyReduce_4 = happySpecReduce_1  2# happyReduction_4+happyReduction_4 happy_x_1+	 =  case happyOutTok happy_x_1 of { happy_var_1 -> +	happyIn7+		 (PLeft (mkPosToken happy_var_1)+	)}++happyReduce_5 = happySpecReduce_1  3# happyReduction_5+happyReduction_5 happy_x_1+	 =  case happyOutTok happy_x_1 of { happy_var_1 -> +	happyIn8+		 (PRight (mkPosToken happy_var_1)+	)}++happyReduce_6 = happySpecReduce_1  4# happyReduction_6+happyReduction_6 happy_x_1+	 =  case happyOutTok happy_x_1 of { happy_var_1 -> +	happyIn9+		 (PPath (mkPosToken happy_var_1)+	)}++happyReduce_7 = happySpecReduce_1  5# happyReduction_7+happyReduction_7 happy_x_1+	 =  case happyOutTok happy_x_1 of { happy_var_1 -> +	happyIn10+		 (Ppath (mkPosToken happy_var_1)+	)}++happyReduce_8 = happySpecReduce_1  6# happyReduction_8+happyReduction_8 happy_x_1+	 =  case happyOutTok happy_x_1 of { happy_var_1 -> +	happyIn11+		 (PCoe (mkPosToken happy_var_1)+	)}++happyReduce_9 = happySpecReduce_1  7# happyReduction_9+happyReduction_9 happy_x_1+	 =  case happyOutTok happy_x_1 of { happy_var_1 -> +	happyIn12+		 (PIso (mkPosToken happy_var_1)+	)}++happyReduce_10 = happySpecReduce_1  8# happyReduction_10+happyReduction_10 happy_x_1+	 =  case happyOutTok happy_x_1 of { happy_var_1 -> +	happyIn13+		 (PSqueeze (mkPosToken happy_var_1)+	)}++happyReduce_11 = happySpecReduce_1  9# happyReduction_11+happyReduction_11 happy_x_1+	 =  case happyOutTok happy_x_1 of { happy_var_1 -> +	happyIn14+		 (PLam (mkPosToken happy_var_1)+	)}++happyReduce_12 = happySpecReduce_1  10# happyReduction_12+happyReduction_12 happy_x_1+	 =  case happyOutTok happy_x_1 of { happy_var_1 -> +	happyIn15+		 (PPar (mkPosToken happy_var_1)+	)}++happyReduce_13 = happySpecReduce_1  11# happyReduction_13+happyReduction_13 happy_x_1+	 =  case happyOutTok happy_x_1 of { happy_var_1 -> +	happyIn16+		 (Pus (mkPosToken happy_var_1)+	)}++happyReduce_14 = happySpecReduce_1  12# happyReduction_14+happyReduction_14 happy_x_1+	 =  case happyOutTok happy_x_1 of { happy_var_1 -> +	happyIn17+		 (PIdent (mkPosToken happy_var_1)+	)}++happyReduce_15 = happySpecReduce_1  13# happyReduction_15+happyReduction_15 happy_x_1+	 =  case happyOut20 happy_x_1 of { happy_var_1 -> +	happyIn18+		 (Defs happy_var_1+	)}++happyReduce_16 = happySpecReduce_3  14# happyReduction_16+happyReduction_16 happy_x_3+	happy_x_2+	happy_x_1+	 =  case happyOut17 happy_x_1 of { happy_var_1 -> +	case happyOut34 happy_x_3 of { happy_var_3 -> +	happyIn19+		 (DefType happy_var_1 happy_var_3+	)}}++happyReduce_17 = happySpecReduce_1  14# happyReduction_17+happyReduction_17 happy_x_1+	 =  case happyOut21 happy_x_1 of { happy_var_1 -> +	happyIn19+		 (DefFun happy_var_1+	)}++happyReduce_18 = happySpecReduce_1  14# happyReduction_18+happyReduction_18 happy_x_1+	 =  case happyOut23 happy_x_1 of { happy_var_1 -> +	happyIn19+		 (DefFunEmpty happy_var_1+	)}++happyReduce_19 = happyReduce 5# 14# happyReduction_19+happyReduction_19 (happy_x_5 `HappyStk`+	happy_x_4 `HappyStk`+	happy_x_3 `HappyStk`+	happy_x_2 `HappyStk`+	happy_x_1 `HappyStk`+	happyRest)+	 = case happyOut17 happy_x_2 of { happy_var_2 -> +	case happyOut31 happy_x_3 of { happy_var_3 -> +	case happyOut27 happy_x_5 of { happy_var_5 -> +	happyIn19+		 (DefData happy_var_2 (reverse happy_var_3) happy_var_5+	) `HappyStk` happyRest}}}++happyReduce_20 = happyReduce 9# 14# happyReduction_20+happyReduction_20 (happy_x_9 `HappyStk`+	happy_x_8 `HappyStk`+	happy_x_7 `HappyStk`+	happy_x_6 `HappyStk`+	happy_x_5 `HappyStk`+	happy_x_4 `HappyStk`+	happy_x_3 `HappyStk`+	happy_x_2 `HappyStk`+	happy_x_1 `HappyStk`+	happyRest)+	 = case happyOut17 happy_x_2 of { happy_var_2 -> +	case happyOut31 happy_x_3 of { happy_var_3 -> +	case happyOut27 happy_x_5 of { happy_var_5 -> +	case happyOut22 happy_x_8 of { happy_var_8 -> +	happyIn19+		 (DefDataWith happy_var_2 (reverse happy_var_3) happy_var_5 happy_var_8+	) `HappyStk` happyRest}}}}++happyReduce_21 = happySpecReduce_3  14# happyReduction_21+happyReduction_21 happy_x_3+	happy_x_2+	happy_x_1+	 =  case happyOut17 happy_x_2 of { happy_var_2 -> +	case happyOut31 happy_x_3 of { happy_var_3 -> +	happyIn19+		 (DefDataEmpty happy_var_2 (reverse happy_var_3)+	)}}++happyReduce_22 = happySpecReduce_0  15# happyReduction_22+happyReduction_22  =  happyIn20+		 ([]+	)++happyReduce_23 = happySpecReduce_1  15# happyReduction_23+happyReduction_23 happy_x_1+	 =  case happyOut19 happy_x_1 of { happy_var_1 -> +	happyIn20+		 ((:[]) happy_var_1+	)}++happyReduce_24 = happySpecReduce_3  15# happyReduction_24+happyReduction_24 happy_x_3+	happy_x_2+	happy_x_1+	 =  case happyOut19 happy_x_1 of { happy_var_1 -> +	case happyOut20 happy_x_3 of { happy_var_3 -> +	happyIn20+		 ((:) happy_var_1 happy_var_3+	)}}++happyReduce_25 = happySpecReduce_3  16# happyReduction_25+happyReduction_25 happy_x_3+	happy_x_2+	happy_x_1+	 =  case happyOut23 happy_x_1 of { happy_var_1 -> +	case happyOut34 happy_x_3 of { happy_var_3 -> +	happyIn21+		 (FunCase happy_var_1 happy_var_3+	)}}++happyReduce_26 = happySpecReduce_0  17# happyReduction_26+happyReduction_26  =  happyIn22+		 ([]+	)++happyReduce_27 = happySpecReduce_1  17# happyReduction_27+happyReduction_27 happy_x_1+	 =  case happyOut21 happy_x_1 of { happy_var_1 -> +	happyIn22+		 ((:[]) happy_var_1+	)}++happyReduce_28 = happySpecReduce_3  17# happyReduction_28+happyReduction_28 happy_x_3+	happy_x_2+	happy_x_1+	 =  case happyOut21 happy_x_1 of { happy_var_1 -> +	case happyOut22 happy_x_3 of { happy_var_3 -> +	happyIn22+		 ((:) happy_var_1 happy_var_3+	)}}++happyReduce_29 = happySpecReduce_2  18# happyReduction_29+happyReduction_29 happy_x_2+	happy_x_1+	 =  case happyOut17 happy_x_1 of { happy_var_1 -> +	case happyOut25 happy_x_2 of { happy_var_2 -> +	happyIn23+		 (Pattern happy_var_1 (reverse happy_var_2)+	)}}++happyReduce_30 = happySpecReduce_1  19# happyReduction_30+happyReduction_30 happy_x_1+	 =  case happyOut40 happy_x_1 of { happy_var_1 -> +	happyIn24+		 (ParVar happy_var_1+	)}++happyReduce_31 = happySpecReduce_1  19# happyReduction_31+happyReduction_31 happy_x_1+	 =  case happyOut7 happy_x_1 of { happy_var_1 -> +	happyIn24+		 (ParLeft happy_var_1+	)}++happyReduce_32 = happySpecReduce_1  19# happyReduction_32+happyReduction_32 happy_x_1+	 =  case happyOut8 happy_x_1 of { happy_var_1 -> +	happyIn24+		 (ParRight happy_var_1+	)}++happyReduce_33 = happySpecReduce_2  19# happyReduction_33+happyReduction_33 happy_x_2+	happy_x_1+	 =  case happyOut15 happy_x_1 of { happy_var_1 -> +	happyIn24+		 (ParEmpty happy_var_1+	)}++happyReduce_34 = happySpecReduce_3  19# happyReduction_34+happyReduction_34 happy_x_3+	happy_x_2+	happy_x_1+	 =  case happyOut15 happy_x_1 of { happy_var_1 -> +	case happyOut23 happy_x_2 of { happy_var_2 -> +	happyIn24+		 (ParPat happy_var_1 happy_var_2+	)}}++happyReduce_35 = happySpecReduce_0  20# happyReduction_35+happyReduction_35  =  happyIn25+		 ([]+	)++happyReduce_36 = happySpecReduce_2  20# happyReduction_36+happyReduction_36 happy_x_2+	happy_x_1+	 =  case happyOut25 happy_x_1 of { happy_var_1 -> +	case happyOut24 happy_x_2 of { happy_var_2 -> +	happyIn25+		 (flip (:) happy_var_1 happy_var_2+	)}}++happyReduce_37 = happySpecReduce_2  21# happyReduction_37+happyReduction_37 happy_x_2+	happy_x_1+	 =  case happyOut17 happy_x_1 of { happy_var_1 -> +	case happyOut29 happy_x_2 of { happy_var_2 -> +	happyIn26+		 (Con happy_var_1 (reverse happy_var_2)+	)}}++happyReduce_38 = happySpecReduce_1  22# happyReduction_38+happyReduction_38 happy_x_1+	 =  case happyOut26 happy_x_1 of { happy_var_1 -> +	happyIn27+		 ((:[]) happy_var_1+	)}++happyReduce_39 = happySpecReduce_3  22# happyReduction_39+happyReduction_39 happy_x_3+	happy_x_2+	happy_x_1+	 =  case happyOut26 happy_x_1 of { happy_var_1 -> +	case happyOut27 happy_x_3 of { happy_var_3 -> +	happyIn27+		 ((:) happy_var_1 happy_var_3+	)}}++happyReduce_40 = happyReduce 5# 23# happyReduction_40+happyReduction_40 (happy_x_5 `HappyStk`+	happy_x_4 `HappyStk`+	happy_x_3 `HappyStk`+	happy_x_2 `HappyStk`+	happy_x_1 `HappyStk`+	happyRest)+	 = case happyOut15 happy_x_1 of { happy_var_1 -> +	case happyOut34 happy_x_2 of { happy_var_2 -> +	case happyOut34 happy_x_4 of { happy_var_4 -> +	happyIn28+		 (VarTele happy_var_1 happy_var_2 happy_var_4+	) `HappyStk` happyRest}}}++happyReduce_41 = happySpecReduce_1  23# happyReduction_41+happyReduction_41 happy_x_1+	 =  case happyOut39 happy_x_1 of { happy_var_1 -> +	happyIn28+		 (TypeTele happy_var_1+	)}++happyReduce_42 = happySpecReduce_0  24# happyReduction_42+happyReduction_42  =  happyIn29+		 ([]+	)++happyReduce_43 = happySpecReduce_2  24# happyReduction_43+happyReduction_43 happy_x_2+	happy_x_1+	 =  case happyOut29 happy_x_1 of { happy_var_1 -> +	case happyOut28 happy_x_2 of { happy_var_2 -> +	happyIn29+		 (flip (:) happy_var_1 happy_var_2+	)}}++happyReduce_44 = happyReduce 5# 25# happyReduction_44+happyReduction_44 (happy_x_5 `HappyStk`+	happy_x_4 `HappyStk`+	happy_x_3 `HappyStk`+	happy_x_2 `HappyStk`+	happy_x_1 `HappyStk`+	happyRest)+	 = case happyOut15 happy_x_1 of { happy_var_1 -> +	case happyOut34 happy_x_2 of { happy_var_2 -> +	case happyOut34 happy_x_4 of { happy_var_4 -> +	happyIn30+		 (DataTele happy_var_1 happy_var_2 happy_var_4+	) `HappyStk` happyRest}}}++happyReduce_45 = happySpecReduce_0  26# happyReduction_45+happyReduction_45  =  happyIn31+		 ([]+	)++happyReduce_46 = happySpecReduce_2  26# happyReduction_46+happyReduction_46 happy_x_2+	happy_x_1+	 =  case happyOut31 happy_x_1 of { happy_var_1 -> +	case happyOut30 happy_x_2 of { happy_var_2 -> +	happyIn31+		 (flip (:) happy_var_1 happy_var_2+	)}}++happyReduce_47 = happyReduce 5# 27# happyReduction_47+happyReduction_47 (happy_x_5 `HappyStk`+	happy_x_4 `HappyStk`+	happy_x_3 `HappyStk`+	happy_x_2 `HappyStk`+	happy_x_1 `HappyStk`+	happyRest)+	 = case happyOut15 happy_x_1 of { happy_var_1 -> +	case happyOut34 happy_x_2 of { happy_var_2 -> +	case happyOut34 happy_x_4 of { happy_var_4 -> +	happyIn32+		 (PiTele happy_var_1 happy_var_2 happy_var_4+	) `HappyStk` happyRest}}}++happyReduce_48 = happySpecReduce_1  28# happyReduction_48+happyReduction_48 happy_x_1+	 =  case happyOut32 happy_x_1 of { happy_var_1 -> +	happyIn33+		 ((:[]) happy_var_1+	)}++happyReduce_49 = happySpecReduce_2  28# happyReduction_49+happyReduction_49 happy_x_2+	happy_x_1+	 =  case happyOut32 happy_x_1 of { happy_var_1 -> +	case happyOut33 happy_x_2 of { happy_var_2 -> +	happyIn33+		 ((:) happy_var_1 happy_var_2+	)}}++happyReduce_50 = happyReduce 4# 29# happyReduction_50+happyReduction_50 (happy_x_4 `HappyStk`+	happy_x_3 `HappyStk`+	happy_x_2 `HappyStk`+	happy_x_1 `HappyStk`+	happyRest)+	 = case happyOut14 happy_x_1 of { happy_var_1 -> +	case happyOut41 happy_x_2 of { happy_var_2 -> +	case happyOut34 happy_x_4 of { happy_var_4 -> +	happyIn34+		 (Lam happy_var_1 happy_var_2 happy_var_4+	) `HappyStk` happyRest}}}++happyReduce_51 = happySpecReduce_1  29# happyReduction_51+happyReduction_51 happy_x_1+	 =  case happyOut35 happy_x_1 of { happy_var_1 -> +	happyIn34+		 (happy_var_1+	)}++happyReduce_52 = happySpecReduce_3  30# happyReduction_52+happyReduction_52 happy_x_3+	happy_x_2+	happy_x_1+	 =  case happyOut36 happy_x_1 of { happy_var_1 -> +	case happyOut35 happy_x_3 of { happy_var_3 -> +	happyIn35+		 (Arr happy_var_1 happy_var_3+	)}}++happyReduce_53 = happySpecReduce_3  30# happyReduction_53+happyReduction_53 happy_x_3+	happy_x_2+	happy_x_1+	 =  case happyOut33 happy_x_1 of { happy_var_1 -> +	case happyOut35 happy_x_3 of { happy_var_3 -> +	happyIn35+		 (Pi happy_var_1 happy_var_3+	)}}++happyReduce_54 = happySpecReduce_1  30# happyReduction_54+happyReduction_54 happy_x_1+	 =  case happyOut36 happy_x_1 of { happy_var_1 -> +	happyIn35+		 (happy_var_1+	)}++happyReduce_55 = happySpecReduce_3  31# happyReduction_55+happyReduction_55 happy_x_3+	happy_x_2+	happy_x_1+	 =  case happyOut37 happy_x_1 of { happy_var_1 -> +	case happyOut37 happy_x_3 of { happy_var_3 -> +	happyIn36+		 (PathImp happy_var_1 happy_var_3+	)}}++happyReduce_56 = happySpecReduce_1  31# happyReduction_56+happyReduction_56 happy_x_1+	 =  case happyOut37 happy_x_1 of { happy_var_1 -> +	happyIn36+		 (happy_var_1+	)}++happyReduce_57 = happySpecReduce_3  32# happyReduction_57+happyReduction_57 happy_x_3+	happy_x_2+	happy_x_1+	 =  case happyOut37 happy_x_1 of { happy_var_1 -> +	case happyOut38 happy_x_3 of { happy_var_3 -> +	happyIn37+		 (At happy_var_1 happy_var_3+	)}}++happyReduce_58 = happySpecReduce_1  32# happyReduction_58+happyReduction_58 happy_x_1+	 =  case happyOut38 happy_x_1 of { happy_var_1 -> +	happyIn37+		 (happy_var_1+	)}++happyReduce_59 = happySpecReduce_2  33# happyReduction_59+happyReduction_59 happy_x_2+	happy_x_1+	 =  case happyOut38 happy_x_1 of { happy_var_1 -> +	case happyOut39 happy_x_2 of { happy_var_2 -> +	happyIn38+		 (App happy_var_1 happy_var_2+	)}}++happyReduce_60 = happySpecReduce_1  33# happyReduction_60+happyReduction_60 happy_x_1+	 =  case happyOut39 happy_x_1 of { happy_var_1 -> +	happyIn38+		 (happy_var_1+	)}++happyReduce_61 = happySpecReduce_1  34# happyReduction_61+happyReduction_61 happy_x_1+	 =  case happyOut40 happy_x_1 of { happy_var_1 -> +	happyIn39+		 (Var happy_var_1+	)}++happyReduce_62 = happySpecReduce_1  34# happyReduction_62+happyReduction_62 happy_x_1+	 =  case happyOut5 happy_x_1 of { happy_var_1 -> +	happyIn39+		 (Universe happy_var_1+	)}++happyReduce_63 = happySpecReduce_1  34# happyReduction_63+happyReduction_63 happy_x_1+	 =  case happyOut6 happy_x_1 of { happy_var_1 -> +	happyIn39+		 (Interval happy_var_1+	)}++happyReduce_64 = happySpecReduce_1  34# happyReduction_64+happyReduction_64 happy_x_1+	 =  case happyOut7 happy_x_1 of { happy_var_1 -> +	happyIn39+		 (ELeft happy_var_1+	)}++happyReduce_65 = happySpecReduce_1  34# happyReduction_65+happyReduction_65 happy_x_1+	 =  case happyOut8 happy_x_1 of { happy_var_1 -> +	happyIn39+		 (ERight happy_var_1+	)}++happyReduce_66 = happySpecReduce_1  34# happyReduction_66+happyReduction_66 happy_x_1+	 =  case happyOut9 happy_x_1 of { happy_var_1 -> +	happyIn39+		 (Path happy_var_1+	)}++happyReduce_67 = happySpecReduce_1  34# happyReduction_67+happyReduction_67 happy_x_1+	 =  case happyOut10 happy_x_1 of { happy_var_1 -> +	happyIn39+		 (PathCon happy_var_1+	)}++happyReduce_68 = happySpecReduce_1  34# happyReduction_68+happyReduction_68 happy_x_1+	 =  case happyOut11 happy_x_1 of { happy_var_1 -> +	happyIn39+		 (Coe happy_var_1+	)}++happyReduce_69 = happySpecReduce_1  34# happyReduction_69+happyReduction_69 happy_x_1+	 =  case happyOut12 happy_x_1 of { happy_var_1 -> +	happyIn39+		 (Iso happy_var_1+	)}++happyReduce_70 = happySpecReduce_1  34# happyReduction_70+happyReduction_70 happy_x_1+	 =  case happyOut13 happy_x_1 of { happy_var_1 -> +	happyIn39+		 (Squeeze happy_var_1+	)}++happyReduce_71 = happySpecReduce_3  34# happyReduction_71+happyReduction_71 happy_x_3+	happy_x_2+	happy_x_1+	 =  case happyOut15 happy_x_1 of { happy_var_1 -> +	case happyOut34 happy_x_2 of { happy_var_2 -> +	happyIn39+		 (Paren happy_var_1 happy_var_2+	)}}++happyReduce_72 = happySpecReduce_1  35# happyReduction_72+happyReduction_72 happy_x_1+	 =  case happyOut17 happy_x_1 of { happy_var_1 -> +	happyIn40+		 (Arg happy_var_1+	)}++happyReduce_73 = happySpecReduce_1  35# happyReduction_73+happyReduction_73 happy_x_1+	 =  case happyOut16 happy_x_1 of { happy_var_1 -> +	happyIn40+		 (NoArg happy_var_1+	)}++happyReduce_74 = happySpecReduce_1  36# happyReduction_74+happyReduction_74 happy_x_1+	 =  case happyOut40 happy_x_1 of { happy_var_1 -> +	happyIn41+		 ((:[]) happy_var_1+	)}++happyReduce_75 = happySpecReduce_2  36# happyReduction_75+happyReduction_75 happy_x_2+	happy_x_1+	 =  case happyOut40 happy_x_1 of { happy_var_1 -> +	case happyOut41 happy_x_2 of { happy_var_2 -> +	happyIn41+		 ((:) happy_var_1 happy_var_2+	)}}++happyNewToken action sts stk [] =+	happyDoAction 26# notHappyAtAll action sts stk []++happyNewToken action sts stk (tk:tks) =+	let cont i = happyDoAction i tk action sts stk tks in+	case tk of {+	PT _ (TS _ 1) -> cont 1#;+	PT _ (TS _ 2) -> cont 2#;+	PT _ (TS _ 3) -> cont 3#;+	PT _ (TS _ 4) -> cont 4#;+	PT _ (TS _ 5) -> cont 5#;+	PT _ (TS _ 6) -> cont 6#;+	PT _ (TS _ 7) -> cont 7#;+	PT _ (TS _ 8) -> cont 8#;+	PT _ (TS _ 9) -> cont 9#;+	PT _ (TS _ 10) -> cont 10#;+	PT _ (TS _ 11) -> cont 11#;+	PT _ (T_U _) -> cont 12#;+	PT _ (T_I _) -> cont 13#;+	PT _ (T_PLeft _) -> cont 14#;+	PT _ (T_PRight _) -> cont 15#;+	PT _ (T_PPath _) -> cont 16#;+	PT _ (T_Ppath _) -> cont 17#;+	PT _ (T_PCoe _) -> cont 18#;+	PT _ (T_PIso _) -> cont 19#;+	PT _ (T_PSqueeze _) -> cont 20#;+	PT _ (T_PLam _) -> cont 21#;+	PT _ (T_PPar _) -> cont 22#;+	PT _ (T_Pus _) -> cont 23#;+	PT _ (T_PIdent _) -> cont 24#;+	_ -> cont 25#;+	_ -> happyError' (tk:tks)+	}++happyError_ 26# tk tks = happyError' tks+happyError_ _ tk tks = happyError' (tk:tks)++happyThen :: () => Err a -> (a -> Err b) -> Err b+happyThen = (thenM)+happyReturn :: () => a -> Err a+happyReturn = (returnM)+happyThen1 m k tks = (thenM) m (\a -> k a tks)+happyReturn1 :: () => a -> b -> Err a+happyReturn1 = \a tks -> (returnM) a+happyError' :: () => [(Token)] -> Err a+happyError' = happyError++pDefs tks = happySomeParser where+  happySomeParser = happyThen (happyParse 0# tks) (\x -> happyReturn (happyOut18 x))++pExpr tks = happySomeParser where+  happySomeParser = happyThen (happyParse 1# tks) (\x -> happyReturn (happyOut34 x))++happySeq = happyDontSeq+++returnM :: a -> Err a+returnM = return++thenM :: Err a -> (a -> Err b) -> Err b+thenM = (>>=)++happyError :: [Token] -> Err a+happyError ts =+  Bad $ "syntax error at " ++ tokenPos ts ++ +  case ts of+    [] -> []+    [Err _] -> " due to lexer error"+    _ -> " before " ++ unwords (map (id . prToken) (take 4 ts))++myLexer = tokens+{-# LINE 1 "templates/GenericTemplate.hs" #-}+{-# LINE 1 "templates/GenericTemplate.hs" #-}+{-# LINE 1 "<command-line>" #-}+{-# LINE 1 "templates/GenericTemplate.hs" #-}+-- Id: GenericTemplate.hs,v 1.26 2005/01/14 14:47:22 simonmar Exp ++{-# LINE 30 "templates/GenericTemplate.hs" #-}+++data Happy_IntList = HappyCons Happy_GHC_Exts.Int# Happy_IntList++++++{-# LINE 51 "templates/GenericTemplate.hs" #-}++{-# LINE 61 "templates/GenericTemplate.hs" #-}++{-# LINE 70 "templates/GenericTemplate.hs" #-}++infixr 9 `HappyStk`+data HappyStk a = HappyStk a (HappyStk a)++-----------------------------------------------------------------------------+-- starting the parse++happyParse start_state = happyNewToken start_state notHappyAtAll notHappyAtAll++-----------------------------------------------------------------------------+-- Accepting the parse++-- If the current token is 0#, it means we've just accepted a partial+-- parse (a %partial parser).  We must ignore the saved token on the top of+-- the stack in this case.+happyAccept 0# tk st sts (_ `HappyStk` ans `HappyStk` _) =+	happyReturn1 ans+happyAccept j tk st sts (HappyStk ans _) = +	(happyTcHack j (happyTcHack st)) (happyReturn1 ans)++-----------------------------------------------------------------------------+-- Arrays only: do the next action++++happyDoAction i tk st+	= {- nothing -}+++	  case action of+		0#		  -> {- nothing -}+				     happyFail i tk st+		-1# 	  -> {- nothing -}+				     happyAccept i tk st+		n | (n Happy_GHC_Exts.<# (0# :: Happy_GHC_Exts.Int#)) -> {- nothing -}++				     (happyReduceArr Happy_Data_Array.! rule) i tk st+				     where rule = (Happy_GHC_Exts.I# ((Happy_GHC_Exts.negateInt# ((n Happy_GHC_Exts.+# (1# :: Happy_GHC_Exts.Int#))))))+		n		  -> {- nothing -}+++				     happyShift new_state i tk st+				     where (new_state) = (n Happy_GHC_Exts.-# (1# :: Happy_GHC_Exts.Int#))+   where (off)    = indexShortOffAddr happyActOffsets st+         (off_i)  = (off Happy_GHC_Exts.+# i)+	 check  = if (off_i Happy_GHC_Exts.>=# (0# :: Happy_GHC_Exts.Int#))+			then (indexShortOffAddr happyCheck off_i Happy_GHC_Exts.==#  i)+			else False+         (action)+          | check     = indexShortOffAddr happyTable off_i+          | otherwise = indexShortOffAddr happyDefActions st++{-# LINE 130 "templates/GenericTemplate.hs" #-}+++indexShortOffAddr (HappyA# arr) off =+	Happy_GHC_Exts.narrow16Int# i+  where+        i = Happy_GHC_Exts.word2Int# (Happy_GHC_Exts.or# (Happy_GHC_Exts.uncheckedShiftL# high 8#) low)+        high = Happy_GHC_Exts.int2Word# (Happy_GHC_Exts.ord# (Happy_GHC_Exts.indexCharOffAddr# arr (off' Happy_GHC_Exts.+# 1#)))+        low  = Happy_GHC_Exts.int2Word# (Happy_GHC_Exts.ord# (Happy_GHC_Exts.indexCharOffAddr# arr off'))+        off' = off Happy_GHC_Exts.*# 2#++++++data HappyAddr = HappyA# Happy_GHC_Exts.Addr#+++++-----------------------------------------------------------------------------+-- HappyState data type (not arrays)++{-# LINE 163 "templates/GenericTemplate.hs" #-}++-----------------------------------------------------------------------------+-- Shifting a token++happyShift new_state 0# tk st sts stk@(x `HappyStk` _) =+     let (i) = (case Happy_GHC_Exts.unsafeCoerce# x of { (Happy_GHC_Exts.I# (i)) -> i }) in+--     trace "shifting the error token" $+     happyDoAction i tk new_state (HappyCons (st) (sts)) (stk)++happyShift new_state i tk st sts stk =+     happyNewToken new_state (HappyCons (st) (sts)) ((happyInTok (tk))`HappyStk`stk)++-- happyReduce is specialised for the common cases.++happySpecReduce_0 i fn 0# tk st sts stk+     = happyFail 0# tk st sts stk+happySpecReduce_0 nt fn j tk st@((action)) sts stk+     = happyGoto nt j tk st (HappyCons (st) (sts)) (fn `HappyStk` stk)++happySpecReduce_1 i fn 0# tk st sts stk+     = happyFail 0# tk st sts stk+happySpecReduce_1 nt fn j tk _ sts@((HappyCons (st@(action)) (_))) (v1`HappyStk`stk')+     = let r = fn v1 in+       happySeq r (happyGoto nt j tk st sts (r `HappyStk` stk'))++happySpecReduce_2 i fn 0# tk st sts stk+     = happyFail 0# tk st sts stk+happySpecReduce_2 nt fn j tk _ (HappyCons (_) (sts@((HappyCons (st@(action)) (_))))) (v1`HappyStk`v2`HappyStk`stk')+     = let r = fn v1 v2 in+       happySeq r (happyGoto nt j tk st sts (r `HappyStk` stk'))++happySpecReduce_3 i fn 0# tk st sts stk+     = happyFail 0# tk st sts stk+happySpecReduce_3 nt fn j tk _ (HappyCons (_) ((HappyCons (_) (sts@((HappyCons (st@(action)) (_))))))) (v1`HappyStk`v2`HappyStk`v3`HappyStk`stk')+     = let r = fn v1 v2 v3 in+       happySeq r (happyGoto nt j tk st sts (r `HappyStk` stk'))++happyReduce k i fn 0# tk st sts stk+     = happyFail 0# tk st sts stk+happyReduce k nt fn j tk st sts stk+     = case happyDrop (k Happy_GHC_Exts.-# (1# :: Happy_GHC_Exts.Int#)) sts of+	 sts1@((HappyCons (st1@(action)) (_))) ->+        	let r = fn stk in  -- it doesn't hurt to always seq here...+       		happyDoSeq r (happyGoto nt j tk st1 sts1 r)++happyMonadReduce k nt fn 0# tk st sts stk+     = happyFail 0# tk st sts stk+happyMonadReduce k nt fn j tk st sts stk =+        happyThen1 (fn stk tk) (\r -> happyGoto nt j tk st1 sts1 (r `HappyStk` drop_stk))+       where (sts1@((HappyCons (st1@(action)) (_)))) = happyDrop k (HappyCons (st) (sts))+             drop_stk = happyDropStk k stk++happyMonad2Reduce k nt fn 0# tk st sts stk+     = happyFail 0# tk st sts stk+happyMonad2Reduce k nt fn j tk st sts stk =+       happyThen1 (fn stk tk) (\r -> happyNewToken new_state sts1 (r `HappyStk` drop_stk))+       where (sts1@((HappyCons (st1@(action)) (_)))) = happyDrop k (HappyCons (st) (sts))+             drop_stk = happyDropStk k stk++             (off) = indexShortOffAddr happyGotoOffsets st1+             (off_i) = (off Happy_GHC_Exts.+# nt)+             (new_state) = indexShortOffAddr happyTable off_i+++++happyDrop 0# l = l+happyDrop n (HappyCons (_) (t)) = happyDrop (n Happy_GHC_Exts.-# (1# :: Happy_GHC_Exts.Int#)) t++happyDropStk 0# l = l+happyDropStk n (x `HappyStk` xs) = happyDropStk (n Happy_GHC_Exts.-# (1#::Happy_GHC_Exts.Int#)) xs++-----------------------------------------------------------------------------+-- Moving to a new state after a reduction+++happyGoto nt j tk st = +   {- nothing -}+   happyDoAction j tk new_state+   where (off) = indexShortOffAddr happyGotoOffsets st+         (off_i) = (off Happy_GHC_Exts.+# nt)+         (new_state) = indexShortOffAddr happyTable off_i+++++-----------------------------------------------------------------------------+-- Error recovery (0# is the error token)++-- parse error if we are in recovery and we fail again+happyFail 0# tk old_st _ stk@(x `HappyStk` _) =+     let (i) = (case Happy_GHC_Exts.unsafeCoerce# x of { (Happy_GHC_Exts.I# (i)) -> i }) in+--	trace "failing" $ +        happyError_ i tk++{-  We don't need state discarding for our restricted implementation of+    "error".  In fact, it can cause some bogus parses, so I've disabled it+    for now --SDM++-- discard a state+happyFail  0# tk old_st (HappyCons ((action)) (sts)) +						(saved_tok `HappyStk` _ `HappyStk` stk) =+--	trace ("discarding state, depth " ++ show (length stk))  $+	happyDoAction 0# tk action sts ((saved_tok`HappyStk`stk))+-}++-- Enter error recovery: generate an error token,+--                       save the old token and carry on.+happyFail  i tk (action) sts stk =+--      trace "entering error recovery" $+	happyDoAction 0# tk action sts ( (Happy_GHC_Exts.unsafeCoerce# (Happy_GHC_Exts.I# (i))) `HappyStk` stk)++-- Internal happy errors:++notHappyAtAll :: a+notHappyAtAll = error "Internal Happy error\n"++-----------------------------------------------------------------------------+-- Hack to get the typechecker to accept our action functions+++happyTcHack :: Happy_GHC_Exts.Int# -> a -> a+happyTcHack x y = y+{-# INLINE happyTcHack #-}+++-----------------------------------------------------------------------------+-- Seq-ing.  If the --strict flag is given, then Happy emits +--	happySeq = happyDoSeq+-- otherwise it emits+-- 	happySeq = happyDontSeq++happyDoSeq, happyDontSeq :: a -> b -> b+happyDoSeq   a b = a `seq` b+happyDontSeq a b = b++-----------------------------------------------------------------------------+-- Don't inline any functions from the template.  GHC has a nasty habit+-- of deciding to inline happyGoto everywhere, which increases the size of+-- the generated parser quite a bit.+++{-# NOINLINE happyDoAction #-}+{-# NOINLINE happyTable #-}+{-# NOINLINE happyCheck #-}+{-# NOINLINE happyActOffsets #-}+{-# NOINLINE happyGotoOffsets #-}+{-# NOINLINE happyDefActions #-}++{-# NOINLINE happyShift #-}+{-# NOINLINE happySpecReduce_0 #-}+{-# NOINLINE happySpecReduce_1 #-}+{-# NOINLINE happySpecReduce_2 #-}+{-# NOINLINE happySpecReduce_3 #-}+{-# NOINLINE happyReduce #-}+{-# NOINLINE happyMonadReduce #-}+{-# NOINLINE happyGoto #-}+{-# NOINLINE happyFail #-}++-- end of Happy Template.

@@ -0,0 +1,122 @@+-- Pi types+id : (A : Type) -> A -> A+id A a = a++-- Universes+-- Type and Type0 are synonyms+universes : (f : Type1 -> Type0) -> f Type0 -> f Type0+universes f = id (f Type0)++-- Universes are cumulative+cumulative : Type3 -> Type8+cumulative A = A++-- Lambdas+compose : (A B C : Type) -> (B -> C) -> (A -> B) -> A -> C+compose A B C = \g f a -> g (f a)++-- Data types+data Bool = false | true++data Nat = zero | suc Nat++data List (A : Type) = nil | cons A (List A)++-- Pattern matching+not : Bool -> Bool+not true = false+not false = true++and : Bool -> Bool -> Bool+and true true = true+and _ _ = false++-- Recursive functions+plus : Nat -> Nat -> Nat+plus zero y = y+plus (suc x) y = suc (plus x y)++ack : Nat -> Nat -> Nat+ack zero n = suc n+ack (suc m) zero = ack m (suc zero)+ack (suc m) (suc n) = ack m (ack (suc m) n)++-- Interval type+-- I is a type with constructors left : I and right : I+-- coe and squeeze are primitive operators which satisfy the following rules:+-- +-- coe : (A : I -> Type) (i : I) -> A i -> (j : I) -> A j+-- coe A i a i = a+-- coe (\_ -> A) i a j = a+-- +-- squeeze : I -> I -> I+-- squeeze left _ = left+-- squeeze right j = j+-- squeeze _ left = left+-- squeeze i right = i++-- Path types+-- Path A a a' is a type with constructor path : (f : (i : I) -> A i) -> Path A (f left) (f right)+-- a = a' is a synonym for Path (\_ -> A) a a'+-- @ is an eliminator for Path, it has type Path A a a' -> (i : I) -> A i+-- path f @ i = f i++idp : (A : Type) (a : A) -> a = a+idp A a = path (\_ -> a)++transport : (A : Type) (B : A -> Type) (a a' : A) -> a = a' -> B a -> B a'+transport A B _ _ p x = coe (\i -> B (p @ i)) left x right++J : (A : Type) (B : (a a' : A) -> a = a' -> Type) -> ((a : A) -> B a a (idp A a)) -> (a a' : A) (p : a = a') -> B a a' p+J A B d a a' p = coe (\i -> B a (p @ i) (path (\j -> p @ squeeze i j))) left (d a) right++ext : (A : Type) (B : A -> Type) (f g : (a : A) -> B a) -> ((a : A) -> f a = g a) -> f = g+ext A B f g p = path (\i a -> p a @ i)++-- Univalence+not-not : (x : Bool) -> not (not x) = x+not-not true  = idp Bool true+not-not false = idp Bool false++biso : Bool = Bool+biso = path (iso Bool Bool not not not-not not-not)++-- coe satisfies the following rules:+-- coe (iso A B f g p q) left a right = f a+-- coe (iso A B f g p q) right b left = g b+biso-not : coe (\i -> biso @ i) left true right = false+biso-not = idp Bool false++biso-not-not : coe (\i -> biso @ i) right (coe (\i -> biso @ i) left true right) left = true+biso-not-not = idp Bool true++-- Data types with conditions+data Z = positive Nat | negative Nat with+    negative zero = positive zero++-- Now, this works,+succ : Z -> Z+succ (positive x)       = positive (suc x)+succ (negative zero)    = positive (suc zero)+succ (negative (suc x)) = negative x++-- but this don't+succ' : Z -> Z+succ' (positive x)       = positive (suc x)+succ' (negative zero)    = positive zero+succ' (negative (suc x)) = negative x++-- We can define higher inductive types using data types with conditions and the interval object+data Circle = base | loop I with+    loop left  = base+    loop right = base++Circle-elim : (P : Circle -> Type) (b : P base) -> Path (\i -> P (loop i)) b b -> (x : Circle) -> P x+Circle-elim P b t base     = b+Circle-elim P b t (loop i) = t @ i++Circle-elim' : (P : Circle -> Type) (b : P base) -> transport Circle P base base (path loop) b = b -> (x : Circle) -> P x+Circle-elim' P b t base     = b+Circle-elim' P b t (loop i) = +    coe  (\j -> Path (\k -> P (loop k)) b (t @ j)) left+    (path (\j -> coe (\k -> P (loop k)) left b j)) right @ i

@@ -0,0 +1,152 @@+data Nat = zero | suc Nat++data Z = positive Nat | negative Nat with+    negative zero = positive zero++Z-isSet : (x y : Z) (p q : x = y) -> p = q+Z-isSet = NotImplemented++succ : Z -> Z+succ (positive x)       = positive (suc x)+succ (negative zero)    = positive (suc zero)+succ (negative (suc x)) = negative x++pred : Z -> Z+pred (positive zero)    = negative (suc zero)+pred (positive (suc x)) = positive x+pred (negative x)       = negative (suc x)++data Circle = base | loop I with+    loop left  = base+    loop right = base++idp : (A : Type) (a : A) -> a = a+idp A a = path (\_ -> a)++transport : (A : Type) (B : A -> Type) (a a' : A) -> a = a' -> B a -> B a'+transport A B _ _ p x = coe (\i -> B (p @ i)) left x right++psqueeze : (A : Type) (a a' : A) (p : a = a') (i : I) -> a = p @ i+psqueeze A a a' p i = path (\j -> p @ squeeze i j)++J : (A : Type) (a : A) (B : (a' : A) -> a = a' -> Type) -> B a (idp A a) -> (a' : A) (p : a = a') -> B a' p+J A a B b a' p = coe (\i -> B (p @ i) (psqueeze A a a' p i)) left b right++inv : (A : Type) (a a' : A) -> a = a' -> a' = a+inv A a a' p = transport A (\x -> x = a) a a' p (idp A a)++comp : (A : Type) (a a' a'' : A) -> a = a' -> a' = a'' -> a = a''+comp A a a' a'' p q = transport A (\x -> a = x) a' a'' q p++comp' : base = base -> base = base -> base = base+comp' = comp Circle base base base++inv' : base = base -> base = base+inv' = inv Circle base base++wind : Z -> base = base+wind (positive zero)    = idp Circle base+wind (positive (suc x)) = comp' (wind (positive x)) (path loop)+wind (negative (suc x)) = comp' (wind (negative x)) (inv' (path loop))++pred-succ : (x : Z) -> pred (succ x) = x+pred-succ (positive x) = idp Z (positive x)+pred-succ (negative (suc x)) = idp Z (negative (suc x))++succ-pred : (x : Z) -> succ (pred x) = x+succ-pred (positive zero) = idp Z (positive zero)+succ-pred (positive (suc x)) = idp Z (positive (suc x))+succ-pred (negative x) = idp Z (negative x)++iter : I -> Type+iter i = iso Z Z succ pred pred-succ succ-pred i++code : Circle -> Type+code base     = Z+code (loop i) = iter i++encode : (x : Circle) -> base = x -> code x+encode _ p = coe (\i -> code (p @ i)) left (positive zero) right++assoc : (p q r : base = base) -> comp' (comp' p q) r = comp' p (comp' q r)+assoc p q = J Circle base+    (\x s -> comp Circle base base x (comp' p q) s = comp Circle base base x p (comp Circle base base x q s))+    (idp (base = base) (comp' p q)) base++map : (A B : Type) (f : A -> B) -> (a a' : A) -> a = a' -> f a = f a'+map A B f a a' p = transport A (\x -> f a = f x) a a' p (idp B (f a))++inv-idp : (p : base = base) -> comp' (inv' p) p = idp Circle base+inv-idp = J Circle base (\x q -> comp Circle x base x (inv Circle base x q) q = idp Circle x)+    (idp (base = base) (idp Circle base)) base++wind-succ-loop-neg : (x : Nat) -> comp' (wind (pred (negative x))) (path loop) = wind (negative x)+wind-succ-loop-neg x =+    comp (base = base) (comp' (comp' (wind (negative x)) (inv' (path loop))) (path loop))+                       (comp' (wind (negative x)) (comp' (inv' (path loop)) (path loop)))+                       (wind (negative x))+    (assoc (wind (negative x)) (inv' (path loop)) (path loop))+    (map (base = base) (base = base) (comp' (wind (negative x)))+        (comp' (inv' (path loop)) (path loop)) (idp Circle base) (inv-idp (path loop)))++wind-succ-loop : (x : Z) -> comp' (wind (pred x)) (path loop) = wind x+wind-succ-loop (positive zero) = wind-succ-loop-neg zero+wind-succ-loop (positive (suc x)) = idp (base = base) (wind (positive (suc x)))+wind-succ-loop (negative x) = wind-succ-loop-neg x++decode : (x : Circle) -> code x -> base = x+decode base     = wind+decode (loop i) =+    coe (\j -> Path (\k -> iter k -> base = loop k) wind (\y -> wind-succ-loop y @ j)) left+    (path (\k y -> comp Circle base base (loop k) (wind (coe iter k y left)) (psqueeze Circle base base (path loop) k)))+    right @ i++encode-decode : (x : Circle) (p : base = x) -> decode x (encode x p) = p+encode-decode = J Circle base (\x p -> decode x (encode x p) = p) (idp (base = base) (idp Circle base))++coe-comp : (p q : base = base) (z : Z) ->+    coe (\i -> code (comp' p q @ i)) left z right =+    coe (\i -> code (q @ i)) left (coe (\i -> code (p @ i)) left z right) right+coe-comp p q z = J Circle base (\x s -> coe (\i -> code (comp Circle base base x p s @ i)) left z right =+    coe (\i -> code (s @ i)) left (coe (\i -> code (p @ i)) left z right) right)+    (idp Z (coe (\i -> code (p @ i)) left z right)) base q++coe-inv : (p : base = base) (z : Z) -> coe (\i -> code (inv' p @ i)) left z right = coe (\i -> code (p @ i)) right z left+coe-inv = J Circle base (\x s -> (y : code x) ->+    coe (\i -> code (inv Circle base x s @ i)) left y right = coe (\i -> code (s @ i)) right y left) (idp Z) base++decode-encode-base : (z : Z) -> encode base (wind z) = z+decode-encode-base (positive zero) = idp Z (positive zero)+decode-encode-base (positive (suc x)) =+    comp Z (coe (\i -> code (comp' (wind (positive x)) (path loop) @ i)) left (positive zero) right)+           (succ (coe (\i -> code (wind (positive x) @ i)) left (positive zero) right))+           (positive (suc x))+    (coe-comp (wind (positive x)) (path loop) (positive zero))+    (map Z Z succ (coe (\i -> code (wind (positive x) @ i)) left (positive zero) right) (positive x)+        (decode-encode-base (positive x)))+decode-encode-base (negative (suc x)) =+    comp Z (coe (\i -> code (comp' (wind (negative x)) (inv' (path loop)) @ i)) left (positive zero) right)+           (coe (\i -> code (inv' (path loop) @ i)) left (coe (\i -> code (wind (negative x) @ i)) left (positive zero) right) right)+           (negative (suc x))+    (coe-comp (wind (negative x)) (inv' (path loop)) (positive zero))+    (comp Z (coe (\i -> code (inv' (path loop) @ i)) left (coe (\i -> code (wind (negative x) @ i)) left (positive zero) right) right)+            (pred (coe (\i -> code (wind (negative x) @ i)) left (positive zero) right))+            (negative (suc x))+    (coe-inv (path loop) (coe (\i -> code (wind (negative x) @ i)) left (positive zero) right))+    (map Z Z pred (coe (\i -> code (wind (negative x) @ i)) left (positive zero) right) (negative x) (decode-encode-base (negative x)))+    )++Circle-elim' : (P : Circle -> Type) (b : P base) -> transport Circle P base base (path loop) b = b -> (x : Circle) -> P x+Circle-elim' P b t base     = b+Circle-elim' P b t (loop i) = +    coe  (\j -> Path (\k -> P (loop k)) b (t @ j)) left+    (path (\j -> coe (\k -> P (loop k)) left b j)) right @ i++decode-encode : (x : Circle) (z : code x) -> encode x (decode x z) = z+decode-encode = Circle-elim' (\x -> (z : code x) -> encode x (decode x z) = z) decode-encode-base+    (path (\i z -> Z-isSet (coe (\i -> code (wind z @ i)) left (positive zero) right) z+    (transport Circle (\x -> (z : code x) -> encode x (decode x z) = z) base base (path loop) decode-encode-base z)+    (decode-encode-base z) @ i))++Circle-loop-space-is-Z : (base = base) = Z+Circle-loop-space-is-Z = path (iso (base = base) Z (encode base) (decode base) (encode-decode base) (decode-encode base))

@@ -0,0 +1,77 @@+data Nat = zero | suc Nat++data Sigma (A : Type) (B : A -> Type) = pair (a : A) (B a)++proj1 : (A : Type) (B : A -> Type) -> Sigma A B -> A+proj1 _ _ (pair a _) = a++proj2 : (A : Type) (B : A -> Type) (x : Sigma A B) -> B (proj1 A B x)+proj2 _ _ (pair _ b) = b++isContr : Type -> Type+isContr A = Sigma A (\a -> (a' : A) -> a = a')++I-isContr : isContr I+I-isContr = pair left (\i -> path (\j -> squeeze i j))++isProp : Type -> Type+isProp A = (a a' : A) -> a = a'++isSet : Type -> Type+isSet A = (a a' : A) -> isProp (a = a')++of-hlevel : Nat -> Type -> Type+of-hlevel zero A = isContr A+of-hlevel (suc n) A = (a a' : A) -> of-hlevel n (a = a')++h1-prop : (A : Type) -> of-hlevel (suc zero) A -> isProp A+h1-prop A f a a' = proj1 (a = a') (\p -> (p' : a = a') -> p = p') (f a a')++idp : (A : Type) (a : A) -> a = a+idp A a = path (\_ -> a)++transport : (A : Type) (B : A -> Type) (a a' : A) -> a = a' -> B a -> B a'+transport A B _ _ p x = coe (\i -> B (p @ i)) left x right++psqueeze : (A : Type) (a a' : A) (p : a = a') (i : I) -> a = p @ i+psqueeze A a a' p i = path (\j -> p @ squeeze i j)++J : (A : Type) (a : A) (B : (a' : A) -> a = a' -> Type) -> B a (idp A a) -> (a' : A) (p : a = a') -> B a' p+J A a B b a' p = coe (\i -> B (p @ i) (psqueeze A a a' p i)) left b right++inv : (A : Type) (a a' : A) -> a = a' -> a' = a+inv A a a' p = transport A (\x -> x = a) a a' p (idp A a)++comp : (A : Type) (a a' a'' : A) -> a = a' -> a' = a'' -> a = a''+comp A a a' a'' p q = transport A (\x -> a = x) a' a'' q p++inv-comp : (A : Type) (a a' : A) (p : a = a') -> comp A a' a a' (inv A a a' p) p = idp A a'+inv-comp A a a' p = J A a (\x q -> comp A x a x (inv A a x q) q = idp A x) (idp (a = a) (idp A a)) a' p++contr-prop : (A : Type) -> isContr A -> isProp A+contr-prop A (pair c f) a a' = comp A a c a' (inv A c a (f a)) (f a')++prop-h1 : (A : Type) -> isProp A -> of-hlevel (suc zero) A+prop-h1 A f a a' = pair (comp A a a a' (inv A a a (f a a)) (f a a'))+                        (J A a (\x q -> comp A a a x (inv A a a (f a a)) (f a x) = q) (inv-comp A a a (f a a)) a')++prop-set : (A : Type) -> isProp A -> isSet A+prop-set A p a a' = contr-prop (a = a') (prop-h1 A p a a')++isProp-isProp : (A : Type) -> isProp (isProp A)+isProp-isProp A f g = path (\i a a' -> prop-set A f a a' (f a a') (g a a') @ i)++Sigma-eq : (A : Type) (B : A -> Type) (a a' : A) (b : B a) (b' : B a') (p : a = a')+    -> transport A B a a' p b = b' -> Path (\_ -> Sigma A B) (pair a b) (pair a' b')+Sigma-eq A B a a' b b' p = J A a+    (\a' p -> (b' : B a') -> transport A B a a' p b = b' -> Path (\_ -> Sigma A B) (pair a b) (pair a' b'))+    (\b' q -> path (\i -> pair a (q @ i))) a' p b'++isContr-isProp : (A : Type) -> isProp (isContr A)+isContr-isProp A (pair a1 f1) (pair a2 f2) = Sigma-eq A (\a -> (a' : A) -> a = a') a1 a2 f1 f2 (f1 a2)+    (path (\i a' -> prop-set A (contr-prop A (pair a1 f1)) a2 a'+        (transport A (\a -> (a' : A) -> a = a') a1 a2 (f1 a2) f1 a') (f2 a') @ i))++of-hlevel-isProp : (n : Nat) (A : Type) -> isProp (of-hlevel n A)+of-hlevel-isProp zero A = isContr-isProp A+of-hlevel-isProp (suc n) A f g = path (\i a a' -> of-hlevel-isProp n (a = a') (f a a') (g a a') @ i)

@@ -0,0 +1,37 @@+data E+data S = s+data B = true | false++E-elim : (A : Type) -> E -> A+E-elim A ()++T : B -> Type+T true  = S+T false = E++not : B -> B+not true  = false+not false = true++not-not : (x : B) -> not (not x) = x+not-not true  = path (\_ -> true)+not-not false = path (\_ -> false)++biso : I -> Type+biso i = iso B B not not not-not not-not i++not-eq : (b : B) -> not b = b -> E+not-eq true  p = coe (\i -> T (p @ i)) right s left+not-eq false p = coe (\i -> T (p @ i)) left  s right++transport : (A : Type) (B : A -> Type) (a a' : A) -> a = a' -> B a -> B a'+transport A B _ _ p x = coe (\i -> B (p @ i)) left x right++comp : (A : Type) (a a' a'' : A) -> a = a' -> a' = a'' -> a = a''+comp A a a' a'' p q = transport A (\x -> a = x) a' a'' q p++not-lem : ((A : Type) -> ((A -> E) -> E) -> A) -> E+not-lem f = not-eq (f B (\g -> g true))+    (comp B (not (f B (\g -> g true))) (f B (\g -> g false)) (f B (\g -> g true))+        (path (\i -> coe biso i (f (biso i) (\g -> g (coe biso left true i))) right))+        (path (\i -> f B (\g -> g (E-elim (false = true) (g true) @ i)))))

@@ -0,0 +1,55 @@+name:                hoq+version:             0.1.0.0+synopsis:            A language based on homotopy type theory with an interval object+-- description:         +tested-with:         GHC == 7.6.3+homepage:            http://github.com/valis/hoq+license:             GPL-2+license-file:        LICENSE+author:              isaev+maintainer:          valery.isaev@gmail.com+category:            Dependent Types+build-type:          Custom+cabal-version:       >=1.10+data-dir:            data+data-files:          hoq.vim+extra-source-files:  README.md,+                     src/Syntax/Grammar.cf,+                     examples/basics.hoq,+                     examples/hlevel.hoq,+                     examples/circle.hoq,+                     examples/lem.hoq++source-repository head+  type:     git+  location: git://github.com/valis/hoq.git++executable hoq+  main-is:             Main.hs+  other-modules:       REPL,+                       Normalization, +                       File.Load,+                       Syntax.BNFC.ParGrammar,+                       Syntax.BNFC.LexGrammar,+                       Syntax.Term, Syntax.Scope,+                       Syntax.Expr, Syntax.PrettyPrinter,+                       Syntax.ErrorDoc, Syntax.Pattern,+                       TypeChecking.Definitions.Patterns,+                       TypeChecking.Definitions.Coverage,+                       TypeChecking.Definitions.DataTypes,+                       TypeChecking.Definitions.Functions,+                       TypeChecking.Definitions.Conditions,+                       TypeChecking.Definitions.Termination,+                       TypeChecking.Definitions,+                       TypeChecking.Expressions,+                       TypeChecking.Monad.Scope,+                       TypeChecking.Monad.Warn,+                       TypeChecking.Monad,+                       TypeChecking.Context+  build-depends:       base >=4.6 && <4.7, mtl >=2.1,+                       BNFC >= 2.5, array >= 0.4, pretty >=1.1,+                       prelude-extras >=0.4, readline >=1.0+  build-tools:         happy >= 1.15 && < 2,+                       alex >= 2.3.1 && < 3.1+  hs-source-dirs:      src+  default-language:    Haskell2010

@@ -0,0 +1,35 @@+module File.Load+    ( loadFile+    ) where++import System.IO+import Control.Monad.Fix+import Control.Monad.Trans+import Control.Exception++import Syntax.BNFC.ErrM+import Syntax.BNFC.ParGrammar+import Syntax.BNFC.LayoutGrammar+import Syntax.ErrorDoc+import Syntax.PrettyPrinter()+import Syntax.Expr+import TypeChecking.Definitions+import TypeChecking.Monad++loadFile :: (MonadIO m, MonadFix m) => String -> ScopeM m ()+loadFile filename = do+    (errs, _) <- runWarnT $ do+        mcnt <- liftIO $ fmap Right (readFile filename)+                        `catch` \e -> return $ Left $ show (e :: SomeException)+        case mcnt of+            Right cnt -> parseDefs cnt+            Left err  -> warn [emsg err enull]+    liftIO $ mapM_ (hPutStrLn stderr . erenderWithFilename filename) errs++parseDefs :: MonadFix m => String -> TCM m ()+parseDefs s = case parser s of+    Ok (Defs defs) -> typeCheckDefs defs+    Bad err          -> warn [emsg err enull]+  where+    parser :: String -> Err Defs+    parser = pDefs . resolveLayout True . myLexer

@@ -0,0 +1,12 @@+module Main where++import System.Environment++import File.Load+import TypeChecking.Monad.Scope+import REPL++main :: IO ()+main = do+    args <- getArgs+    runScopeT $ mapM_ loadFile args >> repl

@@ -0,0 +1,104 @@+module Normalization+    ( NF(..), nf+    , nfType, nfScope+    ) where++import Control.Monad+import Data.Traversable++import Syntax.Term++data NF = NF | HNF | WHNF deriving Eq++nf :: Eq a => NF -> Term a -> Term a+nf mode e = go e []+  where+    go (App a b)          ts = go a (b:ts)+    go e@Var{}            ts = apps e (nfs mode ts)+    go e@Universe{}       _  = e+    go (Pi a b lvl)       _  | mode == NF = Pi (nfType NF a) (nfScope b) lvl+    go e@Pi{}             _  = e+    go e@Interval         _  = e+    go e@(ICon _)         _  = e+    go (PCon Nothing)     [] = PCon Nothing+    go (PCon Nothing)  (e:_) = PCon $ Just   $ if mode == NF then nf NF e else e+    go (PCon (Just e))    _  = PCon $ Just   $ if mode == NF then nf NF e else e+    go (Con c lc n [] es) [] = Con c lc n [] $ nfs mode es+    go (Con c lc n [] es) ts = Con c lc n [] $ nfs mode (es ++ ts)+    go (DataType d e es)  [] = DataType d e  $ nfs mode es+    go (DataType d e es)  ts = DataType d e  $ nfs mode (es ++ ts)+    go (Path h ma es)     [] = Path h (if mode == NF then fmap (nf NF) ma else ma) $ nfs mode es+    go (Path h ma es)     ts = Path h (if mode == NF then fmap (nf NF) ma else ma) $ nfs mode (es ++ ts)+    go (Lam (Scope1 v t)) [] = Lam $ Scope1 v $ if mode == WHNF then t else nf mode t+    go (Lam (Scope1 _ s)) (t:ts) = go (instantiate1 t s) ts+    go (FunSyn _ term)    ts = go term ts+    go (Con c lc n conds es) ts =+        let es' = if null ts then es else es ++ ts in+        case instantiateCases conds es' of+            Just (r,ts') -> go r ts'+            Nothing      -> Con c lc n conds (if mode == NF then map (nf NF) es' else es')+    go fc@(FunCall _ _ []) ts = apps fc (nfs mode ts)+    go fc@(FunCall _ _ clauses) ts = case instantiateCases clauses ts of+        Just (r,ts') -> go r ts'+        Nothing      -> apps fc (nfs mode ts)+    go (At a b e1 e2) ts = case (nf WHNF e1, nf WHNF e2) of+        (_, ICon ILeft)      -> go a ts+        (_, ICon IRight)     -> go b ts+        (PCon (Just t1), t2) -> go t1 (t2:ts)+        (t1, t2)             -> apps (At (go a []) (go b []) (go t1 []) (go t2 [])) (nfs mode ts)+    go (Coe es) ts = case es ++ ts of+        es'@(e1:e2:e3:e4:es'') ->+            let e1' = nf WHNF e1+                e2' = nf NF e2+                e4' = nf NF e4+            in case (e2' == e4' || isStationary e1', e2' == ICon ILeft && e4' == ICon IRight,+                                                     e2' == ICon IRight && e4' == ICon ILeft, e1') of+                (True, _, _, _) -> go e3 es''+                (_, b1, b2, Iso [t1,t2,t3,t4,t5,t6]) | b1 || b2 -> go (App (if b1 then t3 else t4) e3) es''+                (_, b1, b2, _) | b1 || b2 -> case nf NF $ App (fmap Free e1') (Var Bound) of+                    Iso [t1,t2,t3,t4,t5,t6, Var Bound] -> case sequenceA $ Iso [t1,t2,t3,t4,t5,t6] of+                        Free (Iso [t1',t2',t3',t4',t5',t6']) -> go (App (if b1 then t3' else t4') e3) es''+                        _ -> Coe (nfs mode es')+                    _ -> Coe (nfs mode es')+                _ -> Coe (nfs mode es')+        es' -> Coe (nfs mode es')+    go (Iso es) ts = case map (nf WHNF) (es ++ ts) of+        t1:t2:t3:t4:t5:t6: ICon ILeft  : _ -> go t1 []+        t1:t2:t3:t4:t5:t6: ICon IRight : _ -> go t2 []+        _                                  -> Iso $ nfs mode (es ++ ts)+    go (Squeeze es) ts = case map (nf WHNF) (es ++ ts) of+        ICon ILeft  : _ : _ -> ICon ILeft+        ICon IRight : j : _ -> if mode == WHNF then j else nf mode j+        _ : ICon ILeft  : _ -> ICon ILeft+        i : ICon IRight : _ -> if mode == WHNF then i else nf mode i+        es'                 -> Squeeze $ nfs mode (es ++ ts)++nfType :: Eq a => NF -> Type a -> Type a+nfType mode (Type t lvl) = Type (nf mode t) lvl++nfScope :: Eq a => Scope s Term a -> Scope s Term a+nfScope (ScopeTerm t) = ScopeTerm (nf NF t)+nfScope (Scope v   s) = Scope v (nfScope s)++isStationary :: Eq a => Term a -> Bool+isStationary t = case sequenceA (nf NF $ App (fmap Free t) $ Var Bound) of+    Free _ -> True+    Bound  -> False++nfs :: Eq a => NF -> [Term a] -> [Term a]+nfs NF terms = map (nf NF) terms+nfs _  terms = terms++instantiatePat :: Eq a => [Pattern c] -> Scope b Term a -> [Term a] -> Maybe (Term a, [Term a])+instantiatePat [] (ScopeTerm term) terms = Just (term, terms)+instantiatePat (PatternVar  _ : pats) (Scope _ scope) (term:terms) = instantiatePat pats (instantiateScope term scope) terms+instantiatePat (PatternI con : pats) scope (term:terms) = case nf WHNF term of+    ICon i | i == con -> instantiatePat pats scope terms+    _ -> Nothing+instantiatePat (Pattern (PatternCon con _ _ _) pats1 : pats) scope (term:terms) = case nf WHNF term of+    Con i _ n _ terms1 | i == con -> instantiatePat (pats1 ++ pats) scope (terms1 ++ terms)+    _ -> Nothing+instantiatePat _ _ _ = Nothing++instantiateCases :: Eq a => [([Pattern c], Closed (Scope b Term))] -> [Term a] -> Maybe (Term a, [Term a])+instantiateCases clauses terms = msum $ map (\(pats, Closed scope) -> instantiatePat pats scope terms) clauses

@@ -0,0 +1,53 @@+module REPL+    ( repl+    ) where++import System.Console.Readline+import System.Exit+import System.IO+import Control.Monad+import Control.Monad.Trans+import Text.PrettyPrint++import Syntax.BNFC.ParGrammar+import Syntax.BNFC.ErrM+import Syntax.Term+import Syntax.PrettyPrinter+import Syntax.ErrorDoc+import TypeChecking.Monad+import TypeChecking.Expressions+import Normalization++parseExpr :: Monad m => String -> TCM m (Term String)+parseExpr s = case pExpr (myLexer s) of+    Bad err -> throwError [emsg err enull]+    Ok expr -> liftM fst (typeCheck expr Nothing)++ep :: NF -> String -> ScopeM IO ()+ep mode str = do+    mres <- runWarnT (parseExpr str)+    liftIO $ case mres of+        ([], Nothing)   -> return ()+        ([], Just term) -> putStrLn $ render $ ppTerm (nf mode term)+        (errs, _)       -> mapM_ (hPutStrLn stderr . erender) errs++processCmd :: String -> String -> ScopeM IO ()+processCmd "quit" _   = liftIO exitSuccess+processCmd "nf"   str = ep NF str+processCmd "hnf"  str = ep HNF str+processCmd "whnf" str = ep WHNF str+processCmd cmd _ = liftIO $ hPutStrLn stderr $ "Unknown command " ++ cmd++repl :: ScopeM IO ()+repl = go ""+  where+    go last = do+        mline <- liftIO $ readline "> "+        case mline of+            Nothing   -> liftIO $ putStrLn ""+            Just line -> case break (== ' ') line of+                ("",_)      -> go last+                (c:cmd,line') -> do+                    when (line /= last) $ liftIO (addHistory line)+                    if c == ':' then processCmd cmd line' else ep NF line+                    go line

@@ -0,0 +1,209 @@+-- -*- haskell -*-+-- This Alex file was machine-generated by the BNF converter+{+{-# OPTIONS -fno-warn-incomplete-patterns #-}+{-# OPTIONS_GHC -w #-}+module Syntax.BNFC.LexGrammar where++++import qualified Data.Bits+import Data.Word (Word8)+}+++$l = [a-zA-Z\192 - \255] # [\215 \247]    -- isolatin1 letter FIXME+$c = [A-Z\192-\221] # [\215]    -- capital isolatin1 letter FIXME+$s = [a-z\222-\255] # [\247]    -- small isolatin1 letter FIXME+$d = [0-9]                -- digit+$i = [$l $d _ ']          -- identifier character+$u = [\0-\255]          -- universal: any character++@rsyms =    -- symbols and non-identifier-like reserved words+   \: | \= | \{ | \} | \; | \) | \| | \- \> | \@++:-+"--" [.]* ; -- Toss single line comments+"{-" ([$u # \-] | \- [$u # \}])* ("-")+ "}" ; ++$white+ ;+@rsyms { tok (\p s -> PT p (eitherResIdent (TV . share) s)) }+T y p e $d * { tok (\p s -> PT p (eitherResIdent (T_U . share) s)) }+I { tok (\p s -> PT p (eitherResIdent (T_I . share) s)) }+l e f t { tok (\p s -> PT p (eitherResIdent (T_PLeft . share) s)) }+r i g h t { tok (\p s -> PT p (eitherResIdent (T_PRight . share) s)) }+P a t h { tok (\p s -> PT p (eitherResIdent (T_PPath . share) s)) }+p a t h { tok (\p s -> PT p (eitherResIdent (T_Ppath . share) s)) }+c o e { tok (\p s -> PT p (eitherResIdent (T_PCoe . share) s)) }+i s o { tok (\p s -> PT p (eitherResIdent (T_PIso . share) s)) }+s q u e e z e { tok (\p s -> PT p (eitherResIdent (T_PSqueeze . share) s)) }+\\ { tok (\p s -> PT p (eitherResIdent (T_PLam . share) s)) }+\( { tok (\p s -> PT p (eitherResIdent (T_PPar . share) s)) }+\_ { tok (\p s -> PT p (eitherResIdent (T_Pus . share) s)) }+$l ($l | $d | \' | \_ | \-)* { tok (\p s -> PT p (eitherResIdent (T_PIdent . share) s)) }++$l $i*   { tok (\p s -> PT p (eitherResIdent (TV . share) s)) }++++++{++tok f p s = f p s++share :: String -> String+share = id++data Tok =+   TS !String !Int    -- reserved words and symbols+ | TL !String         -- string literals+ | TI !String         -- integer literals+ | TV !String         -- identifiers+ | TD !String         -- double precision float literals+ | TC !String         -- character literals+ | T_U !String+ | T_I !String+ | T_PLeft !String+ | T_PRight !String+ | T_PPath !String+ | T_Ppath !String+ | T_PCoe !String+ | T_PIso !String+ | T_PSqueeze !String+ | T_PLam !String+ | T_PPar !String+ | T_Pus !String+ | T_PIdent !String++ deriving (Eq,Show,Ord)++data Token = +   PT  Posn Tok+ | Err Posn+  deriving (Eq,Show,Ord)++tokenPos (PT (Pn _ l _) _ :_) = "line " ++ show l+tokenPos (Err (Pn _ l _) :_) = "line " ++ show l+tokenPos _ = "end of file"++tokenPosn (PT p _) = p+tokenPosn (Err p) = p+tokenLineCol = posLineCol . tokenPosn+posLineCol (Pn _ l c) = (l,c)+mkPosToken t@(PT p _) = (posLineCol p, prToken t)++prToken t = case t of+  PT _ (TS s _) -> s+  PT _ (TL s)   -> s+  PT _ (TI s)   -> s+  PT _ (TV s)   -> s+  PT _ (TD s)   -> s+  PT _ (TC s)   -> s+  PT _ (T_U s) -> s+  PT _ (T_I s) -> s+  PT _ (T_PLeft s) -> s+  PT _ (T_PRight s) -> s+  PT _ (T_PPath s) -> s+  PT _ (T_Ppath s) -> s+  PT _ (T_PCoe s) -> s+  PT _ (T_PIso s) -> s+  PT _ (T_PSqueeze s) -> s+  PT _ (T_PLam s) -> s+  PT _ (T_PPar s) -> s+  PT _ (T_Pus s) -> s+  PT _ (T_PIdent s) -> s+++data BTree = N | B String Tok BTree BTree deriving (Show)++eitherResIdent :: (String -> Tok) -> String -> Tok+eitherResIdent tv s = treeFind resWords+  where+  treeFind N = tv s+  treeFind (B a t left right) | s < a  = treeFind left+                              | s > a  = treeFind right+                              | s == a = t++resWords = b "@" 6 (b ":" 3 (b "->" 2 (b ")" 1 N N) N) (b "=" 5 (b ";" 4 N N) N)) (b "{" 9 (b "with" 8 (b "data" 7 N N) N) (b "}" 11 (b "|" 10 N N) N))+   where b s n = let bs = id s+                  in B bs (TS bs n)++unescapeInitTail :: String -> String+unescapeInitTail = id . unesc . tail . id where+  unesc s = case s of+    '\\':c:cs | elem c ['\"', '\\', '\''] -> c : unesc cs+    '\\':'n':cs  -> '\n' : unesc cs+    '\\':'t':cs  -> '\t' : unesc cs+    '"':[]    -> []+    c:cs      -> c : unesc cs+    _         -> []++-------------------------------------------------------------------+-- Alex wrapper code.+-- A modified "posn" wrapper.+-------------------------------------------------------------------++data Posn = Pn !Int !Int !Int+      deriving (Eq, Show,Ord)++alexStartPos :: Posn+alexStartPos = Pn 0 1 1++alexMove :: Posn -> Char -> Posn+alexMove (Pn a l c) '\t' = Pn (a+1)  l     (((c+7) `div` 8)*8+1)+alexMove (Pn a l c) '\n' = Pn (a+1) (l+1)   1+alexMove (Pn a l c) _    = Pn (a+1)  l     (c+1)++type Byte = Word8++type AlexInput = (Posn,     -- current position,+                  Char,     -- previous char+                  [Byte],   -- pending bytes on the current char+                  String)   -- current input string++tokens :: String -> [Token]+tokens str = go (alexStartPos, '\n', [], str)+    where+      go :: AlexInput -> [Token]+      go inp@(pos, _, _, str) =+               case alexScan inp 0 of+                AlexEOF                   -> []+                AlexError (pos, _, _, _)  -> [Err pos]+                AlexSkip  inp' len        -> go inp'+                AlexToken inp' len act    -> act pos (take len str) : (go inp')++alexGetByte :: AlexInput -> Maybe (Byte,AlexInput)+alexGetByte (p, c, (b:bs), s) = Just (b, (p, c, bs, s))+alexGetByte (p, _, [], s) =+  case  s of+    []  -> Nothing+    (c:s) ->+             let p'     = alexMove p c+                 (b:bs) = utf8Encode c+              in p' `seq` Just (b, (p', c, bs, s))++alexInputPrevChar :: AlexInput -> Char+alexInputPrevChar (p, c, bs, s) = c++  -- | Encode a Haskell String to a list of Word8 values, in UTF8 format.+utf8Encode :: Char -> [Word8]+utf8Encode = map fromIntegral . go . ord+ where+  go oc+   | oc <= 0x7f       = [oc]++   | oc <= 0x7ff      = [ 0xc0 + (oc `Data.Bits.shiftR` 6)+                        , 0x80 + oc Data.Bits..&. 0x3f+                        ]++   | oc <= 0xffff     = [ 0xe0 + (oc `Data.Bits.shiftR` 12)+                        , 0x80 + ((oc `Data.Bits.shiftR` 6) Data.Bits..&. 0x3f)+                        , 0x80 + oc Data.Bits..&. 0x3f+                        ]+   | otherwise        = [ 0xf0 + (oc `Data.Bits.shiftR` 18)+                        , 0x80 + ((oc `Data.Bits.shiftR` 12) Data.Bits..&. 0x3f)+                        , 0x80 + ((oc `Data.Bits.shiftR` 6) Data.Bits..&. 0x3f)+                        , 0x80 + oc Data.Bits..&. 0x3f+                        ]+}

@@ -0,0 +1,215 @@+-- This Happy file was machine-generated by the BNF converter+{+{-# OPTIONS_GHC -fno-warn-incomplete-patterns -fno-warn-overlapping-patterns #-}+module Syntax.BNFC.ParGrammar where+import Syntax.BNFC.AbsGrammar+import Syntax.BNFC.LexGrammar+import Syntax.BNFC.ErrM++}++%name pDefs Defs+%name pExpr Expr++-- no lexer declaration+%monad { Err } { thenM } { returnM }+%tokentype { Token }++%token + ')' { PT _ (TS _ 1) }+ '->' { PT _ (TS _ 2) }+ ':' { PT _ (TS _ 3) }+ ';' { PT _ (TS _ 4) }+ '=' { PT _ (TS _ 5) }+ '@' { PT _ (TS _ 6) }+ 'data' { PT _ (TS _ 7) }+ 'with' { PT _ (TS _ 8) }+ '{' { PT _ (TS _ 9) }+ '|' { PT _ (TS _ 10) }+ '}' { PT _ (TS _ 11) }++L_U { PT _ (T_U _) }+L_I { PT _ (T_I _) }+L_PLeft { PT _ (T_PLeft _) }+L_PRight { PT _ (T_PRight _) }+L_PPath { PT _ (T_PPath _) }+L_Ppath { PT _ (T_Ppath _) }+L_PCoe { PT _ (T_PCoe _) }+L_PIso { PT _ (T_PIso _) }+L_PSqueeze { PT _ (T_PSqueeze _) }+L_PLam { PT _ (T_PLam _) }+L_PPar { PT _ (T_PPar _) }+L_Pus { PT _ (T_Pus _) }+L_PIdent { PT _ (T_PIdent _) }+L_err    { _ }+++%%++U    :: { U} : L_U { U (mkPosToken $1)}+I    :: { I} : L_I { I (mkPosToken $1)}+PLeft    :: { PLeft} : L_PLeft { PLeft (mkPosToken $1)}+PRight    :: { PRight} : L_PRight { PRight (mkPosToken $1)}+PPath    :: { PPath} : L_PPath { PPath (mkPosToken $1)}+Ppath    :: { Ppath} : L_Ppath { Ppath (mkPosToken $1)}+PCoe    :: { PCoe} : L_PCoe { PCoe (mkPosToken $1)}+PIso    :: { PIso} : L_PIso { PIso (mkPosToken $1)}+PSqueeze    :: { PSqueeze} : L_PSqueeze { PSqueeze (mkPosToken $1)}+PLam    :: { PLam} : L_PLam { PLam (mkPosToken $1)}+PPar    :: { PPar} : L_PPar { PPar (mkPosToken $1)}+Pus    :: { Pus} : L_Pus { Pus (mkPosToken $1)}+PIdent    :: { PIdent} : L_PIdent { PIdent (mkPosToken $1)}++Defs :: { Defs }+Defs : ListDef { Defs $1 } +++Def :: { Def }+Def : PIdent ':' Expr { DefType $1 $3 } +  | FunCase { DefFun $1 }+  | Pattern { DefFunEmpty $1 }+  | 'data' PIdent ListDataTele '=' ListCon { DefData $2 (reverse $3) $5 }+  | 'data' PIdent ListDataTele '=' ListCon 'with' '{' ListFunCase '}' { DefDataWith $2 (reverse $3) $5 $8 }+  | 'data' PIdent ListDataTele { DefDataEmpty $2 (reverse $3) }+++ListDef :: { [Def] }+ListDef : {- empty -} { [] } +  | Def { (:[]) $1 }+  | Def ';' ListDef { (:) $1 $3 }+++FunCase :: { FunCase }+FunCase : Pattern '=' Expr { FunCase $1 $3 } +++ListFunCase :: { [FunCase] }+ListFunCase : {- empty -} { [] } +  | FunCase { (:[]) $1 }+  | FunCase ';' ListFunCase { (:) $1 $3 }+++Pattern :: { Pattern }+Pattern : PIdent ListParPat { Pattern $1 (reverse $2) } +++ParPat :: { ParPat }+ParPat : Arg { ParVar $1 } +  | PLeft { ParLeft $1 }+  | PRight { ParRight $1 }+  | PPar ')' { ParEmpty $1 }+  | PPar Pattern ')' { ParPat $1 $2 }+++ListParPat :: { [ParPat] }+ListParPat : {- empty -} { [] } +  | ListParPat ParPat { flip (:) $1 $2 }+++Con :: { Con }+Con : PIdent ListConTele { Con $1 (reverse $2) } +++ListCon :: { [Con] }+ListCon : Con { (:[]) $1 } +  | Con '|' ListCon { (:) $1 $3 }+++ConTele :: { ConTele }+ConTele : PPar Expr ':' Expr ')' { VarTele $1 $2 $4 } +  | Expr5 { TypeTele $1 }+++ListConTele :: { [ConTele] }+ListConTele : {- empty -} { [] } +  | ListConTele ConTele { flip (:) $1 $2 }+++DataTele :: { DataTele }+DataTele : PPar Expr ':' Expr ')' { DataTele $1 $2 $4 } +++ListDataTele :: { [DataTele] }+ListDataTele : {- empty -} { [] } +  | ListDataTele DataTele { flip (:) $1 $2 }+++PiTele :: { PiTele }+PiTele : PPar Expr ':' Expr ')' { PiTele $1 $2 $4 } +++ListPiTele :: { [PiTele] }+ListPiTele : PiTele { (:[]) $1 } +  | PiTele ListPiTele { (:) $1 $2 }+++Expr :: { Expr }+Expr : PLam ListArg '->' Expr { Lam $1 $2 $4 } +  | Expr1 { $1 }+++Expr1 :: { Expr }+Expr1 : Expr2 '->' Expr1 { Arr $1 $3 } +  | ListPiTele '->' Expr1 { Pi $1 $3 }+  | Expr2 { $1 }+++Expr2 :: { Expr }+Expr2 : Expr3 '=' Expr3 { PathImp $1 $3 } +  | Expr3 { $1 }+++Expr3 :: { Expr }+Expr3 : Expr3 '@' Expr4 { At $1 $3 } +  | Expr4 { $1 }+++Expr4 :: { Expr }+Expr4 : Expr4 Expr5 { App $1 $2 } +  | Expr5 { $1 }+++Expr5 :: { Expr }+Expr5 : Arg { Var $1 } +  | U { Universe $1 }+  | I { Interval $1 }+  | PLeft { ELeft $1 }+  | PRight { ERight $1 }+  | PPath { Path $1 }+  | Ppath { PathCon $1 }+  | PCoe { Coe $1 }+  | PIso { Iso $1 }+  | PSqueeze { Squeeze $1 }+  | PPar Expr ')' { Paren $1 $2 }+++Arg :: { Arg }+Arg : PIdent { Arg $1 } +  | Pus { NoArg $1 }+++ListArg :: { [Arg] }+ListArg : Arg { (:[]) $1 } +  | Arg ListArg { (:) $1 $2 }++++{++returnM :: a -> Err a+returnM = return++thenM :: Err a -> (a -> Err b) -> Err b+thenM = (>>=)++happyError :: [Token] -> Err a+happyError ts =+  Bad $ "syntax error at " ++ tokenPos ts ++ +  case ts of+    [] -> []+    [Err _] -> " due to lexer error"+    _ -> " before " ++ unwords (map (id . prToken) (take 4 ts))++myLexer = tokens+}+

@@ -0,0 +1,93 @@+{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-}++module Syntax.ErrorDoc+    ( EMsg, EDoc+    , Pretty(..), Pretty1(..), epretty+    , enull, (<>), (<+>), ($$)+    , emsg, emsgL, emsgLC+    , erender, erenderWithFilename+    ) where++import qualified Text.PrettyPrint as P++data EMsg f = EMsg (Maybe Int) (Maybe Int) String (EDoc f)+data EDoc f = EDoc P.Doc | ENull | ETerm (f (EDoc f)) | EAbove (EDoc f) (EDoc f) | EBeside (EDoc f) Bool (EDoc f)++class Functor f => Pretty1 f where+    pretty1 :: f P.Doc -> P.Doc++instance Pretty1 f => Show (EDoc f) where+    show = P.render . edocToDoc++class Pretty a f where+    pretty :: a -> EDoc f++instance Pretty P.Doc f where+    pretty = EDoc++instance Pretty String f where+    pretty = etext++instance (Pretty a f, Pretty b f) => Pretty (Either a b) f where+    pretty (Left a)  = pretty a+    pretty (Right b) = pretty b++etext :: String -> EDoc f+etext "" = enull+etext s = EDoc (P.text s)++epretty :: f (EDoc f) -> EDoc f+epretty = ETerm++eprettyDoc :: Functor f => f P.Doc -> EDoc f+eprettyDoc = ETerm . fmap EDoc++eprettyStr :: Functor f => f String -> EDoc f+eprettyStr = ETerm . fmap etext++enull :: EDoc f+enull = ENull++infixl 6 <>, <+>+infixl 5 $$+(<>) :: EDoc f -> EDoc f -> EDoc f+d1 <> d2 = EBeside d1 False d2++(<+>) :: EDoc f -> EDoc f -> EDoc f+d1 <+> d2 = EBeside d1 True d2++($$) :: EDoc f -> EDoc f -> EDoc f+($$) = EAbove++emsg :: String -> EDoc f -> EMsg f+emsg = EMsg Nothing Nothing++emsgL :: Int -> String -> EDoc f -> EMsg f+emsgL l = EMsg (Just l) Nothing++emsgLC :: (Int,Int) -> String -> EDoc f -> EMsg f+emsgLC (l,c) = EMsg (Just l) (Just c)++erender :: Pretty1 f => EMsg f -> String+erender (EMsg l c s d) = P.render (msgToDoc Nothing l c s d)++erenderWithFilename :: Pretty1 f => String -> EMsg f -> String+erenderWithFilename fn (EMsg l c s d) = P.render (msgToDoc (Just fn) l c s d)++msgToDoc :: Pretty1 f => Maybe String -> Maybe Int -> Maybe Int -> String -> EDoc f -> P.Doc+msgToDoc Nothing l c "" d =+    maybe P.empty (\ln -> P.text $ show ln ++ ":") l P.<>+    maybe P.empty (\cn -> P.text $ show cn ++ ":") c P.<+>+    edocToDoc d+msgToDoc fn l c s d = P.hang (+    maybe P.empty (\s -> P.text $ s ++ ":") fn P.<>+    maybe P.empty (\ln -> P.text $ show ln ++ ":") l P.<>+    maybe P.empty (\cn -> P.text $ show cn ++ ":") c P.<+> P.text s) 4 (edocToDoc d)++edocToDoc :: Pretty1 f => EDoc f -> P.Doc+edocToDoc ENull = P.empty+edocToDoc (EDoc d) = d+edocToDoc (EBeside d1 False d2) = edocToDoc d1 P.<> edocToDoc d2+edocToDoc (EBeside d1 True d2) = edocToDoc d1 P.<+> edocToDoc d2+edocToDoc (EAbove d1 d2) = edocToDoc d1 P.$+$ edocToDoc d2+edocToDoc (ETerm e) = pretty1 (fmap edocToDoc e)

@@ -0,0 +1,43 @@+module Syntax.Expr+    ( module Syntax.BNFC.AbsGrammar+    , getPos, argGetPos, parPatGetPos+    , unArg+    ) where++import Syntax.BNFC.AbsGrammar++getPos :: Expr -> (Int,Int)+getPos (Lam (PLam (p,_)) _ _) = p+getPos (Arr e _) = getPos e+getPos (Pi [] e) = getPos e+getPos (Pi (PiTele (PPar (p,_)) _ _ : _) _) = p+getPos (App e _) = getPos e+getPos (Var (Arg (PIdent (p,_)))) = p+getPos (Var (NoArg (Pus (p,_)))) = p+getPos (Universe (U (p,_))) = p+getPos (Paren (PPar (p,_)) _) = p+getPos (PathImp e _) = getPos e+getPos (Interval (I (p,_))) = p+getPos (ELeft (PLeft (p,_))) = p+getPos (ERight (PRight (p,_))) = p+getPos (Path (PPath (p,_))) = p+getPos (PathCon (Ppath (p,_))) = p+getPos (At e _) = getPos e+getPos (Coe (PCoe (p,_))) = p+getPos (Iso (PIso (p,_))) = p+getPos (Squeeze (PSqueeze (p,_))) = p++argGetPos :: Arg -> (Int,Int)+argGetPos (Arg (PIdent (p,_))) = p+argGetPos (NoArg (Pus  (p,_))) = p++parPatGetPos :: ParPat -> (Int,Int)+parPatGetPos (ParVar arg) = argGetPos arg+parPatGetPos (ParEmpty (PPar (p,_))) = p+parPatGetPos (ParPat (PPar (p,_)) _) = p+parPatGetPos (ParLeft (PLeft (p,_))) = p+parPatGetPos (ParRight (PRight (p,_))) = p++unArg :: Arg -> String+unArg NoArg{} = "_"+unArg (Arg (PIdent (_,s))) = s

@@ -0,0 +1,81 @@+entrypoints Defs, Expr;++comment "--";+comment "{-" "-}";++layout "with";+layout toplevel;++Defs.         Defs  ::= [Def];+DefType.      Def   ::= PIdent ":" Expr;+DefFun.       Def   ::= FunCase;+DefFunEmpty.  Def   ::= Pattern;+DefData.      Def   ::= "data" PIdent [DataTele] "=" [Con];+DefDataWith.  Def   ::= "data" PIdent [DataTele] "=" [Con] "with" "{" [FunCase] "}";+DefDataEmpty. Def   ::= "data" PIdent [DataTele];+separator     Def   ";";++FunCase.   FunCase  ::= Pattern "=" Expr;+separator  FunCase  ";";++Pattern.   Pattern  ::= PIdent [ParPat];+ParVar.    ParPat   ::= Arg;+ParLeft.   ParPat   ::= PLeft;+ParRight.  ParPat   ::= PRight;+ParEmpty.  ParPat   ::= PPar ")";+ParPat.    ParPat   ::= PPar Pattern ")";+terminator ParPat   "";++Con.       Con      ::= PIdent [ConTele];+separator  nonempty Con "|";++VarTele.   ConTele  ::= PPar Expr ":" Expr ")";+TypeTele.  ConTele  ::= Expr5;+terminator ConTele  "";++DataTele.  DataTele ::= PPar Expr ":" Expr ")";+terminator DataTele "";++PiTele.    PiTele   ::= PPar Expr ":" Expr ")";+terminator nonempty PiTele "";++Lam.       Expr     ::= PLam [Arg] "->" Expr;+Arr.       Expr1    ::= Expr2 "->" Expr1;+Pi.        Expr1    ::= [PiTele] "->" Expr1;+PathImp.   Expr2    ::= Expr3 "=" Expr3;+At.        Expr3    ::= Expr3 "@" Expr4;+App.       Expr4    ::= Expr4 Expr5;+Var.       Expr5    ::= Arg;+Universe.  Expr5    ::= U;+Interval.  Expr5    ::= I;+ELeft.     Expr5    ::= PLeft;+ERight.    Expr5    ::= PRight;+Path.      Expr5    ::= PPath;+PathCon.   Expr5    ::= Ppath;+Coe.       Expr5    ::= PCoe;+Iso.       Expr5    ::= PIso;+Squeeze.   Expr5    ::= PSqueeze;+_.         Expr     ::= Expr1;+_.         Expr1    ::= Expr2;+_.         Expr2    ::= Expr3;+_.         Expr3    ::= Expr4;+_.         Expr4    ::= Expr5;+Paren.     Expr5    ::= PPar Expr ")";++Arg.       Arg      ::= PIdent;+NoArg.     Arg      ::= Pus;+separator  nonempty Arg "";++position token U ('T' 'y' 'p' 'e' digit*);+position token I 'I';+position token PLeft 'l' 'e' 'f' 't';+position token PRight 'r' 'i' 'g' 'h' 't';+position token PPath 'P' 'a' 't' 'h';+position token Ppath 'p' 'a' 't' 'h';+position token PCoe 'c' 'o' 'e';+position token PIso 'i' 's' 'o';+position token PSqueeze 's' 'q' 'u' 'e' 'e' 'z' 'e';+position token PLam '\\';+position token PPar '(';+position token Pus '_';+position token PIdent (letter(letter|digit|'\''|'_'|'-')*);

@@ -0,0 +1,14 @@+module Syntax.Pattern where++data ICon = ILeft | IRight deriving Eq+data PatternCon c = PatternCon Int Int String [([Pattern c], c)]+data Pattern c = Pattern (PatternCon c) [Pattern c] | PatternVar String | PatternI ICon++instance Eq (PatternCon c) where+    PatternCon i _ _ _ == PatternCon i' _ _ _ = i == i'++instance Eq (Pattern c) where+    PatternI c   == PatternI c'  = c == c'+    PatternVar _ == PatternVar _ = True+    Pattern c _  == Pattern c' _ = c == c'+    _            == _            = False

@@ -0,0 +1,97 @@+module Syntax.PrettyPrinter+    ( ppTerm+    , scopeToTerm+    ) where++import Text.PrettyPrint+import Data.Foldable++import Syntax.Term+import qualified Syntax.ErrorDoc as E++instance E.Pretty1 Term where+    pretty1 t = ppTermCtx (toList $ fmap render t) t++ppTerm :: Term String -> Doc+ppTerm t = ppTermCtx (toList t) (fmap text t)++ppTermCtx :: [String] -> Term Doc -> Doc+ppTermCtx _ (Var d) = d+ppTermCtx _ (Universe NoLevel) = text "Type"+ppTermCtx _ (Universe l) = text $ "Type" ++ show l+ppTermCtx ctx t@(App e1 e2) = ppTermPrec (prec t) ctx e1 <+> ppTermPrec (prec t + 1) ctx e2+ppTermCtx ctx t@(Pi (Type a _) b _) =+    let (vs, b') = ppScopePrec (prec t) ctx b+    in (if null vs then ppTermPrec (prec t + 1) ctx a else parens $ hsep vs <+> colon <+> ppTermCtx ctx a) <+> b'+ppTermCtx ctx t@Lam{} = go ctx [] t+  where+    go ctx vars (Lam (Scope1 n s)) =+        let (ctx', n') = renameName n ctx+        in go ctx' (text n' : vars) $ instantiate1 (Var $ text n') s+    go ctx vars t' = text "\\" <> hsep (reverse vars) <+> arrow <+> ppTermPrec (prec t) ctx t'+ppTermCtx ctx t@(Con _ _ n _ as) = text n <+> ppList ctx t as+ppTermCtx _ (FunSyn n _) = text n+ppTermCtx _ (FunCall _ n _) = text n+ppTermCtx ctx t@(DataType d _ as) = text d <+> ppList ctx t as+ppTermCtx _ Interval = text "I"+ppTermCtx _ (ICon ILeft) = text "left"+ppTermCtx _ (ICon IRight) = text "right"+ppTermCtx ctx t@(Path Implicit _ [e2,e3]) = ppTermPrec (prec t + 1) ctx e2 <+> equals <+> ppTermPrec (prec t + 1) ctx e3+ppTermCtx ctx t@(Path _ me es) = text "Path" <+> ppList ctx t (maybe (Var $ text "_") id me : es)+ppTermCtx ctx t@(PCon me) = text "path" <+> maybe empty (ppTermPrec (prec t + 1) ctx) me+ppTermCtx ctx t@(At _ _ e1 e2) = ppTermPrec (prec t) ctx e1 <+> text "@" <+> ppTermPrec (prec t + 1) ctx e2+ppTermCtx ctx t@(Coe es) = text "coe" <+> ppList ctx t es+ppTermCtx ctx t@(Iso es) = text "iso" <+> ppList ctx t es+ppTermCtx ctx t@(Squeeze es) = text "squeeze" <+> ppList ctx t es++ppList :: [String] -> Term Doc -> [Term Doc] -> Doc+ppList ctx t ts = hsep $ map (ppTermPrec (prec t + 1) ctx) ts++ppScopePrec :: Int -> [String] -> Scope String Term Doc -> ([Doc], Doc)+ppScopePrec p ctx t =+    let (vars, b, ctx', t') = scopeToTerm ctx text t+    in (map text vars, (if null vars || b then arrow else empty) <+> ppTermPrec p ctx' t')++scopeToTerm :: [String] -> (String -> a) -> Scope String Term a -> ([String], Bool, [String], Term a)+scopeToTerm ctx f (ScopeTerm t@(Pi _ ScopeTerm{} _)) = ([], False, ctx, t)+scopeToTerm ctx f (ScopeTerm t) = ([], True, ctx, t)+scopeToTerm ctx f (Scope v s) =+    let (ctx', v') = renameName v ctx+        (vs, b, ctx'', d) = scopeToTerm ctx' f $ instantiateScope (Var $ f v') s+    in  (v' : vs, b, ctx'', d)++ppTermPrec :: Int -> [String] -> Term Doc -> Doc+ppTermPrec p ctx t = if p > prec t then parens (ppTermCtx ctx t) else ppTermCtx ctx t++arrow :: Doc+arrow = text "->"++renameName :: String -> [String] -> ([String], String)+renameName var ctx = if var `Prelude.elem` ctx then renameName (var ++ "'") ctx else (var:ctx,var)++prec :: Term a                 -> Int+prec Var{}                      = 10+prec Universe{}                 = 10+prec FunSyn{}                   = 10+prec FunCall{}                  = 10+prec (Con _ _ _ _ [])           = 10+prec (DataType _ _ [])          = 10+prec (Path Explicit Nothing []) = 10+prec (PCon Nothing)             = 10+prec Interval                   = 10+prec ICon{}                     = 10+prec (Coe [])                   = 10+prec (Iso [])                   = 10+prec (Squeeze [])               = 10+prec App{}                      = 9+prec Con{}                      = 9+prec DataType{}                 = 9+prec (Path Explicit _ _)        = 9+prec PCon{}                     = 9+prec Coe{}                      = 9+prec Iso{}                      = 9+prec Squeeze{}                  = 9+prec At{}                       = 8+prec (Path Implicit _ _)        = 7+prec Pi{}                       = 6+prec Lam{}                      = 5

@@ -0,0 +1,105 @@+{-# LANGUAGE RankNTypes #-}++module Syntax.Scope where++import Prelude.Extras+import Control.Monad+import Control.Applicative+import Data.Maybe+import Data.Monoid+import Data.Foldable+import Data.Traversable++newtype Closed f = Closed (forall a. f a)++data Scoped a = Free a | Bound deriving Eq++instance Functor Scoped where+    fmap _ Bound    = Bound+    fmap f (Free a) = Free (f a)++instance Foldable Scoped where+    foldMap _ Bound    = mempty+    foldMap f (Free a) = f a++instance Traversable Scoped where+    traverse _ Bound    = pure Bound+    traverse f (Free a) = Free <$> f a++instance Applicative Scoped where+    pure              = Free+    Bound  <*> _      = Bound+    _      <*> Bound  = Bound+    Free f <*> Free a = Free (f a)++class MonadF t where+    (>>>=) :: Monad f => t f a -> (a -> f b) -> t f b++data Scope1 s f a = Scope1 s (f (Scoped a))++unScope1 :: Scope1 s f a -> f (Scoped a)+unScope1 (Scope1 _ t) = t++instance (Eq1 f, Eq a) => Eq (Scope1 s f a) where+    Scope1 _ t1 == Scope1 _ t2 = t1 ==# t2++instance Functor f => Functor (Scope1 s f) where+    fmap f (Scope1 s t) = Scope1 s $ fmap (fmap f) t++instance Foldable f => Foldable (Scope1 s f) where+    foldMap f (Scope1 _ t) = foldMap (foldMap f) t++instance Traversable f => Traversable (Scope1 s f) where+    traverse f (Scope1 s t) = Scope1 s <$> traverse (traverse f) t++instance MonadF (Scope1 s) where+    Scope1 s t >>>= k = Scope1 s $ t >>= \v -> case v of+        Bound  -> return Bound+        Free a -> liftM Free (k a)++instantiate1 :: Monad f => f a -> f (Scoped a) -> f a+instantiate1 s t = t >>= \v -> case v of+    Bound  -> s+    Free a -> return a++data Scope s f a = ScopeTerm (f a) | Scope s (Scope s f (Scoped a))++instance (Eq1 f, Eq a) => Eq (Scope s f a) where+    ScopeTerm t1 == ScopeTerm t2 = t1 ==# t2+    Scope _ t1 == Scope _ t2 = t1 == t2+    _ == _ = False++instance Functor f => Functor (Scope s f) where+    fmap f (ScopeTerm t) = ScopeTerm (fmap f t)+    fmap f (Scope s   t) = Scope s $ fmap (fmap f) t++instance Foldable f => Foldable (Scope s f) where+    foldMap f (ScopeTerm t) = foldMap f t+    foldMap f (Scope _   t) = foldMap (foldMap f) t++instance Traversable f => Traversable (Scope s f) where+    traverse f (ScopeTerm t) = ScopeTerm <$> traverse f t+    traverse f (Scope s   t) = Scope s   <$> traverse (traverse f) t++instance MonadF (Scope s) where+    ScopeTerm t >>>= k = ScopeTerm (t >>=  k)+    Scope s   t >>>= k = Scope s $ t >>>= \v -> case v of+        Bound  -> return Bound+        Free a -> liftM Free (k a)++instantiateScope :: Monad f => f a -> Scope s f (Scoped a) -> Scope s f a+instantiateScope t s = s >>>= \v -> case v of+    Bound  -> t+    Free a -> return a++instantiate :: Monad f => [f a] -> Scope s f a -> f a+instantiate t (ScopeTerm s) = s+instantiate [] _ = error "instantiate"+instantiate (t:ts) (Scope _ s) = instantiate ts (instantiateScope t s)++closed :: Traversable f => f a -> Closed f+closed t = Closed $ fromJust $ traverse (const Nothing) t++mapScope :: (s -> t) -> Scope s f a -> Scope t f a+mapScope _ (ScopeTerm t) = ScopeTerm t+mapScope f (Scope s t)   = Scope (f s) (mapScope f t)

@@ -0,0 +1,200 @@+module Syntax.Term+    ( Term(..), Type(..)+    , Level(..), level+    , Explicit(..), PatternC+    , module Syntax.Scope, module Syntax.Pattern+    , POrd(..), lessOrEqual+    , apps, collect, dropOnePi+    ) where++import Prelude.Extras+import Data.Function+import Data.Traversable hiding (mapM)+import Data.Foldable hiding (msum)+import Control.Applicative+import Control.Monad++import Syntax.Scope+import Syntax.Pattern++data Level = Level Int | NoLevel++instance Eq Level where+    (==) = (==) `on` level++instance Ord Level where+    compare = compare `on` level++instance Show Level where+    show = show . level++instance Enum Level where+    toEnum 0 = NoLevel+    toEnum n = Level n+    fromEnum = level++level :: Level -> Int+level (Level l) = l+level NoLevel = 0++data Term a+    = Var a+    | App (Term a) (Term a)+    | Lam (Scope1 String Term a)+    | Pi (Type a) (Scope String Term a) Level+    | Con Int (Int,Int) String [([PatternC], Closed (Scope String Term))] [Term a]+    | FunCall (Int,Int) String [([PatternC], Closed (Scope String Term))]+    | FunSyn String (Term a)+    | Universe Level+    | DataType String Int [Term a]+    | Interval+    | ICon ICon+    | Path Explicit (Maybe (Term a)) [Term a]+    | PCon (Maybe (Term a))+    | At (Term a) (Term a) (Term a) (Term a)+    | Coe [Term a]+    | Iso [Term a]+    | Squeeze [Term a]+data Type a = Type (Term a) Level+data Explicit = Explicit | Implicit+type PatternC = Pattern (Closed (Scope String Term))++instance Eq a => Eq (Term a) where+    e1 == e2 = go e1 [] e2 []+      where+        go :: Eq a => Term a -> [Term a] -> Term a -> [Term a] -> Bool+        go (Var a) es (Var a') es' = a == a' && es == es'+        go (App a b) es e2 es' = go a (b:es) e2 es'+        go e1 es (App a b) es' = go e1 es a (b:es')+        go (Lam s) es (Lam s') es' = s == s' && es == es'+        go (Lam (Scope1 _ s)) es t es' =+            let (l1,l2) = splitAt (length es' - length es) es'+            in l2 == es && go s [] (fmap Free t) (map (fmap Free) l1 ++ [Var Bound])+        go t es t'@Lam{} es' = go t' es' t es+        go e1@Pi{} es e2@Pi{} es' = pcompare e1 e2 == Just EQ && es == es'+        go (Con c _ _ _ as) es (Con c' _ _ _ as') es' = c == c' && as ++ es == as' ++ es'+        go (FunCall _ n _) es (FunCall _ n' _) es' = n == n' && es == es'+        go (FunSyn n _) es (FunSyn n' _) es' = n == n' && es == es'+        go (Universe u) es (Universe u') es' = u == u' && es == es'+        go (DataType d _ as) es (DataType d' _ as') es' = d == d' && as ++ es == as' ++ es'+        go Interval es Interval es' = es == es'+        go (ICon c) es (ICon c') es' = c == c' && es == es'+        go (Path Explicit a as) es (Path Explicit a' as') es' = a == a' && as ++ es == as' ++ es'+        go (Path _ _ as) es (Path _ _ as') es' = as ++ es == as' ++ es'+        go (PCon f) es (PCon f') es' = maybe [] return f ++ es == maybe [] return f' ++ es'+        go (PCon e) es e' es' = case maybe [] return e ++ es of+            e1:es1 -> e1 == Lam (Scope1 "" $ At (error "") (error "") (fmap Free e') $ Var Bound) && es1 == es'+            _ -> False+        go e es e'@PCon{} es' = go e' es' e es+        go (At _ _ a b) es (At _ _ a' b') es' = a == a' && b == b' && es == es'+        go (Coe as) es (Coe as') es' = as ++ es == as' ++ es'+        go (Iso as) es (Iso as') es' = as ++ es == as' ++ es'+        go (Squeeze as) es (Squeeze as') es' = as ++ es == as' ++ es'+        go _ _ _ _ = False++instance Eq a => Eq (Type a) where+    Type t _ == Type t' _ = t == t'++instance Eq1 Term where (==#) = (==)++class POrd a where+    pcompare :: a -> a -> Maybe Ordering++instance Eq a => POrd (Term a) where+    pcompare (Pi a (ScopeTerm b) _) (Pi a' b'@Scope{} lvl') =+        contraCovariant (pcompare a a') $ pcompare (fmap Free b) (unScope1 $ dropOnePi a' b' lvl')+    pcompare (Pi a b@Scope{} lvl) (Pi a' (ScopeTerm b') _) =+        contraCovariant (pcompare a a') $ pcompare (unScope1 $ dropOnePi a b lvl) (fmap Free b')+    pcompare (Pi a b lvl) (Pi a' b' lvl') = contraCovariant (pcompare a a') $ pcompareScopes a b lvl a' b' lvl'+      where+        pcompareScopes :: Eq a => Type a -> Scope String Term a -> Level -> Type a -> Scope String Term a -> Level -> Maybe Ordering+        pcompareScopes _ (ScopeTerm b) _   _  (ScopeTerm b') _    = pcompare b b'+        pcompareScopes _ (ScopeTerm b) _   a'            b'  lvl' = pcompare b (Pi a' b' lvl')+        pcompareScopes a            b  lvl _  (ScopeTerm b') _    = pcompare (Pi a b lvl) b'+        pcompareScopes a (Scope _   b) lvl a' (Scope _   b') lvl' = pcompareScopes (fmap Free a) b lvl (fmap Free a') b' lvl'+    pcompare (Universe u) (Universe u') = Just $ compare (level u) (level u')+    pcompare e1 e2 = if e1 == e2 then Just EQ else Nothing++instance Eq a => POrd (Type a) where+    pcompare (Type t _) (Type t' _) = pcompare t t'++contraCovariant :: Maybe Ordering -> Maybe Ordering -> Maybe Ordering+contraCovariant (Just LT) (Just r) | r == EQ || r == GT = Just GT+contraCovariant (Just EQ) r                             = r+contraCovariant (Just GT) (Just r) | r == LT || r == EQ = Just LT+contraCovariant _ _                                     = Nothing++lessOrEqual :: POrd a => a -> a -> Bool+lessOrEqual a b = case pcompare a b of+    Just r | r == EQ || r == LT -> True+    _                           -> False++instance Functor  Term where fmap    = fmapDefault+instance Foldable Term where foldMap = foldMapDefault++instance Functor  Type where+    fmap f (Type t l) = Type (fmap f t) l++instance Applicative Term where+    pure  = Var+    (<*>) = ap++instance Traversable Term where+    traverse f (Var a)            = Var            <$> f a+    traverse f (App e1 e2)        = App            <$> traverse f e1 <*> traverse f e2+    traverse f (Lam s)            = Lam            <$> traverse f s+    traverse f (At e1 e2 e3 e4)   = At             <$> traverse f e1 <*> traverse f e2 <*> traverse f e3 <*> traverse f e4+    traverse f (Pi (Type e1 lvl1) e2 lvl2) = (\e1' e2' -> Pi (Type e1' lvl1) e2' lvl2) <$> traverse f e1 <*> traverse f e2+    traverse f (Path h me es)     = Path h         <$> traverse (traverse f) me <*> traverse (traverse f) es+    traverse f (PCon e)           = PCon           <$> traverse (traverse f) e+    traverse f (Con c lc n cs as) = Con c lc n cs  <$> traverse (traverse f) as+    traverse f (Coe as)           = Coe            <$> traverse (traverse f) as+    traverse f (Iso as)           = Iso            <$> traverse (traverse f) as+    traverse f (Squeeze as)       = Squeeze        <$> traverse (traverse f) as+    traverse f (FunSyn n e)       = FunSyn n       <$> traverse f e+    traverse f (DataType d e as)  = DataType d e   <$> traverse (traverse f) as+    traverse _ (FunCall lc n cs)  = pure (FunCall lc n cs)+    traverse _ (Universe l)       = pure (Universe l)+    traverse _ Interval           = pure Interval+    traverse _ (ICon c)           = pure (ICon c)++instance Monad Term where+    return                          = Var+    Var a                     >>= k = k a+    App e1 e2                 >>= k = App (e1 >>= k) (e2 >>= k)+    Lam e                     >>= k = Lam (e >>>= k)+    Pi (Type e1 lvl1) e2 lvl2 >>= k = Pi (Type (e1 >>= k) lvl1) (e2 >>>= k) lvl2+    Con c lc n cs as          >>= k = Con c lc n cs (map (>>= k) as)+    FunCall lc n cs           >>= k = FunCall lc n cs+    FunSyn n e                >>= k = FunSyn n (e >>= k)+    Universe l                >>= _ = Universe l+    DataType d e as           >>= k = DataType d e $ map (>>= k) as+    Interval                  >>= _ = Interval+    ICon c                    >>= _ = ICon c+    Path h me1 es             >>= k = Path h (fmap (>>= k) me1) $ map (>>= k) es+    PCon e                    >>= k = PCon $ fmap (>>= k) e+    At e1 e2 e3 e4            >>= k = At (e1 >>= k) (e2 >>= k) (e3 >>= k) (e4 >>= k)+    Coe es                    >>= k = Coe $ map (>>= k) es+    Iso es                    >>= k = Iso $ map (>>= k) es+    Squeeze es                >>= k = Squeeze $ map (>>= k) es++apps :: Term a -> [Term a] -> Term a+apps e [] = e+apps e1 (e2:es) = apps (App e1 e2) es++collect :: Term a -> Term a+collect term = go term []+  where+    go (App e1 e2) ts = go e1 (e2:ts)+    go (Con a b c d es) ts = Con a b c d (es ++ ts)+    go (DataType a b es) ts = DataType a b (es ++ ts)+    go (Path a b es) ts = Path a b (es ++ ts)+    go (Coe es) ts = Coe (es ++ ts)+    go (Iso es) ts = Iso (es ++ ts)+    go (Squeeze es) ts = Squeeze (es ++ ts)+    go _ _ = term++dropOnePi :: Type a -> Scope String Term a -> Level -> Scope1 String Term a+dropOnePi _ (ScopeTerm b) _ = Scope1 "_" (fmap Free b)+dropOnePi _ (Scope s (ScopeTerm b)) _ = Scope1 s b+dropOnePi a (Scope s b) lvl = Scope1 s $ Pi (fmap Free a) b lvl

@@ -0,0 +1,42 @@+{-# LANGUAGE GADTs #-}++module TypeChecking.Context where++import Control.Monad++import Syntax.Scope++data Ctx s f b a where+    Nil  :: Ctx s f b b+    Snoc :: Ctx s f b a -> s -> f a -> Ctx s f b (Scoped a)++(+++) :: Ctx s f a b -> Ctx s f b c -> Ctx s f a c+ctx +++ Nil = ctx+ctx +++ Snoc ctx' s t = Snoc (ctx +++ ctx') s t++lengthCtx :: Ctx s f b a -> Int+lengthCtx Nil = 0+lengthCtx (Snoc ctx _ _) = lengthCtx ctx + 1++lookupCtx :: (Monad g, Functor f, Eq s) => s -> Ctx s f b a -> Maybe (g a, f a)+lookupCtx _ Nil = Nothing+lookupCtx s (Snoc ctx s' t) = if s == s'+    then Just (return Bound, fmap Free t)+    else fmap (\(te, ty) -> (liftM Free te, fmap Free ty)) (lookupCtx s ctx)++close :: Monad f => Ctx b g b a -> f a -> f b+close Nil            t = t+close (Snoc ctx s _) t = close ctx $ t >>= \v -> return $ case v of+    Bound  -> liftBase ctx s+    Free a -> a++liftBase :: Ctx s f b a -> b -> a+liftBase Nil = id+liftBase (Snoc ctx _ _) = Free . liftBase ctx++abstractTermInCtx :: Ctx s g b a -> f a -> Scope s f b+abstractTermInCtx ctx term = go ctx (ScopeTerm term)+  where+    go :: Ctx s g b a -> Scope s f a -> Scope s f b+    go Nil t = t+    go (Snoc ctx s _) t = go ctx (Scope s t)

@@ -0,0 +1,62 @@+module TypeChecking.Definitions+    ( typeCheckDefs+    ) where++import Control.Monad+import Control.Monad.Error++import Syntax.Expr as E+import Syntax.Term as T+import Syntax.ErrorDoc+import TypeChecking.Expressions+import TypeChecking.Definitions.DataTypes+import TypeChecking.Definitions.Functions+import TypeChecking.Monad++type Tele = [([Arg], Expr)]++typeCheckDefs :: MonadFix m => [Def] -> TCM m ()+typeCheckDefs [] = return ()+typeCheckDefs (DefType p@(PIdent (lc,name)) ty : defs) =+    case span (theSameAs name) defs of+        ([],_) -> do+            warn [emsgLC lc ("Missing a realization of function " ++ show name) enull]+            typeCheckDefs defs+        (defs1,defs2) -> do+            typeCheckFunction p ty (map defToPDef defs1)+            typeCheckDefs defs2+  where+    defToPDef :: Def -> ((Int, Int), [ParPat], Maybe Expr)+    defToPDef (DefFun (FunCase (E.Pattern (PIdent (lc,_)) pats) expr)) = (lc, pats, Just expr)+    defToPDef (DefFunEmpty (E.Pattern (PIdent (lc,_)) pats))           = (lc, pats, Nothing)+    defToPDef _                                                        = error "defToPDef"+typeCheckDefs (DefFun (FunCase (E.Pattern p@(PIdent (_,name)) []) expr) : defs) = do+    (term, ty) <- typeCheck expr Nothing+    addFunctionCheck p (FunSyn name term) ty+    typeCheckDefs defs+typeCheckDefs (DefFun (FunCase (E.Pattern (PIdent (lc,name)) _) _) : defs) = do+    warn [inferErrorMsg lc "the argument"]+    typeCheckDefs $ dropWhile (theSameAs name) defs+typeCheckDefs (DefFunEmpty (E.Pattern (PIdent (lc,name)) []) : defs) = do+    warn [emsgLC lc "Expected right hand side" enull]+    typeCheckDefs $ dropWhile (theSameAs name) defs+typeCheckDefs (DefFunEmpty (E.Pattern (PIdent (lc,name)) _) : defs) = do+    warn [inferErrorMsg lc "the argument"]+    typeCheckDefs $ dropWhile (theSameAs name) defs+typeCheckDefs (DefDataEmpty p teles : defs) = typeCheckDefs (DefDataWith p teles [] [] : defs)+typeCheckDefs (DefData p teles cons : defs) = typeCheckDefs (DefDataWith p teles cons [] : defs)+typeCheckDefs (DefDataWith p teles cons conds : defs) = do+    dataTeles <- forM teles $ \(DataTele _ e1 e2) -> liftM (\vs -> (vs, e2)) (exprToVars e1)+    conTeles  <- forM cons $ \(E.Con p teles) -> do+        teles' <- forM teles $ \tele ->+            case tele of+                VarTele _ e1 e2 -> liftM (\vs -> (vs, e2)) (exprToVars e1)+                TypeTele e2     -> return ([], e2)+        return (p, teles')+    typeCheckDataType p dataTeles conTeles $ map (\(FunCase pat expr) -> (pat, expr)) conds+    typeCheckDefs defs++theSameAs :: String -> Def -> Bool+theSameAs name (DefFun (FunCase (E.Pattern (PIdent (_,name')) _) _)) = name == name'+theSameAs name (DefFunEmpty (E.Pattern (PIdent (_,name')) _)) = name == name'+theSameAs _ _ = False

@@ -0,0 +1,140 @@+{-# LANGUAGE GADTs, ExistentialQuantification #-}++module TypeChecking.Definitions.Conditions+    ( checkConditions+    ) where++import Control.Monad+import Control.Monad.State+import Data.Maybe++import Syntax.Term+import Syntax.ErrorDoc+import Syntax.PrettyPrinter+import TypeChecking.Context+import Normalization++checkConditions :: (Int,Int) -> Closed Term -> [([PatternC], Closed (Scope String Term))] -> [EMsg Term]+checkConditions lc func cs =+    maybeToList $ msum $ map (\(p, scope) -> fmap (uncurry msg) $ checkPatterns func (map fst cs) p scope) cs+  where+    msg :: Scope String Term String -> Scope String Term String -> EMsg Term+    msg t1 t2 = emsgLC lc "Conditions check failed:" $+        scopeToEDoc t1 <+> pretty "is not equal to" <+> scopeToEDoc t2+    +    scopeToEDoc :: Scope String Term String -> EDoc Term+    scopeToEDoc t = epretty $ fmap pretty $ let (_,_,_,t') = scopeToTerm [] id t in t'++data TermInCtx  f b = forall a. TermInCtx  (Ctx String f b a) (f a)+data TermsInCtx f b = forall a. TermsInCtx (Ctx String f b a) [f a]+data TermsInCtx2 f b = forall a. TermsInCtx2 (Ctx String f b a) [f a] [f a]++checkPatterns :: Closed Term -> [[PatternC]] -> [PatternC] -> Closed (Scope String Term)+    -> Maybe (Scope String Term String, Scope String Term String)+checkPatterns (Closed func) cs pats (Closed scope) =+    listToMaybe $ findSuspiciousPairs cs pats >>= \(TermsInCtx2 ctx terms terms') ->+        let nscope1 = nfAppsScope $ abstractTermInCtx ctx (apps func terms)+            nscope2 = abstractTermInCtx ctx (instantiate terms' scope)+        in if nfScope nscope1 == nfScope nscope2 then [] else [(nscope1,nscope2)]+  where+    nfApps :: Eq a => Term a -> Term a+    nfApps (App a b) = App (nfApps a) (nf WHNF b)+    nfApps (Con i lc name conds terms) = Con i lc name conds $ map (nf WHNF) terms+    nfApps t = t+    +    nfAppsScope :: Eq a => Scope String Term a -> Scope String Term a+    nfAppsScope (ScopeTerm t) = ScopeTerm (nfApps t)+    nfAppsScope (Scope v t) = Scope v (nfAppsScope t)++findSuspiciousPairs :: [[PatternC]] -> [PatternC] -> [TermsInCtx2 Term b]+findSuspiciousPairs _ [] = []+findSuspiciousPairs cs (pat@(PatternI con) : pats) = map ext $ findSuspiciousPairs (mapTail pat cs) pats+  where ext (TermsInCtx2 ctx terms1 terms2) = (TermsInCtx2 ctx (ICon con : terms1) terms2)+findSuspiciousPairs cs (pat@(PatternVar var) : pats) =+    check ILeft ++ check IRight ++ map ext (findSuspiciousPairs (mapTail pat cs) pats)+  where+    ext (TermsInCtx2 ctx terms1 terms2) = TermsInCtx2 (Snoc ctx var $ error "") (Var Bound : map (fmap Free) terms1)+                                                                                (Var Bound : map (fmap Free) terms2)+    check con = if null $ filter (\p -> p == PatternI con) (mapHead cs)+        then []+        else case patternsToTerms pats of+            TermsInCtx ctx terms -> [TermsInCtx2 ctx (ICon con : terms) (ICon con : ctxToVars ctx)]+findSuspiciousPairs cs (pat@(Pattern con@(PatternCon i _ name conds) args) : pats) =+    (conds >>= \(cond,_) -> case unifyPatternLists args cond of+        Nothing -> []+        Just args' -> [ext0 args $ patternsToTerms args']) +++    map ext1 (findSuspiciousPairs cs' args) ++ case patternsToTerms args of+        TermsInCtx ctx terms -> map (ext2 ctx terms) (findSuspiciousPairs (mapTail pat cs) pats)+  where+    cs' = cs >>= \as -> case as of+            Pattern con' args' : _ | con == con' -> [args']+            _ -> []+    +    ext0 :: [PatternC] -> TermsInCtx Term b -> TermsInCtx2 Term b+    ext0 args (TermsInCtx ctx terms) = case patternsToTerms pats of+        TermsInCtx ctx' terms' -> TermsInCtx2 (ctx +++ ctx')+            (fmap (liftBase ctx') (Con i (0,0) name conds $ substPatterns args terms) : terms')+            (map (fmap $ liftBase ctx') terms ++ ctxToVars ctx')+    +    ext1 :: TermsInCtx2 Term b -> TermsInCtx2 Term b+    ext1 (TermsInCtx2 ctx terms1 terms2) = case patternsToTerms pats of+        TermsInCtx ctx' terms' -> TermsInCtx2 (ctx +++ ctx') (fmap (liftBase ctx') (Con i (0,0) name conds terms1) : terms')+                                                             (map (fmap $ liftBase ctx') terms2 ++ ctxToVars ctx')+    +    ext2 :: Ctx String Term a b -> [Term b] -> TermsInCtx2 Term b -> TermsInCtx2 Term a+    ext2 ctx terms (TermsInCtx2 ctx' terms1 terms2) =+        TermsInCtx2 (ctx +++ ctx') (fmap (liftBase ctx') (Con i (0,0) name conds terms) : terms1)+                                   (map (fmap $ liftBase ctx') (ctxToVars ctx) ++ terms2)++unifyPatterns :: PatternC -> PatternC -> Maybe [PatternC]+unifyPatterns (PatternI con) (PatternI con') | con == con' = Just []+unifyPatterns (PatternVar _) p = Just [p]+unifyPatterns p (PatternVar _) = Just (varList p)+unifyPatterns (Pattern con pats) (Pattern con' pats') | con == con' = unifyPatternLists pats pats'+unifyPatterns _ _ = Nothing++unifyPatternLists :: [PatternC] -> [PatternC] -> Maybe [PatternC]+unifyPatternLists pats pats' = fmap concat $ sequence (zipWith unifyPatterns pats pats')++varList :: Pattern c -> [Pattern c]+varList (PatternI _) = []+varList pat@(PatternVar _) = [pat]+varList (Pattern _ pats) = pats >>= varList++substPatterns :: [PatternC] -> [Term a] -> [Term a]+substPatterns pats terms = evalState (mapM substPattern pats) terms+  where+    substPattern :: PatternC -> State [Term a] (Term a)+    substPattern (PatternI con) = return (ICon con)+    substPattern (PatternVar _) = do+        term:terms <- get+        put terms+        return term+    substPattern (Pattern (PatternCon i _ name conds) pats) = do+        terms <- mapM substPattern pats+        return (Con i (0,0) name conds terms)++patternToTerm :: PatternC -> TermInCtx Term a+patternToTerm (PatternI con) = TermInCtx Nil (ICon con)+patternToTerm (PatternVar var) = TermInCtx (Snoc Nil var $ error "") (Var Bound)+patternToTerm (Pattern (PatternCon i _ name conds) pats) = case patternsToTerms pats of+    TermsInCtx ctx' terms -> TermInCtx ctx' $ Con i (0,0) name conds terms++patternsToTerms :: [PatternC] -> TermsInCtx Term a+patternsToTerms [] = TermsInCtx Nil []+patternsToTerms (pat:pats) = case patternToTerm pat of+    TermInCtx ctx' term -> case patternsToTerms pats of+        TermsInCtx ctx'' terms -> TermsInCtx (ctx' +++ ctx'') $ fmap (liftBase ctx'') term : terms++ctxToVars :: Ctx s f b a -> [Term a]+ctxToVars = reverse . go+  where+    go :: Ctx s f b a -> [Term a]+    go Nil = []+    go (Snoc ctx _ _) = Var Bound : map (fmap Free) (go ctx)++mapHead :: [[a]] -> [a]+mapHead cs = cs >>= \as -> if null as then [] else [head as]++mapTail :: Eq a => a -> [[a]] -> [[a]]+mapTail a cs = cs >>= \as -> if null as || not (head as == a) then [] else [tail as]

@@ -0,0 +1,89 @@+module TypeChecking.Definitions.Coverage+    ( checkCoverage+    ) where++import Data.List++import Syntax.Pattern++data PatternType c = Interval | DataType Int [(Int, [Pattern c])] | Unknown++data OK = OK | Incomplete deriving Eq+data Result = Result OK [Int]++checkCoverage :: [((Int,Int),[Pattern c])] -> Maybe [(Int,Int)]+checkCoverage []      = Just []+checkCoverage clauses = case checkClauses (map snd clauses) of+    Result Incomplete _ -> Nothing+    Result OK used -> Just $ map (\i -> fst $ clauses !! i) $ [0 .. length clauses - 1] \\ used++checkClauses :: [[Pattern c]] -> Result+checkClauses [] = Result Incomplete []+checkClauses clauses =+    let (t, clauses', b) = checkNull 0 Unknown clauses in+    case (b, checkNonEmptyClauses t clauses') of+        (Just i, Result Incomplete u) -> Result OK (i:u)+        (_, r) -> r++checkNull :: Int -> PatternType c -> [[Pattern c]] -> (PatternType c, [(Pattern c, [Pattern c])], Maybe Int)+checkNull _ t [] = (t, [], Nothing)+checkNull i t ([] : cs) = (t, [], Just i)+checkNull i t ((pat:pats) : cs) =+    let (t1, cs', b) = checkNull (i + 1) t cs+        t2 = case pat of+                PatternI _                     -> Interval+                PatternVar _                   -> t1+                Pattern (PatternCon _ n _ _) _ ->+                    let heads = pat : concatMap (\c -> if null c then [] else [head c]) cs+                    in DataType n $ heads >>= \p -> case p of+                        Pattern (PatternCon i _ _ conds) _ -> map (\(cond,_) -> (i,cond)) conds+                        _ -> []+    in (t2, (pat, pats) : cs', b)++checkNonEmptyClauses :: PatternType c -> [(Pattern c, [Pattern c])] -> Result+checkNonEmptyClauses _ [] = Result Incomplete []+checkNonEmptyClauses Interval           clauses = checkIntervalClauses clauses+checkNonEmptyClauses (DataType n conds) clauses = checkDataTypeClauses n conds clauses+checkNonEmptyClauses Unknown            clauses = checkClauses (map snd clauses)++checkIntervalClauses :: [(Pattern c, [Pattern c])] -> Result+checkIntervalClauses clauses =+    let get con = map (\(i,(_,ps)) -> (i,ps)) $ filterWithIndex (\(c,_) -> c == con) clauses+        lefts   = get (PatternI ILeft)+        rights  = get (PatternI IRight)+        vars    = get (PatternVar "")+        Result _  is0 = checkClauses (map snd lefts)+        Result _  is1 = checkClauses (map snd rights)+        Result ok is2 = checkClauses (map snd vars)+    in  Result ok $ getIndices lefts is0 ++ getIndices rights is1 ++ getIndices vars is2++checkDataTypeClauses :: Int -> [(Int, [Pattern c])] -> [(Pattern c, [Pattern c])] -> Result+checkDataTypeClauses n conds clauses = getResults $ flip map [0 .. n-1] $ \j ->+    let getLength [] = 0+        getLength (Pattern (PatternCon i _ _ _) args : _) | i == j = length args+        getLength (_ : pats) = getLength pats+        len = getLength (map fst clauses)+        +        getPatterns (Pattern _ pats) = pats+        getPatterns _                = replicate len (PatternVar "_")+    in map (\(i,(p,ps)) -> (i, getPatterns p ++ ps))+           (filterWithIndex (\(c,_) -> c == Pattern (PatternCon j n "" []) [] || c == PatternVar "") clauses)+       ++ (conds >>= \(c,ps) -> if j == c then [(-1, ps)] else [])+  where+    getResults :: [[(Int, [Pattern c])]] -> Result+    getResults [] = Result OK []+    getResults (con:cons) =+        let Result ok1 is1 = checkClauses (map snd con)+            Result ok2 is2 = getResults cons+        in Result (if ok1 == OK && ok2 == OK then OK else Incomplete) (getIndices con is1 ++ is2)++getIndices :: [(Int,b)] -> [Int] -> [Int]+getIndices list = filter (>= 0) . map (\i -> fst $ list !! i)++filterWithIndex :: (a -> Bool) -> [a] -> [(Int,a)]+filterWithIndex p = go 0+  where+    go _ [] = []+    go i (x:xs) =+        let rs = go (i + 1) xs+        in if p x then (i,x):rs else rs

@@ -0,0 +1,115 @@+{-# LANGUAGE RecursiveDo #-}++module TypeChecking.Definitions.DataTypes+    ( typeCheckDataType+    ) where++import Control.Monad+import Control.Monad.Fix+import Data.List++import Syntax.Expr as E+import Syntax.Term as T+import Syntax.ErrorDoc+import TypeChecking.Monad+import TypeChecking.Context+import TypeChecking.Expressions+import TypeChecking.Definitions.Patterns+import TypeChecking.Definitions.Conditions+import TypeChecking.Definitions.Termination+import Normalization++type Tele = [([Arg], Expr)]++typeCheckDataType :: MonadFix m => PIdent -> Tele -> [(PIdent,Tele)] -> [(E.Pattern, Expr)] -> TCM m ()+typeCheckDataType p@(PIdent (lc,dt)) params cons conds = mdo+    let lcons = length cons+    (SomeEq ctx, dataType@(Type dtTerm _)) <- checkTele Nil params $ Closed (T.Universe NoLevel)+    addDataTypeCheck p dataType lcons+    cons' <- forW (zip cons [0..]) $ \((con@(PIdent (lc,conName)),tele),i) -> do+        (_, Type conType conLevel) <- checkTele ctx tele $ Closed $ DataType dt lcons []+        checkPositivity p (nf WHNF conType)+        let conTerm = T.Con i lc conName (map snd $ filter (\(c,_) -> c == conName) conds') []+        return $ Just (con, conTerm, Type conType conLevel)+    forM_ cons' $ \(con, te, Type ty lvl) ->+        addConstructorCheck con dt lcons (abstractTermInCtx ctx te) (abstractTermInCtx ctx ty) lvl+    conds' <- forW conds $ \(E.Pattern (E.PIdent (lc,con)) pats,expr) ->+        case find (\(PIdent (_,c),_,_) -> c == con) cons' of+            Nothing -> do+                warn [notInScope lc "data constructor" con]+                return Nothing+            Just (_, _, ty) -> do+                (bf, TermsInCtx ctx' _ ty', rtpats) <- typeCheckPatterns ctx (nfType WHNF ty) pats+                when bf $ warn [emsgLC lc "Absurd patterns are not allowed in conditions" enull]+                (term, _) <- typeCheckCtx (ctx +++ ctx') expr (Just ty')+                let scope = closed (abstractTermInCtx ctx' term)+                throwErrors (checkTermination con rtpats scope)+                return $ Just (con, (rtpats, scope))+    lift $ deleteDataType dt+    let lvls = map (\(_, _, Type _ lvl) -> lvl) cons'+        lvl = if null lvls then NoLevel else maximum lvls+    lift $ addDataType dt (Type (replaceLevel dtTerm lvl) lvl) lcons+    forM_ cons' $ \(_, T.Con i lc' conName conConds [], _) -> do+        warn $ checkConditions lc (Closed $ T.Con i lc' conName conConds []) conConds++checkTele :: (Monad m, Eq a) => Ctx String Type String a -> Tele -> Closed Term+    -> TCM m (SomeEq (Ctx String Type String), Type a)+checkTele ctx [] (Closed term) = return (SomeEq ctx, Type term NoLevel)+checkTele ctx ((args,expr):tele) term = do+    (r1, Type t1 _) <- typeCheckCtx ctx expr Nothing+    lvl1 <- checkIsType ctx expr (nf WHNF t1)+    case extendCtx (map unArg args) Nil (Type r1 lvl1) of+        SomeEq ctx' -> do+            (rctx, Type r2 lvl2) <- checkTele (ctx +++ ctx') tele term+            return (rctx, Type (T.Pi (Type r1 lvl1) (abstractTermInCtx ctx' r2) lvl2) $ max lvl1 lvl2)++replaceLevel :: Term a -> Level -> Term a+replaceLevel (T.Pi r1 r2 lvl2) lvl = T.Pi r1 (replaceLevelScope r2) lvl2+  where+    replaceLevelScope :: Scope String Term a -> Scope String Term a+    replaceLevelScope (ScopeTerm t) = ScopeTerm (replaceLevel t lvl)+    replaceLevelScope (Scope v t) = Scope v (replaceLevelScope t)+replaceLevel _ lvl = T.Universe lvl++checkPositivity :: (Eq a, Monad m) => PIdent -> Term a -> EDocM m ()+checkPositivity dt (T.Pi (Type a _) b _) = checkNoNegative dt (nf WHNF a) >> checkPositivityScope b+  where+    checkPositivityScope :: (Eq a, Monad m) => Scope String Term a -> EDocM m ()+    checkPositivityScope (ScopeTerm t) = checkPositivity dt (nf WHNF t)+    checkPositivityScope (Scope v t) = checkPositivityScope t+checkPositivity _ _ = return ()++checkNoNegative :: (Eq a, Monad m) => PIdent -> Term a -> EDocM m ()+checkNoNegative dt (T.Pi (Type a _) b _) = checkNoDataType dt a >> checkNoNegativeScope b+  where+    checkNoNegativeScope :: (Eq a, Monad m) => Scope String Term a -> EDocM m ()+    checkNoNegativeScope (ScopeTerm t) = checkNoNegative dt (nf WHNF t)+    checkNoNegativeScope (Scope v t) = checkNoNegativeScope t+checkNoNegative _ _ = return ()++checkNoDataType :: Monad m => PIdent -> Term a -> EDocM m ()+checkNoDataType (PIdent (lc,dt)) t = when (dt `elem` collectDataTypes t) $+    throwError [emsgLC lc "Data type is not strictly positive" enull]++collectDataTypes :: Term a            -> [String]+collectDataTypes T.Var{}               = []+collectDataTypes (T.App e1 e2)         = collectDataTypes e1 ++ collectDataTypes e2+collectDataTypes (T.Lam (Scope1 _ e))  = collectDataTypes e+collectDataTypes (T.Pi (Type e _) s _) = collectDataTypes e ++ go s+  where+    go :: Scope s Term a -> [String]+    go (ScopeTerm t) = collectDataTypes t+    go (Scope _   s) = go s+collectDataTypes (T.Con _ _ _ _ as)    = as >>= collectDataTypes+collectDataTypes FunCall{}             = []+collectDataTypes FunSyn{}              = []+collectDataTypes (DataType d _ as)     = d : (as >>= collectDataTypes)+collectDataTypes T.Universe{}          = []+collectDataTypes T.Interval            = []+collectDataTypes ICon{}                = []+collectDataTypes (T.Path _ me1 es)     = maybe [] collectDataTypes me1 ++ (es >>= collectDataTypes)+collectDataTypes (PCon me)             = maybe [] collectDataTypes me+collectDataTypes (T.At _ _ e3 e4)      = collectDataTypes e3 ++ collectDataTypes e4+collectDataTypes (T.Coe es)            = es >>= collectDataTypes+collectDataTypes (T.Iso es)            = es >>= collectDataTypes+collectDataTypes (T.Squeeze es)        = es >>= collectDataTypes

@@ -0,0 +1,53 @@+{-# LANGUAGE RecursiveDo #-}++module TypeChecking.Definitions.Functions+    ( typeCheckFunction+    ) where++import Control.Monad+import Control.Monad.Fix+import Data.Maybe++import Syntax.Expr as E+import Syntax.Term as T+import Syntax.ErrorDoc+import TypeChecking.Monad+import TypeChecking.Context+import TypeChecking.Expressions+import TypeChecking.Definitions.Patterns+import TypeChecking.Definitions.Coverage+import TypeChecking.Definitions.Conditions+import TypeChecking.Definitions.Termination+import Normalization++typeCheckFunction :: MonadFix m => PIdent -> Expr -> [((Int, Int), [ParPat], Maybe Expr)] -> TCM m ()+typeCheckFunction p@(PIdent (lc,name)) ety clauses = mdo+    (ty, Type u _) <- typeCheck ety Nothing+    lvl <- case u of+            T.Universe lvl -> return lvl+            _              -> throwError [emsgLC (getPos ety) "" $ pretty "Expected a type" $$+                                                                   pretty "Actual type:" <+> prettyOpen Nil ty]+    addFunctionCheck p (FunCall lc name clauses') (Type ty lvl)+    clausesAndPats <- forW clauses $ \(lc,pats,mexpr) ->  do+        (bf, TermsInCtx ctx _ ty', rtpats) <- typeCheckPatterns Nil (Type (nf WHNF ty) lvl) pats+        case (bf,mexpr) of+            (True,  Nothing) -> return Nothing+            (False, Nothing) -> do+                let msg = "The right hand side can be omitted only if the absurd pattern is given"+                warn [emsgLC lc msg enull]+                return Nothing+            (True, Just expr) -> do+                let msg = "If the absurd pattern is given the right hand side must be omitted"+                warn [emsgLC (getPos expr) msg enull]+                return Nothing+            (False, Just expr) -> do+                (term, _) <- typeCheckCtx ctx expr (Just ty')+                let scope = closed (abstractTermInCtx ctx term)+                throwErrors (checkTermination name rtpats scope)+                return $ Just ((rtpats, scope), (lc, rtpats))+    let clauses' = map fst clausesAndPats+    case checkCoverage (map snd clausesAndPats) of+        Nothing -> when (length clausesAndPats == length (filter (\(_,_,me) -> isJust me) clauses)) $+                warn [emsgLC lc "Incomplete pattern matching" enull]+        Just uc -> warn $ map (\lc -> emsgLC lc "Unreachable clause" enull) uc+    warn $ checkConditions lc (Closed $ FunCall lc name clauses') (map fst clausesAndPats)

@@ -0,0 +1,79 @@+{-# LANGUAGE ExistentialQuantification #-}++module TypeChecking.Definitions.Patterns+    ( typeCheckPatterns+    , TermsInCtx(..)+    ) where++import Syntax.Expr as E+import Syntax.Term as T+import Syntax.ErrorDoc+import TypeChecking.Context+import TypeChecking.Monad+import TypeChecking.Expressions+import Normalization++data TermInCtx b  = forall a. Eq a => TermInCtx  (Ctx String Type b a) (Term a)+data TermsInCtx b = forall a. Eq a => TermsInCtx (Ctx String Type b a) [Term a] (Type a)++typeCheckPattern :: (Monad m, Eq a) => Ctx String Type String a+    -> Type a -> ParPat -> TCM m (Bool, Maybe (TermInCtx a), T.Pattern (Closed (Scope String Term)))+typeCheckPattern ctx (Type T.Interval _) (ParLeft _)  = return (False, Just $ TermInCtx Nil $ ICon ILeft , PatternI ILeft)+typeCheckPattern ctx (Type T.Interval _) (ParRight _) = return (False, Just $ TermInCtx Nil $ ICon IRight, PatternI IRight)+typeCheckPattern ctx (Type (DataType _ 0 _) _) (ParEmpty _) = return (True, Nothing, PatternVar "_")+typeCheckPattern ctx (Type ty _) (ParEmpty (PPar (lc,_))) =+    throwError [emsgLC lc "" $ pretty "Expected non-empty type:" <+> prettyOpen ctx ty]+typeCheckPattern ctx _ (ParVar (NoArg _)) = return (False, Nothing, PatternVar "_")+typeCheckPattern ctx ty@(Type (DataType dt _ params) _) (ParVar (Arg (PIdent (lc,var)))) = do+    cons <- lift $ getConstructor var (Just dt)+    case cons of+        [] -> return (False, Just $ TermInCtx (Snoc Nil var ty) $ T.Var Bound, PatternVar var)+        (n,con,(conType,_)):_ -> if isDataType conType+            then let con'@(T.Con i _ conName conds _) = instantiate params $ fmap (liftBase ctx) con+                 in return (False, Just $ TermInCtx Nil con', T.Pattern (PatternCon i n conName conds) [])+            else throwError [emsgLC lc ("Not enough arguments to " ++ show var) enull]+  where+    isDataType :: Scope a Term b     -> Bool+    isDataType (ScopeTerm DataType{}) = True+    isDataType (ScopeTerm _)          = False+    isDataType (Scope _ t)            = isDataType t+typeCheckPattern ctx ty (ParVar (Arg (PIdent (lc,var)))) =+    return (False, Just $ TermInCtx (Snoc Nil var ty) $ T.Var Bound, PatternVar var)+typeCheckPattern ctx (Type (DataType dt _ params) _) (ParPat _ (E.Pattern (PIdent (lc,conName)) pats)) = do+    cons <- lift $ getConstructor conName (Just dt)+    case cons of+        []        -> throwError [notInScope lc "data constructor" conName]+        (n,con,(conType,lvl)):_ -> do+            let T.Con i _ _ conds _ = instantiate params $ fmap (liftBase ctx) con+                conType' = Type (nf WHNF $ instantiate params $ fmap (liftBase ctx) conType) lvl+            (bf, TermsInCtx ctx' terms (Type ty _), rtpats) <- typeCheckPatterns ctx conType' pats+            let res = TermInCtx ctx' (T.Con i lc conName conds terms)+            case nf WHNF ty of+                DataType{} -> return (bf, Just res, T.Pattern (PatternCon i n conName conds) rtpats)+                _          -> throwError [emsgLC lc "Not enough arguments" enull]+typeCheckPattern ctx (Type ty _) pat =+    throwError [emsgLC (parPatGetPos pat) "" $ pretty "Unexpected pattern" $$+                                               pretty "Expected type:" <+> prettyOpen ctx ty]++typeCheckPatterns :: (Monad m, Eq a) => Ctx String Type String a -> Type a -> [ParPat]+    -> TCM m (Bool, TermsInCtx a, [T.Pattern (Closed (Scope String Term))])+typeCheckPatterns _ ty [] = return (False, TermsInCtx Nil [] ty, [])+typeCheckPatterns ctx (Type (T.Pi a b lvl) _) (pat:pats) = do+    let a' = nfType WHNF a+    (bf1, mte, rtpat) <- typeCheckPattern ctx a' pat+    TermInCtx ctx' te <- case mte of+                            Nothing ->+                                let var = case b of+                                            Scope v _ -> v+                                            _         -> "_"+                                in return $ TermInCtx (Snoc Nil var a') (T.Var Bound)+                            Just te -> return te+    let b' = instantiate1 te $ fmap (fmap $ liftBase ctx') $ unScope1 (dropOnePi a b lvl)+    (bf2, TermsInCtx ctx'' tes ty, rtpats) <- typeCheckPatterns (ctx +++ ctx') (Type (nf WHNF b') lvl) pats+    return (bf1 || bf2, TermsInCtx (ctx' +++ ctx'') (fmap (liftBase ctx'') te : tes) ty, rtpat:rtpats)+typeCheckPatterns _ _ (pat:_) = throwError [emsgLC (parPatGetPos pat) "Too many arguments" enull]++getVariables :: ParPat                    -> [PIdent]+getVariables (ParPat _ (E.Pattern _ pats)) = pats >>= getVariables+getVariables (ParVar (Arg var))            = [var]+getVariables _                             = []

@@ -0,0 +1,87 @@+{-# LANGUAGE GADTs, ExistentialQuantification #-}++module TypeChecking.Definitions.Termination+    ( checkTermination+    ) where++import Control.Monad.State++import Syntax.Term+import Syntax.ErrorDoc+import TypeChecking.Context++checkTermination :: String -> [PatternC] -> Closed (Scope String Term) -> [EMsg Term]+checkTermination name pats (Closed scope) = map msg $ case scopeToCtx Nil scope of+    TermInCtx ctx term -> collectFunCalls ctx name [] term >>= \(lc,mts) -> case mts of+        Nothing -> [lc]+        Just (TermsInCtx ctx ts) -> if evalState (checkTerms ctx pats ts) 0 == LT then [] else [lc]+  where+    msg :: (Int,Int) -> EMsg Term+    msg lc = emsgLC lc "Termination check failed" enull++checkTerm :: Ctx String Term String a -> PatternC -> Term a -> State Int Ordering+checkTerm ctx (PatternI con) (ICon con') | con == con' = return EQ+checkTerm ctx (PatternVar _) (Var v) = do+    s <- get+    put (s + 1)+    return $ if s == lengthCtx ctx - 1 - index ctx v then EQ else GT+  where+    index :: Ctx String Term b a -> a -> Int+    index Nil _ = 0+    index (Snoc ctx _ _) Bound = 0+    index (Snoc ctx _ _) (Free a) = index ctx a + 1+checkTerm ctx (Pattern (PatternCon i _ _ _) pats) term = do+    s <- get+    results <- mapM (\pat -> checkTerm ctx pat term) pats+    let result = minimum (GT:results)+    if result /= GT then return LT else case collect term of+        Con i' _ _ _ terms | i == i' -> do+            put s+            checkTerms ctx pats terms+        _ -> return GT+checkTerm _ _ _ = return GT++checkTerms :: Ctx String Term String a -> [PatternC] -> [Term a] -> State Int Ordering+checkTerms _ [] _ = return EQ+checkTerms _ _ [] = return EQ+checkTerms ctx (pat:pats) (term:terms) = do+    r <- checkTerm ctx pat term+    case r of+        EQ -> checkTerms ctx pats terms+        _  -> return r++data TermInCtx  s f b = forall a. TermInCtx  (Ctx s f b a) (f a)+data TermsInCtx s f b = forall a. TermsInCtx (Ctx s f b a) [f a]++scopeToCtx :: Ctx s f b a -> Scope s f a -> TermInCtx s f b+scopeToCtx ctx (ScopeTerm t) = TermInCtx ctx t+scopeToCtx ctx (Scope s t) = scopeToCtx (Snoc ctx s $ error "") t++collectFunCalls :: Ctx String Term b a -> String -> [Term a] -> Term a -> [((Int,Int), Maybe (TermsInCtx String Term b))]+collectFunCalls _ _ _  Var{} = []+collectFunCalls ctx name ts (App e1 e2) = collectFunCalls ctx name (e2:ts) e1 ++ collectFunCalls ctx name [] e2+collectFunCalls ctx name _  (Lam (Scope1 v e)) = collectFunCalls (Snoc ctx v $ error "") name [] e+collectFunCalls ctx name _  (Pi (Type e _) s _) = collectFunCalls ctx name [] e ++ go ctx s+  where+    go :: Ctx String Term b a -> Scope String Term a -> [((Int,Int), Maybe (TermsInCtx String Term b))]+    go ctx (ScopeTerm t) = collectFunCalls ctx name [] t+    go ctx (Scope v t) = go (Snoc ctx v $ error "") t+collectFunCalls ctx name ts (Con _ lc name' _ as) =+    (if name == name' then [(lc, Just $ TermsInCtx ctx $ as ++ ts)] else []) ++ (as >>= collectFunCalls ctx name [])+collectFunCalls ctx name ts (FunCall lc name' _) = if name == name' then [(lc, Just $ TermsInCtx ctx ts)] else []+collectFunCalls ctx name _  FunSyn{} = []+collectFunCalls ctx name _  (DataType _ _ as) = as >>= collectFunCalls ctx name []+collectFunCalls ctx name _  Universe{} = []+collectFunCalls ctx name _  Interval = []+collectFunCalls ctx name _  ICon{} = []+collectFunCalls ctx name _  (Path _ me1 es) =+    maybe [] (collectFunCalls ctx name []) me1 ++ (es >>= collectFunCalls ctx name [])+collectFunCalls ctx name _  (PCon me) = maybe [] (collectFunCalls ctx name []) me+collectFunCalls ctx name _  (At _ _ e3 e4) = collectFunCalls ctx name [] e3 ++ collectFunCalls ctx name [] e4+collectFunCalls ctx name _  (Coe es) = es >>= collectFunCalls ctx name []+collectFunCalls ctx name _  (Iso es) = es >>= collectFunCalls ctx name []+collectFunCalls ctx name _  (Squeeze es) = es >>= collectFunCalls ctx name []++scopedToMaybe :: Scoped a -> Maybe a+scopedToMaybe Bound = Nothing+scopedToMaybe (Free a) = Just a

@@ -0,0 +1,306 @@+{-# LANGUAGE FlexibleContexts, ExistentialQuantification #-}++module TypeChecking.Expressions+    ( typeCheck, typeCheckCtx+    , notInScope, inferErrorMsg, inferParamsErrorMsg+    , prettyOpen, exprToVars+    , checkUniverses, checkIsType+    , SomeEq(..), extendCtx+    ) where++import Control.Monad+import Data.List+import Data.Maybe++import Syntax.Expr as E+import Syntax.Term as T+import Syntax.ErrorDoc+import TypeChecking.Monad+import TypeChecking.Context+import Normalization++notInScope :: Show a => (Int,Int) -> String -> a -> EMsg f+notInScope lc s a = emsgLC lc ("Not in scope: " ++ (if null s then "" else s ++ " ") ++ show a) enull++inferErrorMsg :: (Int,Int) -> String -> EMsg f+inferErrorMsg lc s = emsgLC lc ("Cannot infer type of " ++ s) enull++inferParamsErrorMsg :: Show a => (Int,Int) -> a -> EMsg f+inferParamsErrorMsg lc d = emsgLC lc ("Cannot infer parameters of data constructor " ++ show d) enull++expectedArgErrorMsg :: Show a => (Int,Int) -> a -> EMsg f+expectedArgErrorMsg lc d = emsgLC lc ("Expected an argument to " ++ show d) enull++prettyOpen :: (Pretty b f, Monad f) => Ctx b g b a -> f a -> EDoc f+prettyOpen ctx term = epretty $ liftM pretty (close ctx term)++exprToVars :: Monad m => Expr -> EDocM m [Arg]+exprToVars = liftM reverse . go+  where+    go (E.Var a) = return [a]+    go (E.App as (E.Var a)) = liftM (a:) (go as)+    go e = throwError [emsgLC (getPos e) "Expected a list of identifiers" enull]++checkUniverses :: (Pretty b Term, Monad m) => Ctx b g b a1 -> Ctx b g b a2+    -> Expr -> Expr -> Term a1 -> Term a2 -> EDocM m Level+checkUniverses ctx1 ctx2 e1 e2 (T.Universe lvl1) (T.Universe lvl2) = return (max lvl1 lvl2)+checkUniverses ctx1 _ e1 _ t1 (T.Universe _) = throwError [typeErrorMsg ctx1 e1 t1]+checkUniverses _ ctx2 _ e2 (T.Universe _) t2 = throwError [typeErrorMsg ctx2 e2 t2]+checkUniverses ctx1 ctx2 e1 e2 t1 t2 = throwError [typeErrorMsg ctx1 e1 t1, typeErrorMsg ctx2 e2 t2]++checkIsType :: (Pretty b Term, Monad m) => Ctx b g b a -> Expr -> Term a -> EDocM m Level+checkIsType _ _ (T.Universe lvl) = return lvl+checkIsType ctx e t = throwError [typeErrorMsg ctx e t]++typeErrorMsg :: Pretty b Term => Ctx b g b a -> Expr -> Term a -> EMsg Term+typeErrorMsg ctx e t = emsgLC (getPos e) "" $ pretty "Expected type: Type" $$+                                              pretty "Actual type:" <+> prettyOpen ctx t++intType :: Type a+intType = Type T.Interval NoLevel++data SomeEq f = forall a. Eq a => SomeEq (f a)++extendCtx :: Eq a => [s] -> Ctx s Type b a -> Type a -> SomeEq (Ctx s Type b)+extendCtx [] ctx _ = SomeEq ctx+extendCtx (x:xs) ctx t = extendCtx xs (Snoc ctx x t) (fmap Free t)++typeCheck :: Monad m => Expr -> Maybe (Type String) -> TCM m (Term String, Type String)+typeCheck = typeCheckCtx Nil++typeCheckCtx :: (Monad m, Eq a) => Ctx String Type String a -> Expr -> Maybe (Type a) -> TCM m (Term a, Type a)+typeCheckCtx ctx expr ty = go ctx expr [] $ fmap (nfType WHNF) ty+  where+    go :: (Monad m, Eq a) => Ctx String Type String a -> Expr -> [Expr] -> Maybe (Type a) -> TCM m (Term a, Type a)+    go ctx (Paren _ e) exprs ty = go ctx e exprs ty+    go ctx (E.App e1 e2) exprs ty = go ctx e1 (e2:exprs) ty+    go ctx (E.Lam _ [] e) exprs ty = go ctx e exprs ty+    go ctx (E.Lam p (arg : args) e) [] (Just (Type ty@(T.Pi a@(Type _ lvl1) b lvl2) lvl)) = do+        let var = unArg arg+        (te, _) <- go (Snoc ctx var a) (E.Lam p args e) [] $ Just $ Type (nf WHNF $ unScope1 $ dropOnePi a b lvl2) lvl2+        return (T.Lam $ Scope1 var te, Type ty $ min lvl $ max lvl1 lvl2)+    go ctx (E.Lam p (arg : args) e) [] (Just (Type ty _)) =+        throwError [emsgLC (argGetPos arg) "" $ pretty "Expected type:" <+> prettyOpen ctx ty $$+                                                pretty "But lambda expression has pi type"]+    go _ e@E.Lam{} _ _ = throwError [inferErrorMsg (getPos e) "the argument"]+    go ctx (E.Var (NoArg (Pus (lc,_)))) exprs mty = throwError [emsgLC lc "Expected an identifier" enull]+    go ctx (E.Var (Arg (PIdent (lc,var)))) exprs mty = do+        (te, Type ty lvl) <- case lookupCtx var ctx of+            Just r  -> return r+            Nothing -> do+                mt <- lift $ getEntry var $ case mty of+                    Just (Type (DataType d _ _) _) -> Just d+                    _                              -> Nothing+                let replaceConPos (T.Con i _ name conds args) = T.Con i lc name conds args+                    replaceConPos t = t+                case mt of+                    [FunctionE (FunCall _ name clauses) ty] -> return (FunCall lc name clauses, fmap (liftBase ctx) ty)+                    [FunctionE te ty]                       -> return (fmap (liftBase ctx) te , fmap (liftBase ctx) ty)+                    DataTypeE ty e : _                      -> return (DataType var e []      , fmap (liftBase ctx) ty)+                    [ConstructorE _ (ScopeTerm con) (ScopeTerm ty, lvl)] ->+                        return (fmap (liftBase ctx) (replaceConPos con), Type (fmap (liftBase ctx) ty) lvl)+                    [ConstructorE _ con (ty, lvl)] -> case mty of+                        Just (Type (DataType _ _ params) _) ->+                            let liftTerm = instantiate params . fmap (liftBase ctx)+                            in  return (replaceConPos (liftTerm con), Type (liftTerm ty) lvl)+                        Just (Type ty _) -> throwError [emsgLC lc "" $ pretty "Expected type:" <+> prettyOpen ctx ty $$+                                                                       pretty ("But given data constructor " ++ show var)]+                        Nothing -> throwError [inferParamsErrorMsg lc var]+                    [] -> do+                        cons <- lift (getConstructorDataTypes var)+                        let Type (DataType dataType _ _) _ = fromJust mty+                        case cons of+                            []    -> throwError [notInScope lc "" var]+                            [act] -> throwError [emsgLC lc "" $+                                pretty ("Expected data type: " ++ dataType) $$+                                pretty ("Actual data type: " ++ act)]+                            acts -> throwError [emsgLC lc "" $+                                pretty ("Expected data type: " ++ dataType) $$+                                pretty ("Posible data types: " ++ intercalate ", " acts)]+                    _  -> throwError [inferErrorMsg lc $ show var]+        (tes, Type ty' lvl') <- typeCheckApps lc ctx exprs (Type ty lvl)+        case (mty, ty') of+            (Nothing, _)  -> return ()+            (Just (Type (DataType edt _ _) _), DataType adt _ []) -> unless (edt == adt) $+                throwError [emsgLC lc "" $ pretty ("Expected data type: " ++ edt) $$+                                           pretty ("Actual data type: " ++ adt)]+            (Just (Type ety _), _) -> actExpType ctx ty' ety lc+        return (apps te tes, Type ty' $ maybe lvl' (\(Type _ lvl'') -> min lvl' lvl'') mty)+    go _ (ELeft _)  [] Nothing = return (ICon ILeft, intType)+    go _ e@ELeft{}  _  Nothing = throwError [emsgLC (getPos e) "\"left\" is applied to arguments" enull]+    go _ (ERight _) [] Nothing = return (ICon IRight, intType)+    go _ e@ERight{} _  Nothing = throwError [emsgLC (getPos e) "\"right\" is applied to arguments" enull]+    go ctx e@PathCon{} es _ | length es > 1 = throwError [emsgLC (getPos e) "A path is applied to arguments" enull]+    go ctx e@PathCon{} [] Nothing = throwError [inferErrorMsg (getPos e) "path"]+    go ctx PathCon{} [e] Nothing = do+        (r, Scope1 v t, lvl) <- typeCheckLambda ctx e intType+        return (r, Type (T.Pi intType (Scope v (ScopeTerm t)) lvl) lvl)+    go ctx e@PathCon{} [] _ = throwError [expectedArgErrorMsg (getPos e) "path"]+    go ctx e'@PathCon{} [e] (Just (Type ty@(T.Path h mt1 _) lvl)) = do+        (r,t) <- go ctx e [] $ fmap (\t1 -> Type+            (T.Pi intType (Scope "i" $ ScopeTerm $ T.App (fmap Free t1) $ T.Var Bound) lvl) lvl) mt1+        let left  = T.App r (ICon ILeft)+            right = T.App r (ICon IRight)+        actExpType ctx (T.Path Implicit Nothing [left,right]) ty (getPos e')+        return (PCon (Just r), Type ty lvl)+    go ctx e'@PathCon{} [e] (Just (Type ty _)) =+        throwError [emsgLC (getPos e') "" $ pretty "Expected type:" <+> prettyOpen ctx ty $$+                                            pretty "Actual type: Path"]+    go ctx (E.At e1 e2) es Nothing = do+        (r1, Type t1 lvl) <- go ctx e1 [] Nothing+        (r2, _) <- go ctx e2 [] (Just intType)+        case nf WHNF t1 of+            T.Path _ (Just a) [b,c] -> do+                (tes, ty) <- typeCheckApps (getPos e1) ctx es $ Type (T.App a r2) lvl+                return (apps (T.At b c r1 r2) tes, ty)+            T.Path _ Nothing _ -> throwError [emsgLC (getPos e1) "Cannot infer type" enull]+            t1' -> throwError [emsgLC (getPos e1) "" $ pretty "Expected type: Path" $$+                                                       pretty "Actual type:" <+> prettyOpen ctx t1']+    go ctx e@E.Coe{} [] Nothing = throwError [expectedArgErrorMsg (getPos e) "coe"]+    go ctx e@E.Coe{} (e1:es) Nothing = do+        (r1, Scope1 v t1, _) <- typeCheckLambda ctx e1 intType+        lvl <- checkIsType (Snoc ctx v $ error "") e1 t1+        let res = T.Pi intType (Scope "r" $ ScopeTerm $ T.App (fmap Free r1) $ T.Var Bound) lvl+        case es of+            [] -> return (T.Coe [r1], Type (T.Pi intType (Scope "l" $ ScopeTerm $+                T.Pi (Type (T.App (fmap Free r1) $ T.Var Bound) lvl) (ScopeTerm $ fmap Free res) lvl) lvl) lvl)+            e2:es1 -> do+                (r2, _) <- go ctx e2 [] $ Just intType+                case es1 of+                    [] -> return (T.Coe [r1,r2], Type (T.Pi (Type (T.App r1 r2) lvl) (ScopeTerm res) lvl) lvl)+                    e3:es2 -> do+                        (r3, _) <- go ctx e3 [] $ Just $ Type (nf WHNF $ T.App r1 r2) lvl+                        case es2 of+                            [] -> return (T.Coe [r1,r2,r3], Type res lvl)+                            e4:es3 -> do+                                (r4, _) <- go ctx e4 [] $ Just intType+                                (tes, ty) <- typeCheckApps (getPos e) ctx es3 $ Type (T.App r1 r4) lvl+                                return (T.Coe $ [r1,r2,r3,r4] ++ tes, ty)+    go ctx e@E.Iso{} es Nothing | length es < 6 =+        throwError [emsgLC (getPos e) "Expected at least 6 arguments to \"iso\"" enull]+    go ctx E.Iso{} (e1:e2:e3:e4:e5:e6:es) Nothing | length es <= 1 = do+        (r1, Type t1 _) <- go ctx e1 [] Nothing+        (r2, Type t2 _) <- go ctx e2 [] Nothing+        let t1' = nf WHNF t1+            t2' = nf WHNF t2+        lvl1 <- checkIsType ctx e1 t1'+        lvl2 <- checkIsType ctx e2 t2'+        let lvl = max lvl1 lvl2+        (r3, _)  <- go ctx e3 [] $ Just $ Type (T.Pi (Type r1 lvl1) (ScopeTerm r2) lvl2) lvl+        (r4, _)  <- go ctx e4 [] $ Just $ Type (T.Pi (Type r2 lvl2) (ScopeTerm r1) lvl1) lvl+        let h e s1 s3 s4 tlvl = go ctx e [] $ Just $ Type (T.Pi (Type s1 tlvl) (Scope "x" $+                ScopeTerm $ T.Path Implicit (Just $ T.Pi intType (ScopeTerm $ fmap Free s1) tlvl)+                [T.App (fmap Free s4) $ T.App (fmap Free s3) $ T.Var Bound, T.Var Bound]) tlvl) tlvl+        (r5, _) <- h e5 r1 r3 r4 lvl1+        (r6, _) <- h e6 r2 r4 r3 lvl2+        case es of+            [] -> return (T.Iso [r1,r2,r3,r4,r5,r6],+                Type (T.Pi intType (ScopeTerm $ T.Universe lvl) $ succ lvl) $ succ lvl)+            e7:_ -> do+                (r7, _) <- go ctx e7 [] $ Just intType+                return (T.Iso [r1,r2,r3,r4,r5,r6,r7], Type (T.Universe lvl) $ succ lvl)+    go ctx e@E.Squeeze{} [] Nothing = return (T.Squeeze [],+        Type (T.Pi intType (ScopeTerm $ T.Pi intType (ScopeTerm T.Interval) NoLevel) NoLevel) NoLevel)+    go ctx e@E.Squeeze{} [e1] Nothing = do+        (r1, _) <- go ctx e1 [] $ Just intType+        return (T.Squeeze [r1], Type (T.Pi intType (ScopeTerm T.Interval) NoLevel) NoLevel)+    go ctx E.Squeeze{} [e1,e2] Nothing = do+        (r1, _) <- go ctx e1 [] $ Just intType+        (r2, _) <- go ctx e2 [] $ Just intType+        return (T.Squeeze [r1,r2], intType)+    go ctx (E.Pi [] e) [] Nothing = go ctx e [] Nothing+    go ctx expr@(E.Pi (PiTele _ e1 e2 : tvs) e) [] Nothing = do+        args <- exprToVars e1+        (r1, Type t1 _) <- typeCheckCtx ctx e2 Nothing+        lvl1 <- checkIsType ctx e2 (nf WHNF t1)+        case extendCtx (map unArg args) Nil (Type r1 lvl1) of+            SomeEq ctx' -> do+                (r2, Type t2 _) <- go (ctx +++ ctx') (E.Pi tvs e) [] Nothing+                lvl2 <- checkIsType (ctx +++ ctx') (E.Pi tvs e) (nf WHNF t2)+                let lvl = max lvl1 lvl2+                return (T.Pi (Type r1 lvl1) (abstractTermInCtx ctx' r2) lvl2, Type (T.Universe lvl) $ succ lvl)+    go ctx (E.Arr e1 e2) [] Nothing = do+        (r1, Type t1 _) <- go ctx e1 [] Nothing+        (r2, Type t2 _) <- go ctx e2 [] Nothing+        lvl1 <- checkIsType ctx e1 (nf WHNF t1)+        lvl2 <- checkIsType ctx e1 (nf WHNF t2)+        let lvl = max lvl1 lvl2+        return (T.Pi (Type r1 lvl1) (ScopeTerm r2) lvl2, Type (T.Universe lvl) $ succ lvl)+    go _ (E.Universe (U (_,u))) [] Nothing =+        let l = parseLevel u+            l' = Level (level l + 1)+        in return (T.Universe l, Type (T.Universe l') $ succ l')+      where+        parseLevel :: String -> Level+        parseLevel "Type" = NoLevel+        parseLevel ('T':'y':'p':'e':s) = Level (read s)+        parseLevel s = error $ "parseLevel: " ++ s+    go _ E.Interval{} [] Nothing = return (T.Interval, Type (T.Universe NoLevel) $ Level 1)+    go ctx e@E.Path{} [] _ = throwError [expectedArgErrorMsg (getPos e) "Path"]+    go ctx E.Path{} (e1:es) Nothing | length es < 3 = do+        (r1, Scope1 v t1, _) <- typeCheckLambda ctx e1 intType+        lvl <- checkIsType (Snoc ctx v $ error "") e1 t1+        let r1' c = Type (T.App r1 $ ICon c) lvl+            mkType t = Type t (succ lvl)+        case es of+            [] -> return (T.Path Explicit (Just r1) [], mkType $+                T.Pi (r1' ILeft) (ScopeTerm $ T.Pi (r1' IRight) (ScopeTerm $ T.Universe lvl) $ succ lvl) $ succ lvl)+            [e2] -> do+                (r2,_) <- go ctx e2 [] $ Just $ nfType WHNF (r1' ILeft)+                return (T.Path Explicit (Just r1) [r2], mkType $+                    T.Pi (r1' IRight) (ScopeTerm $ T.Universe lvl) $ succ lvl)+            [e2,e3] -> do+                (r2,_) <- go ctx e2 [] $ Just $ nfType WHNF (r1' ILeft)+                (r3,_) <- go ctx e3 [] $ Just $ nfType WHNF (r1' IRight)+                return (T.Path Explicit (Just r1) [r2,r3], mkType $ T.Universe lvl)+            _ -> error "typeCheckCtx.Path"+    go ctx (E.PathImp e1 e2) [] Nothing = do+        (r1, Type t1 lvl) <- go ctx e1 [] Nothing+        (r2, _) <- go ctx e2 [] $ Just $ Type (nf WHNF t1) lvl+        return (T.Path Implicit (Just $ T.Lam $ Scope1 "_" $ fmap Free t1) [r1,r2], Type (T.Universe lvl) $ succ lvl)+    go _ e _ Nothing = throwError [emsgLC (getPos e) "A type is applied to arguments" enull]+    go ctx e es (Just (Type ty lvl)) = do+        (r, Type t _) <- go ctx e es Nothing+        actExpType ctx t ty (getPos e)+        return (r, Type ty lvl)++typeCheckLambda :: (Monad m, Eq a) => Ctx String Type String a -> Expr -> Type a+    -> TCM m (Term a, Scope1 String Term a, Level)+typeCheckLambda ctx (Paren _ e) ty = typeCheckLambda ctx e ty+typeCheckLambda ctx (E.Lam _ [] e) ty = typeCheckLambda ctx e ty+typeCheckLambda ctx (E.Lam p (arg:args) e) ty = do+    let var = unArg arg+    (te, Type ty' lvl) <- typeCheckCtx (Snoc ctx var ty) (E.Lam p args e) Nothing+    return (T.Lam $ Scope1 var te, Scope1 var ty', lvl)+typeCheckLambda ctx e ty = do+    (te, Type ty' _) <- typeCheckCtx ctx e Nothing+    case nf WHNF ty' of+        T.Pi a b lvlb ->+            let Type na lvla = nfType NF a+                Type nty lvlty = nfType NF ty+            in if (nty `lessOrEqual` na)+                then return (te, dropOnePi a b lvlb, lvlb)+                else throwError [emsgLC (getPos e) "" $+                        pretty "Expected type:" <+> prettyOpen ctx (T.Pi (Type nty lvla) b lvlb) $$+                        pretty "Actual type:"   <+> prettyOpen ctx (T.Pi (Type na lvlty) b lvlb)]+        _ -> throwError [emsgLC (getPos e) "" $ pretty "Expected pi type" $$+                                                pretty "Actual type:" <+> prettyOpen ctx ty']++actExpType :: (Monad m, Eq a) => Ctx String Type String a -> Term a -> Term a -> (Int,Int) -> EDocM m ()+actExpType ctx act exp lc =+    let act' = nf NF act+        exp' = nf NF exp+    in unless (act' `lessOrEqual` exp') $+        throwError [emsgLC lc "" $ pretty "Expected type:" <+> prettyOpen ctx exp' $$+                                   pretty "Actual type:"   <+> prettyOpen ctx act']++typeCheckApps :: (Monad m, Eq a) => (Int,Int) -> Ctx String Type String a -> [Expr] -> Type a -> TCM m ([Term a], Type a)+typeCheckApps lc ctx exprs ty = go exprs (nfType WHNF ty)+  where+    go [] ty = return ([], ty)+    go (expr:exprs) (Type (T.Pi a b lvl') _) = do+        (term, _)   <- typeCheckCtx ctx expr (Just a)+        (terms, ty) <- go exprs $ Type (nf WHNF $ instantiate1 term $ unScope1 $ dropOnePi a b lvl') lvl'+        return (term:terms, ty)+    go _ (Type ty _) = throwError [emsgLC lc "" $ pretty "Expected pi type" $$+                                                  pretty "Actual type:" <+> prettyOpen ctx ty]

@@ -0,0 +1,50 @@+module TypeChecking.Monad+    ( EDocM, ScopeM, TCM, runTCM+    , addFunctionCheck, addDataTypeCheck, addConstructorCheck+    , module TypeChecking.Monad.Warn+    , module TypeChecking.Monad.Scope+    , lift+    ) where++import Control.Monad+import Control.Monad.Trans(lift)++import TypeChecking.Monad.Warn+import TypeChecking.Monad.Scope+import Syntax.Term+import Syntax.Expr+import Syntax.ErrorDoc++type EDocM = WarnT [EMsg Term]+type ScopeM = ScopeT (Term String) (Type String) (Scope String Term String) (Scope String Term String, Level)+type TCM m = EDocM (ScopeM m)++runTCM :: Monad m => TCM m a -> m (Maybe a)+runTCM = liftM snd . runScopeT . runWarnT++multipleDeclaration :: (Int,Int) -> String -> EMsg f+multipleDeclaration lc var = emsgLC lc ("Multiple declarations of " ++ show var) enull++addFunctionCheck :: Monad m => PIdent -> Term String -> Type String -> TCM m ()+addFunctionCheck (PIdent (lc,var)) te ty = do+    mr <- lift (getEntry var Nothing)+    case mr of+        [] -> lift (addFunction var te ty)+        _  -> warn [multipleDeclaration lc var]++addDataTypeCheck :: Monad m => PIdent -> Type String -> Int -> TCM m ()+addDataTypeCheck (PIdent (lc,var)) ty b = do+    mr <- lift (getEntry var Nothing)+    case mr of+        FunctionE _ _ : _ -> warn [multipleDeclaration lc var]+        DataTypeE _ _ : _ -> warn [multipleDeclaration lc var]+        _                 -> lift (addDataType var ty b)++addConstructorCheck :: Monad m => PIdent -> String -> Int+    -> Scope String Term String -> Scope String Term String -> Level -> TCM m ()+addConstructorCheck (PIdent (lc,var)) dt n te ty lvl = do+    mr <- lift $ getEntry var (Just dt)+    case mr of+        FunctionE    _ _   : _ -> warn [multipleDeclaration lc var]+        ConstructorE _ _ _ : _ -> warn [multipleDeclaration lc var]+        _                      -> lift $ addConstructor var dt n te (ty,lvl)

@@ -0,0 +1,59 @@+{-# LANGUAGE GeneralizedNewtypeDeriving #-}++module TypeChecking.Monad.Scope+    ( ScopeT, runScopeT+    , addFunction, addConstructor, addDataType+    , deleteDataType+    , getConstructor, getConstructorDataTypes+    , Entry(..), getEntry+    ) where++import Control.Monad+import Control.Monad.Fix+import Control.Monad.State+import Control.Applicative+import Data.List+import Data.Maybe++data Entry a b c d = FunctionE a b | DataTypeE b Int | ConstructorE Int c d++data ScopeState a b c d = ScopeState+    { functions    :: [(String, (a, b))]+    , dataTypes    :: [(String, (b, Int))]+    , constructors :: [((String, String), (Int, c, d))]+    }++newtype ScopeT a b c d m a' = ScopeT { unScopeT :: StateT (ScopeState a b c d) m a' }+    deriving (Functor,Monad,MonadTrans,MonadIO,MonadFix,Applicative)++addFunction :: Monad m => String -> a -> b -> ScopeT a b c d m ()+addFunction v te ty = ScopeT $ modify $ \scope -> scope { functions = (v, (te, ty)) : functions scope }++addDataType :: Monad m => String -> b -> Int -> ScopeT a b c d m ()+addDataType v ty b = ScopeT $ modify $ \scope -> scope { dataTypes = (v, (ty, b)) : dataTypes scope }++addConstructor :: Monad m => String -> String -> Int -> c -> d -> ScopeT a b c d m ()+addConstructor con dt n te ty = ScopeT $ modify $ \scope ->+    scope { constructors = ((con, dt), (n, te, ty)) : constructors scope }++deleteDataType :: Monad m => String -> ScopeT a b c d m ()+deleteDataType dt = ScopeT $ modify $ \scope ->+    scope { dataTypes = deleteBy (\(v1,_) (v2,_) -> v1 == v2) (dt, error "") (dataTypes scope) }++getConstructor :: Monad m => String -> Maybe String -> ScopeT a b c d m [(Int, c, d)]+getConstructor con (Just dt) = ScopeT $ liftM (maybeToList . lookup (con, dt) . constructors) get+getConstructor con Nothing   = ScopeT $ liftM (map snd . filter (\((c,_),_) -> con == c) . constructors) get++getConstructorDataTypes :: Monad m => String -> ScopeT a b c d m [String]+getConstructorDataTypes con = ScopeT $ liftM (map (snd . fst) . filter (\((c,_),_) -> con == c) . constructors) get++getEntry :: Monad m => String -> Maybe String -> ScopeT a b c d m [Entry a b c d]+getEntry v dt = ScopeT $ do+    cons  <- unScopeT (getConstructor v dt)+    scope <- get+    return $ map (uncurry FunctionE) (maybeToList $ lookup v $ functions scope)+          ++ (if isNothing dt then map (uncurry DataTypeE) (maybeToList $ lookup v $ dataTypes scope) else [])+          ++ map (\(i,c,d) -> ConstructorE i c d) cons++runScopeT :: Monad m => ScopeT a b c d m a' -> m a'+runScopeT (ScopeT f) = evalStateT f $ ScopeState [] [] []

@@ -0,0 +1,57 @@+{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-}++module TypeChecking.Monad.Warn+    ( WarnT, warn, runWarnT+    , throwError, catchError+    , forW, throwErrors+    ) where++import Control.Monad+import Control.Monad.Fix+import Control.Monad.Trans+import Control.Monad.Error.Class+import Control.Applicative+import Data.Monoid hiding ((<>))+import Data.Maybe++newtype WarnT w m a = WarnT { runWarnT :: m (w, Maybe a) }++instance Functor m => Functor (WarnT w m) where+    fmap f (WarnT m) = WarnT $ fmap (\(w, ma) -> (w, fmap f ma)) m++instance (Monoid w, Applicative m) => Applicative (WarnT w m) where+    pure a = WarnT $ pure (mempty, Just a)+    WarnT f <*> WarnT a = WarnT $ (\(w1, mf) (w2, ma) -> (w1 `mappend` w2, mf <*> ma)) <$> f <*> a++instance (Monoid w, Monad m) => Monad (WarnT w m) where+    return a      = WarnT $ return (mempty, Just a)+    WarnT m >>= k = WarnT $ m >>= \(w, ma) -> case ma of+        Nothing -> return (w, Nothing)+        Just a  -> do+            (w', mb) <- runWarnT (k a)+            return (w `mappend` w', mb)++instance (Monoid w, Monad m) => MonadError w (WarnT w m) where+    throwError w = WarnT $ return (w, Nothing)+    catchError (WarnT m) h = WarnT $ m >>= \(w, ma) -> case ma of+        Nothing -> runWarnT (h w)+        Just _  -> return (w, ma)++instance Monoid w => MonadTrans (WarnT w) where+    lift m = WarnT $ liftM (\a -> (mempty, Just a)) m++instance (Monoid w, MonadIO m) => MonadIO (WarnT w m) where+    liftIO m = WarnT $ liftM (\a -> (mempty, Just a)) (liftIO m)++instance (Monoid w, MonadFix m) => MonadFix (WarnT w m) where+    mfix f = WarnT $ mfix $ \ ~(_, ~(Just a)) -> runWarnT (f a)++warn :: Monad m => w -> WarnT w m ()+warn w = WarnT $ return (w, Just ())++forW :: (Monoid w, Monad m) => [a] -> (a -> WarnT w m (Maybe b)) -> WarnT w m [b]+forW as k = liftM catMaybes $ forM as $ \a -> k a `catchError` \w -> warn w >> return Nothing++throwErrors :: Monad m => [w] -> WarnT [w] m ()+throwErrors [] = return ()+throwErrors ws = throwError ws