diff --git a/Setup.hs b/Setup.hs
--- a/Setup.hs
+++ b/Setup.hs
@@ -1,24 +1,3 @@
 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
+main = defaultMain
diff --git a/data/hoq.vim b/data/hoq.vim
--- a/data/hoq.vim
+++ b/data/hoq.vim
@@ -4,12 +4,14 @@
   finish
 endif
 
-syn keyword hoqConstructor     left right path coe iso squeeze
-syn keyword hoqType            data I Path with
+syn keyword hoqKeyword         import case of infix infixl infixr
+syn keyword hoqConstructor     left right path coe iso squeeze contr
+syn keyword hoqType            data I Path with Contr Prop
 syn match   hoqLineComment     "---*\([^-!#$%&\*\+./<=>\?@\\^|~].*\)\?$"
 syn region  hoqBlockComment    start="{-"  end="-}" contains=hoqBlockComment
 syn match   hoqNumber          "\<[0-9]\+\>"
 syn match   hoqType            "\<Type[0-9]*\>"
+syn match   hoqType            "\<Set[0-9]*\>"
 " syn match   hoqDelimiter       "(\|)\|;\|_\|{\|}"
 syn match   hoqOperator        "=\|:\|->\|\\\|@"
 
@@ -21,6 +23,7 @@
     command -nargs=+ HiLink hi def link <args>
   endif
 
+  HiLink hoqKeyword        Keyword
   HiLink hoqConstructor    Keyword
   HiLink hoqLineComment    hoqComment
   HiLink hoqBlockComment   hoqComment
diff --git a/dist/build/hoq/hoq-tmp/Syntax/BNFC/LexGrammar.hs b/dist/build/hoq/hoq-tmp/Syntax/BNFC/LexGrammar.hs
deleted file mode 100644
--- a/dist/build/hoq/hoq-tmp/Syntax/BNFC/LexGrammar.hs
+++ /dev/null
@@ -1,388 +0,0 @@
-{-# 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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-
-alex_check :: AlexAddr
-alex_check = AlexA# 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-
-alex_deflt :: 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
diff --git a/dist/build/hoq/hoq-tmp/Syntax/BNFC/ParGrammar.hs b/dist/build/hoq/hoq-tmp/Syntax/BNFC/ParGrammar.hs
deleted file mode 100644
--- a/dist/build/hoq/hoq-tmp/Syntax/BNFC/ParGrammar.hs
+++ /dev/null
@@ -1,1277 +0,0 @@
-{-# 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# "\xff\xff\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x18\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x01\x00\x01\x00\x03\x00\x03\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x14\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x1a\x00\x17\x00\x18\x00\x0c\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x14\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x05\x00\x06\x00\x17\x00\x18\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x01\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x18\x00\x05\x00\x0b\x00\x04\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x01\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x18\x00\x09\x00\x03\x00\x08\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0a\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x01\x00\x01\x00\x18\x00\x01\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x05\x00\x0a\x00\x0b\x00\x0c\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x07\x00\x0a\x00\x0b\x00\x0c\x00\x16\x00\x1b\x00\x1c\x00\x06\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x0c\x00\x03\x00\x02\x00\x18\x00\x1b\x00\x1c\x00\x12\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x0a\x00\x0a\x00\x0b\x00\x0c\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x01\x00\x0a\x00\x0b\x00\x0c\x00\x1b\x00\x1c\x00\x0a\x00\x0e\x00\x0f\x00\x0c\x00\x20\x00\x21\x00\x22\x00\x23\x00\x17\x00\x16\x00\x17\x00\x18\x00\x15\x00\x16\x00\x05\x00\x19\x00\x18\x00\x18\x00\x04\x00\x22\x00\x23\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x1a\x00\x0a\x00\x0b\x00\x0c\x00\x00\x00\x01\x00\x02\x00\x03\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x1a\x00\x0a\x00\x0b\x00\x0c\x00\x0b\x00\x0c\x00\x02\x00\x03\x00\x0b\x00\x0c\x00\x0c\x00\x21\x00\x22\x00\x23\x00\x0a\x00\x0b\x00\x0c\x00\x03\x00\x02\x00\x15\x00\x16\x00\x02\x00\x16\x00\x13\x00\x0c\x00\x22\x00\x23\x00\xff\xff\x23\x00\x24\x00\x0c\x00\xff\xff\x23\x00\x24\x00\x10\x00\x11\x00\x12\x00\xff\xff\xff\xff\x23\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x11\x00\x12\x00\x13\x00\x14\x00\x15\x00\x16\x00\x17\x00\x18\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x11\x00\x12\x00\x13\x00\x14\x00\xff\xff\x16\x00\x17\x00\x18\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x0c\x00\x12\x00\x0e\x00\x0f\x00\x10\x00\x0c\x00\x12\x00\xff\xff\xff\xff\x10\x00\x11\x00\x12\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"#
-
-happyTable :: HappyAddr
-happyTable = HappyA# "\x00\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x61\x00\x11\x00\x12\x00\x71\x00\x14\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x40\x00\x40\x00\x6e\x00\x41\x00\x11\x00\x12\x00\x6c\x00\x14\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x30\x00\x11\x00\x12\x00\x67\x00\x14\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x4f\x00\x25\x00\x26\x00\x2d\x00\x11\x00\x12\x00\x5d\x00\x14\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x30\x00\x11\x00\x12\x00\x56\x00\x14\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x35\x00\x36\x00\x25\x00\x26\x00\x11\x00\x12\x00\x57\x00\x14\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x73\x00\x11\x00\x12\x00\x41\x00\x14\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x26\x00\x2f\x00\x6f\x00\x70\x00\x11\x00\x12\x00\x46\x00\x14\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x69\x00\x11\x00\x12\x00\x47\x00\x14\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x26\x00\x67\x00\x5f\x00\x60\x00\x11\x00\x12\x00\x4e\x00\x14\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x61\x00\x11\x00\x12\x00\x3a\x00\x14\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x59\x00\x5a\x00\x26\x00\x40\x00\x11\x00\x12\x00\x13\x00\x14\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x53\x00\x0e\x00\x0f\x00\x10\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x2d\x00\x0e\x00\x0f\x00\x10\x00\x24\x00\x11\x00\x12\x00\x36\x00\x42\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x53\x00\x41\x00\x3e\x00\x26\x00\x11\x00\x12\x00\x54\x00\x43\x00\x15\x00\x16\x00\x17\x00\x18\x00\x19\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x38\x00\x32\x00\x0f\x00\x10\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x56\x00\x62\x00\x0f\x00\x10\x00\x11\x00\x39\x00\x50\x00\x1c\x00\x1d\x00\x5a\x00\x45\x00\x17\x00\x18\x00\x19\x00\x63\x00\x24\x00\x25\x00\x26\x00\x5b\x00\x65\x00\x2f\x00\x51\x00\x26\x00\x26\x00\x30\x00\x64\x00\x19\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\xff\xff\x32\x00\x0f\x00\x10\x00\x04\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\xff\xff\x32\x00\x0f\x00\x10\x00\x0f\x00\x10\x00\x48\x00\x49\x00\x0f\x00\x10\x00\x5a\x00\x44\x00\x18\x00\x19\x00\x4a\x00\x0f\x00\x10\x00\x32\x00\x37\x00\x5b\x00\x5c\x00\x38\x00\x24\x00\x4b\x00\x04\x00\x33\x00\x19\x00\x00\x00\x3b\x00\x3e\x00\x53\x00\x00\x00\x3b\x00\x3c\x00\x69\x00\x70\x00\x6b\x00\x00\x00\x00\x00\x4c\x00\x04\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x24\x00\x25\x00\x26\x00\x04\x00\x1b\x00\x1c\x00\x1d\x00\x1e\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x00\x00\x24\x00\x25\x00\x26\x00\x26\x00\x27\x00\x28\x00\x29\x00\x2a\x00\x26\x00\x2b\x00\x28\x00\x4d\x00\x2a\x00\x53\x00\x2b\x00\x00\x00\x00\x00\x69\x00\x6a\x00\x6b\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\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"#
-
-happyReduceArr = 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.
diff --git a/examples/Paths.hoq b/examples/Paths.hoq
new file mode 100644
--- /dev/null
+++ b/examples/Paths.hoq
@@ -0,0 +1,37 @@
+infixr 5 $
+($) : {A B : Type} -> (A -> B) -> A -> B
+($) _ _ f a = f a
+
+idp : {A : Type} {a : A} -> a = a
+idp _ a = path (\_ -> a)
+
+transport : {A : Type} (B : A -> Type) {a a' : A} -> a = a' -> B a -> B a'
+transport _ 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 _ _ _ p i = path (\j -> p @ squeeze i j)
+
+J : {A : Type} {a : A} (B : {a' : A} -> a = a' -> Type) -> B idp -> {a' : A} (p : a = a') -> B p
+J A a B b a' p = coe (\i -> B (psqueeze p i)) left b right
+
+inv : {A : Type} {a a' : A} -> a = a' -> a' = a
+inv _ a _ p = transport (\x -> x = a) p idp
+
+(*) : {A : Type} {a a' a'' : A} -> a = a' -> a' = a'' -> a = a''
+(*) _ a _ _ p q = transport (\x -> a = x) q p
+
+inv-comp : {A : Type} {a a' : A} (p : a = a') -> inv p * p = idp
+inv-comp _ _ _ p = J (\_ q -> inv q * q = idp) idp p
+
+data QED = qed
+
+(!) : {A : Type} -> (a : A) -> QED -> a = a
+(!) _ _ _ = idp
+
+infix 3 ==<
+(==<) : {A : Type} (a : A) {a' : A} -> a = a' -> a = a'
+(==<) _ _ _ p = p
+
+infixr 2 >==
+(>==) : {A : Type} {a a' a'' : A} -> a = a' -> a' = a'' -> a = a''
+(>==) _ _ _ _ = (*)
diff --git a/examples/basics.hoq b/examples/basics.hoq
--- a/examples/basics.hoq
+++ b/examples/basics.hoq
@@ -1,7 +1,14 @@
 -- Pi types
 id : (A : Type) -> A -> A
-id A a = a
+id _ a = a
 
+-- Implicit arguments
+id' : {A : Type} -> A -> A
+id' _ a = a
+
+test : (A : Type) -> (A -> A) -> (A -> A)
+test _ f = id' f
+
 -- Universes
 -- Type and Type0 are synonyms
 universes : (f : Type1 -> Type0) -> f Type0 -> f Type0
@@ -23,14 +30,16 @@
 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
 
+-- Case construction
+not : Bool -> Bool
+not b = case b of
+    true -> false
+    false -> true
+
 -- Recursive functions
 plus : Nat -> Nat -> Nat
 plus zero y = y
@@ -41,6 +50,13 @@
 ack (suc m) zero = ack m (suc zero)
 ack (suc m) (suc n) = ack m (ack (suc m) n)
 
+-- Infix operators
+infixl 60 `plus`
+infixl 70 *
+(*) : Nat -> Nat -> Nat
+(*) zero _ = zero
+(*) (suc x) y = y `plus` x * y
+
 -- Interval type
 -- I is a type with constructors left : I and right : I
 -- coe and squeeze are primitive operators which satisfy the following rules:
@@ -73,6 +89,15 @@
 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)
 
+-- There are three special subuniverses of Type: Contr, Prop, and Set_i
+-- For each A : Contr, we have contr : A
+-- A path in Set belongs to Prop, and a path in Prop belongs to Contr, that is
+-- Path : (A : I -> Set) -> A left -> A right -> Prop
+-- Path : (A : I -> Prop) -> A left -> A right -> Contr
+-- Data types which use only types in Set (note that I does not belong to Set) also belong to Set
+Nat-isSet : (x y : Nat) (p q : x = y) -> p = q
+Nat-isSet _ _ _ _ = contr
+
 -- Univalence
 not-not : (x : Bool) -> not (not x) = x
 not-not true  = idp Bool true
@@ -101,10 +126,12 @@
 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
diff --git a/examples/circle.hoq b/examples/circle.hoq
--- a/examples/circle.hoq
+++ b/examples/circle.hoq
@@ -1,11 +1,10 @@
+import Paths
+
 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)
@@ -20,133 +19,111 @@
     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))
+wind (positive zero)    = idp
+wind (positive (suc x)) = wind (positive x) * path loop
+wind (negative (suc x)) = 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))
+pred-succ (positive x) = idp
+pred-succ (negative (suc x)) = idp
 
 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)
+succ-pred (positive zero) = idp
+succ-pred (positive (suc x)) = idp
+succ-pred (negative x) = idp
 
-iter : I -> Type
+iter : I -> Set
 iter i = iso Z Z succ pred pred-succ succ-pred i
 
-code : Circle -> Type
+code : Circle -> Set
 code base     = Z
 code (loop i) = iter i
 
-encode : (x : Circle) -> base = x -> code x
+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))
+assoc : (p q r : base = base) -> (p * q) * r = p * (q * r)
+assoc p q = J (\x s -> (p * q) * s = p * (q * s)) idp
 
-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
+map : {A B : Type} (f : A -> B) -> {a a' : A} -> a = a' -> f a = f a'
+map _ _ f a _ p = transport (\x -> f a = f x) p idp
 
-wind-succ-loop-neg : (x : Nat) -> comp' (wind (pred (negative x))) (path loop) = wind (negative x)
+wind-succ-loop-neg : (x : Nat) -> 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)))
+    assoc (wind (negative x)) (inv (path loop)) (path loop) *
+    map (\p -> wind (negative x) * p) (inv-comp (path loop))
 
-wind-succ-loop : (x : Z) -> comp' (wind (pred x)) (path loop) = wind x
+wind-succ-loop : (x : Z) -> 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 (positive (suc x)) = idp
 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)))
+    (path (\k y -> wind (coe iter k y left) * psqueeze (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))
+encode-decode : {x : Circle} (p : base = x) -> decode x (encode p) = p
+encode-decode _ = J (\x p -> decode x (encode p) = p) idp
 
 coe-comp : (p q : base = base) (z : Z) ->
-    coe (\i -> code (comp' p q @ i)) left z right =
+    coe (\i -> code (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-comp p q z = J (\x s -> coe (\i -> code (p * s @ i)) left z right =
+    coe (\i -> code (s @ i)) left (coe (\i -> code (p @ i)) left z right) right) idp 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
+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 (\x s -> (y : code x) ->
+    coe (\i -> code (inv s @ i)) left y right = coe (\i -> code (s @ i)) right y left) (\_ -> idp)
 
-decode-encode-base : (z : Z) -> encode base (wind z) = z
-decode-encode-base (positive zero) = idp Z (positive zero)
+decode-encode-base : (z : Z) -> encode (wind z) = z
+decode-encode-base (positive zero) = idp
 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)))
+    coe-comp (wind (positive x)) (path loop) (positive zero) * map succ (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)))
-    )
+    
+    encode (wind (negative (suc x)))
+    
+  ==< idp >==
+    
+    coe (\i -> code (wind (negative x) * inv (path loop) @ i)) left (positive zero) right
+    
+  ==< coe-comp (wind (negative x)) (inv (path loop)) (positive zero) >==
+    
+    coe (\i -> code (inv (path loop) @ i)) left (coe (\i -> code (wind (negative x) @ i)) left (positive zero) right) right
+    
+  ==< coe-inv (path loop) (coe (\i -> code (wind (negative x) @ i)) left (positive zero) right) >==
+    
+    coe (\i -> code (loop i)) right (coe (\i -> code (wind (negative x) @ i)) left (positive zero) right) left
+    
+  ==< idp >==
+    
+    pred (encode (wind (negative x)))
+    
+  ==< map pred (decode-encode-base (negative x)) >==
+    
+    pred (negative x)
+    
+  ==< idp >==
+    
+    negative (suc x)
+    
+  !qed
 
-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
+Prop-Contr : {A : Prop} (a a' : A) -> a = a'
+Prop-Contr _ _ _ = contr
+
+Circle-elim-Prop : (P : Circle -> Prop) (b : P base) -> (x : Circle) -> P x
+Circle-elim-Prop P b base     = b
+Circle-elim-Prop P b (loop i) = 
+    coe  (\j -> Path (\k -> P (loop k)) b (Prop-Contr (transport P (path loop) b) b @ 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))
+decode-encode : (x : Circle) (z : code x) -> encode (decode x z) = z
+decode-encode = Circle-elim-Prop (\x -> (z : code x) -> encode (decode x z) = z) decode-encode-base
 
 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))
+Circle-loop-space-is-Z = path (iso (base = base) Z encode (decode base) encode-decode (decode-encode base))
diff --git a/examples/hlevel.hoq b/examples/hlevel.hoq
--- a/examples/hlevel.hoq
+++ b/examples/hlevel.hoq
@@ -1,3 +1,5 @@
+import Paths
+
 data Nat = zero | suc Nat
 
 data Sigma (A : Type) (B : A -> Type) = pair (a : A) (B a)
@@ -27,33 +29,11 @@
 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')
+contr-prop A (pair c f) a a' = inv (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-h1 A f a a' = pair (inv (f a a) * f a a') (J (\x q -> inv (f a a) * f a x = q) (inv-comp (f 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')
@@ -62,15 +42,15 @@
 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'
+    -> transport B p b = b' -> Path (\_ -> Sigma A B) (pair a b) (pair a' b')
+Sigma-eq A B a a' b b' p = J
+    (\a' p -> (b' : B a') -> transport B p b = b' -> Path (\_ -> Sigma A B) (pair a b) (pair a' b'))
+    (\b' q -> path (\i -> pair a (q @ i))) 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))
+        (transport (\a -> (a' : A) -> a = a') (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
diff --git a/examples/lem.hoq b/examples/lem.hoq
--- a/examples/lem.hoq
+++ b/examples/lem.hoq
@@ -1,3 +1,5 @@
+import Paths
+
 data E
 data S = s
 data B = true | false
@@ -18,20 +20,13 @@
 not-not false = path (\_ -> false)
 
 biso : I -> Type
-biso i = iso B B not not not-not not-not i
+biso = iso B B not not not-not not-not
 
 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)))))
+not-lem f = not-eq (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)))
diff --git a/hoq.cabal b/hoq.cabal
--- a/hoq.cabal
+++ b/hoq.cabal
@@ -1,12 +1,12 @@
 name:                hoq
-version:             0.1.0.0
-synopsis:            A language based on homotopy type theory with an interval object
+version:             0.2
+synopsis:            A language based on homotopy type theory with an interval type
 -- description:         
 tested-with:         GHC == 7.6.3
 homepage:            http://github.com/valis/hoq
 license:             GPL-2
 license-file:        LICENSE
-author:              isaev
+author:              Valery Isaev
 maintainer:          valery.isaev@gmail.com
 category:            Dependent Types
 build-type:          Custom
@@ -14,7 +14,7 @@
 data-dir:            data
 data-files:          hoq.vim
 extra-source-files:  README.md,
-                     src/Syntax/Grammar.cf,
+                     examples/Paths.hoq,
                      examples/basics.hoq,
                      examples/hlevel.hoq,
                      examples/circle.hoq,
@@ -29,27 +29,29 @@
   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,
+                       Syntax, Syntax.Term, Syntax.Parser,
+                       Syntax.PrettyPrinter, Syntax.ErrorDoc,
+                       Syntax.Parser.Lexer, Syntax.Parser.Parser,
+                       Semantics, Semantics.Value,
                        TypeChecking.Definitions.DataTypes,
                        TypeChecking.Definitions.Functions,
-                       TypeChecking.Definitions.Conditions,
                        TypeChecking.Definitions.Termination,
                        TypeChecking.Definitions,
+                       TypeChecking.Expressions.Utils,
+                       TypeChecking.Expressions.Patterns,
+                       TypeChecking.Expressions.Coverage,
+                       TypeChecking.Expressions.Conditions,
                        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,
+  build-depends:       base >=4 && <5, mtl >=2.1, filepath >=1.3,
+                       bytestring >=0.10, void >= 0.6,
+                       bifunctors >= 4.0,
+                       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
+                       alex >= 2.3.1
   hs-source-dirs:      src
   default-language:    Haskell2010
diff --git a/src/File/Load.hs b/src/File/Load.hs
--- a/src/File/Load.hs
+++ b/src/File/Load.hs
@@ -3,33 +3,64 @@
     ) where
 
 import System.IO
+import System.FilePath
+import Control.Monad
 import Control.Monad.Fix
 import Control.Monad.Trans
+import Control.Monad.State
 import Control.Exception
+import qualified Data.ByteString as B
 
-import Syntax.BNFC.ErrM
-import Syntax.BNFC.ParGrammar
-import Syntax.BNFC.LayoutGrammar
+import Syntax
+import Syntax.Parser
 import Syntax.ErrorDoc
 import Syntax.PrettyPrinter()
-import Syntax.Expr
+import TypeChecking.Expressions.Utils
 import TypeChecking.Definitions
 import TypeChecking.Monad
 
-loadFile :: (MonadIO m, MonadFix m) => String -> ScopeM m ()
+loadFile :: (MonadIO m, MonadFix m) => String -> ScopeT m [(Name,Fixity)]
 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
+    ((errs, _), (_, tab)) <- runStateT (runWarnT $ loadFile' [] filename) ([],[])
+    liftIO $ mapM_ (\(fn, err) -> hPutStrLn stderr $ erenderWithFilename fn $ errorMsg err) errs
+    return tab
 
-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
+loadFile' :: (MonadIO m, MonadFix m) => [String] -> String
+    -> WarnT [(String,Error)] (StateT ([String],[(Name,Fixity)]) (ScopeT m)) ()
+loadFile' checking filename = do
+    mcnt <- liftIO $ fmap Right (B.readFile filename)
+                    `catch` \e -> return $ Left $ show (e :: SomeException)
+    case mcnt of
+        Right cnt -> parseDefs filename checking cnt
+        Left err  -> warn [(filename, Error Other $ emsg err enull)]
+
+parseDefs :: (MonadIO m, MonadFix m) => String -> [String] -> B.ByteString
+    -> WarnT [(String,Error)] (StateT ([String],[(Name,Fixity)]) (ScopeT m)) ()
+parseDefs cur checking s = do
+    defs <- mapWarnT (map $ \e -> (cur,e)) (pDefs s)
+    defs' <- forM defs $ \def -> case def of
+        DefImport moduleName -> do
+            let filename = foldr1 combine moduleName <.> "hoq"
+            if filename `elem` checking
+                then warn [(cur, Error Other $ emsg ("Modules " ++ cur ++ " and " ++ filename ++ " form a cycle") enull)]
+                else do
+                    (checked,_) <- lift get
+                    if filename `elem` checked then return () else loadFile' (cur:checking) filename
+            return def
+        DefFixity pos inf pr ops -> do
+            forM_ ops $ \op -> do
+                (fns,tab) <- lift get
+                case lookup op tab of
+                    Just ft ->
+                        let msg = "Multiple fixity declarations for " ++ nameToInfix op ++ " [" ++ show ft ++ "]"
+                        in warn [(cur, Error Other $ emsgLC pos msg enull)]
+                    Nothing -> return ()
+                lift $ put (fns, (op, Infix inf pr):tab)
+            return def
+        _ -> lift get >>= \(_,tab) -> mapWarnT (map $ \e -> (cur,e)) (fixFixityDef tab def)
+    lift $ modify $ \(fns,tab) -> (cur:fns,tab)
+    (es,mr) <- lift $ lift $ runWarnT (typeCheckDefs defs')
+    let es' = map (\e -> (cur,e)) es
+    case mr of
+        Nothing -> throwError es'
+        Just r -> warn es' >> return r
diff --git a/src/Main.hs b/src/Main.hs
--- a/src/Main.hs
+++ b/src/Main.hs
@@ -9,4 +9,6 @@
 main :: IO ()
 main = do
     args <- getArgs
-    runScopeT $ mapM_ loadFile args >> repl
+    runScopeT $ do
+        tabs <- mapM loadFile args
+        repl (concat tabs)
diff --git a/src/Normalization.hs b/src/Normalization.hs
--- a/src/Normalization.hs
+++ b/src/Normalization.hs
@@ -1,104 +1,103 @@
 module Normalization
     ( NF(..), nf
-    , nfType, nfScope
+    , nfType
     ) where
 
 import Control.Monad
 import Data.Traversable
 
-import Syntax.Term
+import Semantics
+import qualified Syntax as S
+import Semantics.Value
 
-data NF = NF | HNF | WHNF deriving Eq
+data NF = NF | Step | 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)
+nf :: Eq a => NF -> Term Semantics a -> Term Semantics a
+nf mode (Var a ts) = Var a (nfs mode ts)
+nf mode (Apply t ts) = nfSemantics mode t ts
+nf mode (Lambda t) = Lambda $ if mode == WHNF then t else nf mode t
 
-nfType :: Eq a => NF -> Type a -> Type a
-nfType mode (Type t lvl) = Type (nf mode t) lvl
+nfSemantics :: Eq a => NF -> Semantics -> [Term Semantics a] -> Term Semantics a
+nfSemantics mode (Semantics (S.Lam (_:vs)) Lam) (Lambda a@Lambda{} : t : ts) =
+    nfStep mode $ Apply (Semantics (S.Lam vs) Lam) (instantiate1 t a : ts)
+nfSemantics mode (Semantics _ Lam) (Lambda s : t : ts) = nfStep mode $ apps (instantiate1 t s) ts
+nfSemantics mode t@(Semantics _ (Con (DCon _ _ (PatEval conds)))) ts = case instantiateClauses conds ts of
+    Just (t', ts')  -> nfStep mode (apps t' ts')
+    _               -> Apply t (nfs mode ts)
+nfSemantics mode (Semantics _ (FunCall _ (SynEval (Closed t)))) ts = nfStep mode (apps t ts)
+nfSemantics mode t@(Semantics _ (FunCall _ (PatEval clauses))) ts = case instantiateClauses clauses ts of
+    Just (t', ts')  -> nfStep mode (apps t' ts')
+    _               -> Apply t (nfs mode ts)
+nfSemantics mode t@(Semantics _ At) (t1:t2:t3:t4:ts) = case (nf WHNF t3, nf WHNF t4) of
+    (_, Apply (Semantics _ (Con (ICon ILeft)))  _) -> nfStep mode (apps t1 ts)
+    (_, Apply (Semantics _ (Con (ICon IRight))) _) -> nfStep mode (apps t2 ts)
+    (Apply (Semantics _ (Con PCon)) [t3'], t4')    -> nfStep mode $ apps t3' (t4':ts)
+    (t3', t4')                               -> Apply t $ nfs mode (t1:t2:t3':t4':ts)
+nfSemantics mode t@(Semantics _ Coe) (t1:t2:t3:t4:ts) =
+    let t1' = nf WHNF t1
+        t2' = nf NF t2
+        t4' = nf NF t4
+        isICon c (Apply (Semantics _ (Con (ICon c'))) _) = c == c'
+        isICon _ _ = False
+        r = Apply t $ if mode == WHNF then t1':t2':t3:t4':ts else nf mode t1' : t2' : nf mode t3 : t4' : map (nf mode) ts
+    in case (t2' == t4' || isStationary t1', isICon ILeft  t2' && isICon IRight t4',
+                                             isICon IRight t2' && isICon ILeft  t4', t1') of
+        (True, _, _, _) -> nfStep mode (apps t3 ts)
+        (_, True, _, (Apply (Semantics _ Iso) [_,_,c,_,_,_])) -> nfStep mode $ apps c (t3:ts)
+        (_, _, True, (Apply (Semantics _ Iso) [_,_,_,c,_,_])) -> nfStep mode $ apps c (t3:ts)
+        (_, b1, b2, _) | b1 || b2 -> case nf NF $ apps (fmap Free t1') [bvar] of
+            Apply (Semantics _ Iso) [c1, c2, c3, c4, c5, c6, Var Bound []] -> case map sequenceA [c1,c2,c3,c4,c5,c6] of
+                [Free{}, Free{}, Free c3', Free c4', Free{}, Free{}] -> nfStep mode $ apps (if b1 then c3' else c4') (t3:ts)
+                _ -> r
+            _ -> r
+        _ -> r
+nfSemantics mode t@(Semantics _ Iso) ts@[t1,t2,_,_,_,_,t7] = case nf WHNF t7 of
+    Apply (Semantics _ (Con (ICon ILeft)))  _ -> nfStep mode t1
+    Apply (Semantics _ (Con (ICon IRight))) _ -> nfStep mode t2
+    _                                   -> Apply t (nfs mode ts)
+nfSemantics mode t@(Semantics _ Squeeze) [t1,t2] = case (nf WHNF t1, nf WHNF t2) of
+    (Apply t@(Semantics _ (Con (ICon ILeft)))  _, _)  -> capply t
+    (Apply (Semantics _ (Con (ICon IRight))) _, j)    -> if mode == Step then j else nf mode j
+    (_, Apply t@(Semantics _ (Con (ICon ILeft)))  _)  -> capply t
+    (i, Apply (Semantics _ (Con (ICon IRight))) _)    -> if mode == Step then i else nf mode i
+    (t1',t2')                                   -> Apply t $ nfs mode [t1',t2']
+nfSemantics mode t@(Semantics _ (Case pats)) (term:terms) =
+    let (terms1,terms2) = splitAt (length pats) terms
+    in case instantiateCaseClauses (zipWith (\pat te -> ([pat], te)) pats terms1) [term] of
+        Just (t', ts')  -> nfStep mode $ apps t' (ts' ++ terms2)
+        _               -> Apply t $ nfs mode (term:terms)
+nfSemantics mode a as = Apply a (nfs mode as)
 
-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)
+nfStep :: Eq a => NF -> Term Semantics a -> Term Semantics a
+nfStep Step t = t
+nfStep mode t = nf mode t
 
-isStationary :: Eq a => Term a -> Bool
-isStationary t = case sequenceA (nf NF $ App (fmap Free t) $ Var Bound) of
-    Free _ -> True
-    Bound  -> False
+nfType :: Eq a => NF -> Type Semantics a -> Type Semantics a
+nfType mode (Type t lvl) = Type (nf mode t) lvl
 
-nfs :: Eq a => NF -> [Term a] -> [Term a]
-nfs NF terms = map (nf NF) terms
-nfs _  terms = terms
+isStationary :: Eq a => Term Semantics a -> Bool
+isStationary t = case sequenceA $ nf NF $ apps (fmap Free t) [bvar] of
+    Free _  -> True
+    Bound   -> False
 
-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)
+nfs :: Eq a => NF -> [Term Semantics a] -> [Term Semantics a]
+nfs WHNF terms = terms
+nfs mode terms = map (nf mode) terms
+
+instantiatePat :: Eq a => [Term (s, SCon) t] -> Term Semantics a -> [Term Semantics a] -> Maybe (Term Semantics a, [Term Semantics a])
+instantiatePat [] Lambda{} _ = Nothing
+instantiatePat [] term terms = Just (term, terms)
+instantiatePat (Var{} : pats) (Lambda s) (term:terms) = instantiatePat pats (instantiate1 term s) terms
+instantiatePat (Apply (_, con) pats1 : pats) s (term:terms) = case nf WHNF term of
+    Apply (Semantics _ (Con con')) terms1 | con == con' && length pats1 == length terms1 ->
+        instantiatePat (pats1 ++ pats) s (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
+instantiateClauses :: Eq a => [([Term (s, SCon) t], Closed (Term Semantics))]
+    -> [Term Semantics a] -> Maybe (Term Semantics a, [Term Semantics a])
+instantiateClauses clauses terms = msum $ map (\(pats, Closed s) -> instantiatePat pats s terms) clauses
+
+instantiateCaseClauses :: Eq a => [([Term (s, SCon) t], Term Semantics a)]
+    -> [Term Semantics a] -> Maybe (Term Semantics a, [Term Semantics a])
+instantiateCaseClauses clauses terms = msum $ map (\(pats, s) -> instantiatePat pats s terms) clauses
diff --git a/src/REPL.hs b/src/REPL.hs
--- a/src/REPL.hs
+++ b/src/REPL.hs
@@ -8,38 +8,38 @@
 import Control.Monad
 import Control.Monad.Trans
 import Text.PrettyPrint
+import qualified Data.ByteString.Char8 as C
+import Data.Bifunctor
 
-import Syntax.BNFC.ParGrammar
-import Syntax.BNFC.ErrM
-import Syntax.Term
+import Syntax
+import Semantics
+import Syntax.Parser
 import Syntax.PrettyPrinter
 import Syntax.ErrorDoc
 import TypeChecking.Monad
 import TypeChecking.Expressions
+import TypeChecking.Expressions.Utils
 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)
+ep :: [(Name,Fixity)] -> NF -> String -> ScopeT IO ()
+ep tab mode str = do
+    mres <- runWarnT $ do
+        term <- pExpr tab (C.pack str)
+        (term',_) <- typeCheck term Nothing
+        return term'
     liftIO $ case mres of
-        ([], Nothing)   -> return ()
-        ([], Just term) -> putStrLn $ render $ ppTerm (nf mode term)
-        (errs, _)       -> mapM_ (hPutStrLn stderr . erender) errs
+        ([], Just term) -> putStrLn $ render $ ppTerm $ first syntax (nf mode term)
+        (errs, _)       -> mapM_ (hPutStrLn stderr . erender . errorMsg) 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
+processCmd :: [(Name,Fixity)] -> String -> String -> ScopeT IO ()
+processCmd _ "quit" _   = liftIO exitSuccess
+processCmd tab "nf"   str = ep tab NF str
+processCmd tab "step" str = ep tab Step str
+processCmd tab "whnf" str = ep tab WHNF str
+processCmd _ cmd _ = liftIO $ hPutStrLn stderr $ "Unknown command " ++ cmd
 
-repl :: ScopeM IO ()
-repl = go ""
+repl :: [(Name,Fixity)] -> ScopeT IO ()
+repl tab = go ""
   where
     go last = do
         mline <- liftIO $ readline "> "
@@ -49,5 +49,5 @@
                 ("",_)      -> go last
                 (c:cmd,line') -> do
                     when (line /= last) $ liftIO (addHistory line)
-                    if c == ':' then processCmd cmd line' else ep NF line
+                    if c == ':' then processCmd tab cmd line' else ep tab NF line
                     go line
diff --git a/src/Semantics.hs b/src/Semantics.hs
new file mode 100644
--- /dev/null
+++ b/src/Semantics.hs
@@ -0,0 +1,164 @@
+{-# LANGUAGE FlexibleInstances #-}
+
+module Semantics
+    ( Semantics(..), Type(..)
+    , SCon, SValue, SEval
+    , cmpTerms, pcmpTerms
+    , dropOnePi, iCon, universe
+    , path, interval
+    , module Syntax.Term
+    ) where
+
+import Prelude.Extras
+import Data.Foldable(Foldable(..))
+import Data.Traversable(Traversable,traverse,sequenceA,fmapDefault,foldMapDefault)
+import Data.Bifunctor
+
+import Syntax.Term
+import qualified Syntax as S
+import Semantics.Value
+
+data Semantics = Semantics
+    { syntax :: S.Syntax
+    , value :: SValue
+    }
+
+type SCon = Con (Closed (Term Semantics))
+type SValue = Value (Closed (Term Semantics))
+type SEval = Eval (Closed (Term Semantics))
+
+instance Eq Semantics where
+    s1 == s2 = value s1 == value s2
+
+data Type p a = Type { getType :: Term p a, getSort :: Sort }
+
+instance Functor  (Type p) where fmap = fmapDefault
+instance Foldable (Type p) where foldMap = foldMapDefault
+
+instance Traversable (Type p) where
+    traverse f (Type t k) = fmap (\t' -> Type t' k) (traverse f t)
+
+cmpTerms :: Eq a => Term Semantics (Either k a) -> Term Semantics (Either n a)
+    -> (Bool, ([(k, Term Semantics a)], [(n, Term Semantics a)]))
+cmpTerms (Var (Right a) as) (Var (Right a') as') = if a == a' then cmpTermsList as as' else (False, ([],[]))
+cmpTerms (Var (Left k) []) t' = (True, (case sequenceA t' of { Left{} -> []; Right r -> [(k,r)] }, []))
+cmpTerms t (Var (Left k) []) = (True, ([], case sequenceA t of { Left{} -> []; Right r -> [(k,r)] }))
+cmpTerms (Var Left{} _) _ = (True, ([], []))
+cmpTerms _ (Var Left{} _) = (True, ([], []))
+cmpTerms (Lambda t) (Lambda t') = flowerResult $ cmpTerms (fmap sequenceA t) (fmap sequenceA t')
+cmpTerms (Apply (Semantics (S.Lam (_:vs)) Lam) [Lambda t]) (Apply (Semantics (S.Lam (_:vs')) Lam) [Lambda t']) =
+    flowerResult $ cmpTerms (Apply (Semantics (S.Lam vs) Lam) [fmap sequenceA t]) (Apply (Semantics (S.Lam vs') Lam) [fmap sequenceA t'])
+cmpTerms (Apply (Semantics (S.Lam (_:vs)) Lam) [Lambda t]) t' =
+    flowerResult $ cmpTerms (Apply (Semantics (S.Lam vs) Lam) [fmap sequenceA t]) (apps (fmap (sequenceA . Free) t') [fmap Right bvar])
+cmpTerms (Apply (Semantics _ Lam) [t]) t' = cmpTerms t t'
+cmpTerms t (Apply (Semantics (S.Lam (_:vs')) Lam) [Lambda t']) =
+    flowerResult $ cmpTerms (apps (fmap (sequenceA . Free) t) [fmap Right bvar]) (Apply (Semantics (S.Lam vs') Lam) [fmap sequenceA t'])
+cmpTerms t (Apply (Semantics _ Lam) [t']) = cmpTerms t t'
+cmpTerms t@(Apply (Semantics _ Pi{}) _) t'@(Apply (Semantics _ Pi{}) _) = first (== Just EQ) (pcmpTerms t t')
+cmpTerms (Apply (Semantics _ (Con PCon)) ts) (Apply (Semantics _ (Con PCon)) ts') = cmpTermsList ts ts'
+cmpTerms (Apply (Semantics _ (Con PCon)) [Apply (Semantics _ Lam) [Lambda (Apply (Semantics _ At) [_, _, t, Var Bound []])]]) t' =
+    flowerResult $ cmpTerms (fmap sequenceA t) (fmap (sequenceA . Free) t')
+cmpTerms t (Apply (Semantics _ (Con PCon)) [Apply (Semantics _ Lam) [Lambda (Apply (Semantics _ At) [_, _, t', Var Bound []])]]) =
+    flowerResult $ cmpTerms (fmap (sequenceA . Free) t) (fmap sequenceA t')
+cmpTerms (Apply (Semantics _ At) (_:_:ts)) (Apply (Semantics _ At) (_:_:ts')) = cmpTermsList ts ts'
+cmpTerms (Apply s ts) (Apply s' ts') = if s == s'
+    then cmpTermsList ts ts'
+    else (not (isInj $ value s) && hasLefts ts || not (isInj $ value s') && hasLefts ts', ([],[]))
+  where
+    isInj :: Value t -> Bool
+    isInj Lam = True
+    isInj Pi{} = True
+    isInj (Con PCon{}) = True
+    isInj (Con ICon{}) = True
+    isInj (Con (DCon _ _ (PatEval []))) = True
+    isInj (Con DCon{}) = False
+    isInj CCon = True
+    isInj FunCall{} = False
+    isInj Universe{} = True
+    isInj DataType{} = True
+    isInj Interval{} = True
+    isInj Path{} = True
+    isInj At{} = False
+    isInj Coe{} = False
+    isInj Iso{} = False
+    isInj Squeeze{} = False
+    isInj Case{} = False
+    
+    hasLefts :: [Term Semantics (Either k a)] -> Bool
+    hasLefts = any $ \t -> case sequenceA t of
+        Left{} -> True
+        Right{} -> False
+cmpTerms _ _ = (False,([],[]))
+
+cmpTermsList :: Eq a => [Term Semantics (Either k a)] -> [Term Semantics (Either n a)]
+    -> (Bool, ([(k, Term Semantics a)], [(n, Term Semantics a)]))
+cmpTermsList as as' = bimap and (bimap concat concat . unzip) $ unzip (zipWith cmpTerms as as')
+
+flowerResult :: (b, ([(k, Term Semantics (Scoped a))], [(n, Term Semantics (Scoped a))]))
+    -> (b, ([(k, Term Semantics a)], [(n, Term Semantics a)]))
+flowerResult (b, (t1,t2)) = (b, (lowerResult t1, lowerResult t2))
+
+lowerResult :: [(k, Term Semantics (Scoped a))] -> [(k, Term Semantics a)]
+lowerResult ts = ts >>= \(k,t) -> case sequenceA t of
+    Free t' -> [(k,t')]
+    Bound -> []
+
+pcmpTerms :: Eq a => Term Semantics (Either k a) -> Term Semantics (Either n a)
+    -> (Maybe Ordering, ([(k, Term Semantics a)], [(n, Term Semantics a)]))
+pcmpTerms (Apply (Semantics (S.Pi e vs) p@Pi{}) [a, b@Lambda{}]) (Apply (Semantics (S.Pi e' vs') p'@Pi{}) [a', b'@Lambda{}]) =
+    fcontraCovariant (pcmpTerms a a') (go vs a b vs' a' b')
+  where
+    go :: Eq a => [String] -> Term Semantics (Either k a) -> Term Semantics (Either k a)
+               -> [String] -> Term Semantics (Either n a) -> Term Semantics (Either n a)
+               -> (Maybe Ordering, ([(k, Term Semantics a)], [(n, Term Semantics a)]))
+    go (_:vs) a (Lambda b) (_:vs') a' (Lambda b') = flowerResult $
+        go vs (fmap (sequenceA . Free) a) (fmap sequenceA b) vs' (fmap (sequenceA . Free) a') (fmap sequenceA b')
+    go vs a b@Lambda{} _ _ b' = pcmpTerms (Apply (Semantics (S.Pi e vs) p) [a, b]) b'
+    go _ _ b vs' a' b'@Lambda{} = pcmpTerms b $ Apply (Semantics (S.Pi e' vs') p') [a', b']
+    go _ _ b _ _ b' = pcmpTerms b b'
+pcmpTerms (Apply (Semantics S.Pi{} p@Pi{}) [a, Lambda b]) (Apply (Semantics S.Pi{} p'@Pi{}) [a', b']) =
+    fcontraCovariant (pcmpTerms a a') $ flowerResult $ pcmpTerms (fmap sequenceA b) (fmap (sequenceA . Free) b')
+pcmpTerms (Apply (Semantics _ Pi{}) [a, b]) (Apply (Semantics _ Pi{}) [a', Lambda b']) =
+    fcontraCovariant (pcmpTerms a a') $ flowerResult $ pcmpTerms (fmap (sequenceA . Free) b) (fmap sequenceA b')
+pcmpTerms (Apply (Semantics _ Pi{}) [a, b]) (Apply (Semantics _ Pi{}) [a', b']) =
+    fcontraCovariant (pcmpTerms a a') (pcmpTerms b b')
+pcmpTerms (Apply (Semantics _ (Universe k)) _) (Apply (Semantics _ (Universe k')) _) = (pcompare k k', ([], []))
+pcmpTerms t t' = first (\b -> if b then Just EQ else Nothing) (cmpTerms t t')
+
+contraCovariant :: Maybe Ordering -> Maybe Ordering -> Maybe Ordering
+contraCovariant (Just LT) (Just r) | r == EQ || r == GT = Just GT
+contraCovariant (Just EQ) (Just r)                      = Just r
+contraCovariant (Just GT) (Just r) | r == LT || r == EQ = Just LT
+contraCovariant _ _                                     = Nothing
+
+fcontraCovariant :: (Maybe Ordering, ([u],[v])) -> (Maybe Ordering, ([u],[v])) -> (Maybe Ordering, ([u],[v]))
+fcontraCovariant (mo1,(us1,vs1)) (mo2,(us2,vs2)) = (contraCovariant mo1 mo2, (us1 ++ us2, vs1 ++ vs2))
+
+instance Eq a => Eq (Term Semantics a) where
+    t == t' = fst $ cmpTerms (fmap Right t) (fmap Right t')
+
+instance Eq1 (Term Semantics) where (==#) = (==)
+
+instance Eq a => Eq (Type Semantics a) where
+    Type t _ == Type t' _ = t == t'
+
+instance Eq a => POrd (Term Semantics a) where
+    pcompare t t' = fst $ pcmpTerms (fmap Right t) (fmap Right t')
+
+dropOnePi :: Semantics -> Term Semantics a -> Term Semantics a -> (String, Term Semantics (Scoped a))
+dropOnePi (Semantics (S.Pi _ [v]) _) a (Lambda b) = (v, b)
+dropOnePi (Semantics (S.Pi e (v:vs)) s) a (Lambda b) = (v, Apply (Semantics (S.Pi e vs) s) [fmap Free a, b])
+dropOnePi _ _ b = ("_", fmap Free b)
+
+iCon :: ICon -> Term Semantics a
+iCon ILeft  = capply $ Semantics (S.Name S.Prefix $ S.Ident "left")  $ Con (ICon ILeft)
+iCon IRight = capply $ Semantics (S.Name S.Prefix $ S.Ident "right") $ Con (ICon IRight)
+
+path :: [Term Semantics a] -> Term Semantics a
+path = Apply $ Semantics (S.Name S.Prefix $ S.Ident "path") (Con PCon)
+
+interval :: Term Semantics a
+interval = capply $ Semantics (S.Name S.Prefix $ S.Ident "I") Interval
+
+universe :: Sort -> Term Semantics a
+universe k = capply $ Semantics (S.Name S.Prefix $ S.Ident $ show k) (Universe k)
diff --git a/src/Semantics/Value.hs b/src/Semantics/Value.hs
new file mode 100644
--- /dev/null
+++ b/src/Semantics/Value.hs
@@ -0,0 +1,147 @@
+module Semantics.Value
+    ( Value(..), Eval(..)
+    , Level(..), level
+    , Con(..), ICon(..)
+    , ID, Sort(..)
+    , POrd(..), DOrd(..), lessOrEqual
+    ) where
+
+import Syntax.Term
+
+data Value t
+    = Lam
+    | Pi Sort Sort
+    | Con (Con t)
+    | CCon
+    | FunCall ID (Eval t)
+    | Universe Sort
+    | DataType ID Int
+    | Interval
+    | Path Sort
+    | At
+    | Coe
+    | Iso
+    | Squeeze
+    | Case [Term (String, Con t) String]
+
+data Con t = DCon Int Int (Eval t) | PCon | ICon ICon
+data ICon = ILeft | IRight deriving Eq
+
+data Eval t = SynEval t | PatEval [([Term (String, Con t) String], t)]
+
+type ID = Int
+data Level = Level Int | NoLevel
+data Sort = TypeK Level | Set Level | Prop | Contr deriving Eq
+
+instance Eq (Value t) where
+    Lam == Lam = True
+    Pi{} == Pi{} = True
+    Con c == Con c' = c == c'
+    CCon == CCon = True
+    FunCall n _ == FunCall n' _ = n == n'
+    Universe k == Universe k' = k == k'
+    DataType n _ == DataType n' _ = n == n'
+    Interval == Interval = True
+    Path{} == Path{} = True
+    At == At = True
+    Coe == Coe = True
+    Iso == Iso = True
+    Squeeze == Squeeze = True
+    Case pats == Case pats' = and (zipWith cmpPats pats pats')
+      where
+        cmpPats :: Term (s, Con t) u -> Term (s', Con t) u' -> Bool
+        cmpPats Var{} Var{} = True
+        cmpPats (Apply (_,c) pats) (Apply (_,c') pats') = c == c' && and (zipWith cmpPats pats pats')
+        cmpPats _ _ = False
+    _ == _ = False
+
+instance Eq (Con t) where
+    DCon i _ _ == DCon i' _ _ = i == i'
+    ICon c == ICon c' = c == c'
+    PCon == PCon = True
+    _ == _ = False
+
+instance Eq Level where
+    l1 == l2 = level l1 == level l2
+
+instance Ord Level where
+    compare l1 l2 = compare (level l1) (level l2)
+
+instance Show Level where
+    show NoLevel = ""
+    show (Level l) = show l
+
+instance Read Level where
+    readsPrec _ s = case reads s of
+        [] -> [(NoLevel, s)]
+        is -> map (\(i,r) -> (Level i, r)) is
+
+instance Enum Level where
+    toEnum 0 = NoLevel
+    toEnum n = Level n
+    fromEnum = level
+
+level :: Level -> Int
+level (Level l) = l
+level NoLevel = 0
+
+class POrd a where
+    pcompare :: a -> a -> Maybe Ordering
+
+class POrd a => DOrd a where
+    dmax :: a -> a -> a
+    dmaximum :: [a] -> a
+    dmaximum [] = error "dmaximum: empty list"
+    dmaximum xs = foldl1 dmax xs
+
+lessOrEqual :: POrd a => a -> a -> Bool
+lessOrEqual t t' = case pcompare t t' of
+    Just r | r == EQ || r == LT -> True
+    _                           -> False
+
+instance POrd Sort where
+    pcompare Contr Contr = Just EQ
+    pcompare Contr _ = Just LT
+    pcompare _ Contr = Just GT
+    pcompare Prop Prop = Just EQ
+    pcompare Prop _ = Just LT
+    pcompare _ Prop = Just GT
+    pcompare (Set a) (Set b) = Just (compare a b)
+    pcompare (TypeK a) (TypeK b) = Just (compare a b)
+    pcompare (Set a) (TypeK b) = if a <= b then Just LT else Nothing
+    pcompare (TypeK a) (Set b) = if a >= b then Just GT else Nothing
+
+instance DOrd Sort where
+    dmax a b = case pcompare a b of
+        Just LT -> b
+        Just _  -> a
+        Nothing -> case (a, b) of
+            (Set l1, TypeK l2)  -> TypeK (max l1 l2)
+            (TypeK l1, Set l2)  -> TypeK (max l1 l2)
+            _                   -> a
+    dmaximum [] = TypeK NoLevel
+    dmaximum ks = foldl1 dmax ks
+
+instance Show Sort where
+    show Contr = "Contr"
+    show Prop = "Prop"
+    show (Set a) = "Set" ++ show a
+    show (TypeK a) = "Type" ++ show a
+
+instance Read Sort where
+    readsPrec _ ('C':'o':'n':'t':'r':s) = [(Contr,s)]
+    readsPrec _ ('P':'r':'o':'p':s) = [(Prop,s)]
+    readsPrec _ ('S':'e':'t':s) = map (\(l,s) -> (Set l, s)) (reads s)
+    readsPrec _ ('T':'y':'p':'e':s) = map (\(l,s) -> (TypeK l, s)) (reads s)
+    readsPrec _ _ = []
+
+instance Enum Sort where
+    succ Contr = Prop
+    succ Prop = Set NoLevel
+    succ (Set l) = TypeK (succ l)
+    succ (TypeK l) = TypeK (succ l)
+    toEnum n = TypeK (toEnum n)
+    fromEnum Contr = -2
+    fromEnum Prop = -1
+    fromEnum (Set l) = fromEnum l
+    fromEnum (TypeK l) = fromEnum l
diff --git a/src/Syntax.hs b/src/Syntax.hs
new file mode 100644
--- /dev/null
+++ b/src/Syntax.hs
@@ -0,0 +1,70 @@
+module Syntax
+    ( Syntax(..), Explicit(..)
+    , RawExpr, PIdent(..)
+    , Clause(..), Con(..)
+    , Import, Def(..), Tele(..)
+    , Infix(..), Fixity(..)
+    , Posn, Name(..), PName
+    , nameToString, nameToInfix, nameToPrefix
+    , module Syntax.Term
+    ) where
+
+import Data.Void
+
+import Syntax.Term
+
+data PIdent = PIdent { getPos :: Posn, getName :: String }
+data Clause = Clause PName [Term PName Void] RawExpr
+type Import = [String]
+data Tele = VarsTele [PIdent] RawExpr | TypeTele RawExpr
+data Con = ConDef PIdent [Tele]
+data Infix = InfixL | InfixR | InfixNA deriving Eq
+data Fixity = Infix Infix Int | Prefix deriving Eq
+
+type Posn = (Int, Int)
+data Name = Ident String | Operator String deriving Eq
+type PName = (Posn, Name)
+
+data Def
+    = DefType PName RawExpr
+    | DefFun PName [Term PName Void] (Maybe RawExpr)
+    | DefData PName [Tele] [Con] [Clause]
+    | DefImport Import
+    | DefFixity Posn Infix Int [Name]
+
+data Syntax
+    = Lam [String]
+    | Pi Explicit [String]
+    | PathImp
+    | At
+    | Name Fixity Name
+    | Case [Term PName String]
+    | Null
+
+data Explicit = Explicit | Implicit deriving Eq
+
+type RawExpr = Term (Posn, Syntax) Void
+
+instance Eq PIdent where
+    PIdent _ s == PIdent _ s' = s == s'
+
+instance Show Infix where
+    show InfixL = "infixl"
+    show InfixR = "infixr"
+    show InfixNA = "infix"
+
+instance Show Fixity where
+    show (Infix ia p) = show ia ++ " " ++ show p
+    show Prefix = "prefix"
+
+nameToString :: Name -> String
+nameToString (Ident s) = s
+nameToString (Operator s) = s
+
+nameToInfix :: Name -> String
+nameToInfix (Ident s) = "`" ++ s ++ "`"
+nameToInfix (Operator s) = s
+
+nameToPrefix :: Name -> String
+nameToPrefix (Ident s) = s
+nameToPrefix (Operator s) = "(" ++ s ++ ")"
diff --git a/src/Syntax/BNFC/LexGrammar.x b/src/Syntax/BNFC/LexGrammar.x
deleted file mode 100644
--- a/src/Syntax/BNFC/LexGrammar.x
+++ /dev/null
@@ -1,209 +0,0 @@
--- -*- 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
-                        ]
-}
diff --git a/src/Syntax/BNFC/ParGrammar.y b/src/Syntax/BNFC/ParGrammar.y
deleted file mode 100644
--- a/src/Syntax/BNFC/ParGrammar.y
+++ /dev/null
@@ -1,215 +0,0 @@
--- 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
-}
-
diff --git a/src/Syntax/Expr.hs b/src/Syntax/Expr.hs
deleted file mode 100644
--- a/src/Syntax/Expr.hs
+++ /dev/null
@@ -1,43 +0,0 @@
-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
diff --git a/src/Syntax/Grammar.cf b/src/Syntax/Grammar.cf
deleted file mode 100644
--- a/src/Syntax/Grammar.cf
+++ /dev/null
@@ -1,81 +0,0 @@
-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|'\''|'_'|'-')*);
diff --git a/src/Syntax/Parser.hs b/src/Syntax/Parser.hs
new file mode 100644
--- /dev/null
+++ b/src/Syntax/Parser.hs
@@ -0,0 +1,85 @@
+module Syntax.Parser
+    ( pDefs, pExpr
+    , fixFixity, fixFixityDef
+    ) where
+
+import Data.Maybe
+import Control.Monad.State
+import qualified Data.ByteString as B
+
+import Syntax
+import Syntax.ErrorDoc
+import Syntax.Parser.Lexer
+import qualified Syntax.Parser.Parser as P
+import TypeChecking.Monad.Warn
+import TypeChecking.Expressions.Utils
+
+pDefs :: Monad m => B.ByteString -> WarnT [Error] m [Def]
+pDefs = liftM reverse . runParser P.pDefs
+
+pExpr :: Monad m => [(Name,Fixity)] -> B.ByteString -> WarnT [Error] m RawExpr
+pExpr tab str = runParser P.pExpr str >>= fixFixity tab
+
+runParser :: Monad m => Parser a -> B.ByteString -> WarnT [Error] m a
+runParser p s = case evalState (runWarnT $ p ((1, 1), s)) [Layout 1] of
+    (errs, Nothing) -> throwError (mapErrs errs)
+    (errs, Just a)  -> warn (mapErrs errs) >> return a
+  where
+    mapErrs = map $ \(pos, err) -> Error Other $ emsgLC pos err enull
+
+data Tree p a = Branch Fixity Name Syntax (Tree p a) (Tree p a) | Leaf (Term (p, Syntax) a)
+
+fixFixity :: Monad m => [(Name,Fixity)] -> Term (Posn, Syntax) a -> WarnT [Error] m (Term (Posn, Syntax) a)
+fixFixity tab = go
+  where
+    go :: Monad m => Term (Posn, Syntax) a -> WarnT [Error] m (Term (Posn, Syntax) a)
+    go = liftM treeToExpr . exprToTree
+    
+    exprToTree :: Monad m => Term (Posn, Syntax) a -> WarnT [Error] m (Tree Posn a)
+    exprToTree (Var a ts) = liftM (Leaf . Var a) (mapM go ts)
+    exprToTree (Lambda t) = liftM (Leaf . Lambda) (go t)
+    exprToTree (Apply (_, Name Infix{} s) [t1, t2]) = do
+        t1' <- exprToTree t1
+        t2' <- go t2
+        let ft = fromMaybe (Infix InfixL 90) (lookup s tab)
+        branch ft s (Name ft s) t1' (Leaf t2')
+    exprToTree (Apply (_, At) [t1,t2]) = do
+        t1' <- exprToTree t1
+        t2' <- go t2
+        branch (Infix InfixL 90) (Operator "@") At t1' (Leaf t2')
+    exprToTree (Apply (_, Null) (t:ts)) = liftM Leaf $ go (apps t ts)
+    exprToTree (Apply s ts) = liftM (Leaf . Apply s) (mapM go ts)
+    
+    treeToExpr :: Tree Posn a -> Term (Posn, Syntax) a
+    treeToExpr (Leaf t) = t
+    treeToExpr (Branch ft _ s t1 t2) =
+        let t1' = treeToExpr t1
+        in Apply (termPos t1', s) [t1', treeToExpr t2]
+    
+    branch :: Monad m => Fixity -> Name -> Syntax -> Tree Posn a -> Tree Posn a -> WarnT [Error] m (Tree Posn a)
+    branch ft@(Infix ia p) n s (Branch ft'@(Infix ia' p') n' s' a1 a2) b | p' < p || p == p' && ia == InfixR && ia' == InfixR = do
+        a2' <- branch ft n s a2 b
+        return (Branch ft' n' s' a1 a2')
+    branch ft@(Infix ia p) n s a@(Branch ft'@(Infix ia' p') n' _ _ _) b | p == p' && not (ia == InfixL && ia' == InfixL) = do
+        let showOp ft'' s'' = nameToInfix s'' ++ " [" ++ show ft'' ++ "]"
+            msg = "Precedence parsing error: cannot mix " ++ showOp ft  n ++
+                                                  " and " ++ showOp ft' n' ++ " in the same infix expression"
+        warn [Error Other $ emsgLC (termPos $ treeToExpr a) msg enull]
+        return (Branch ft n s a b)
+    branch ft name syn a b = return (Branch ft name syn a b)
+
+fixFixityDef :: Monad m => [(Name,Fixity)] -> Def -> WarnT [Error] m Def
+fixFixityDef tab (DefType name expr) = liftM (DefType name) (fixFixity tab expr)
+fixFixityDef tab (DefFun name pats (Just expr)) = liftM (DefFun name pats . Just) (fixFixity tab expr)
+fixFixityDef _ d@DefFun{} = return d
+fixFixityDef tab (DefData name params cons clauses) = do
+    params' <- forM params (fixFixityTele tab)
+    cons' <- forM cons $ \(ConDef con teles) -> liftM (ConDef con) $ forM teles (fixFixityTele tab)
+    clauses' <- forM clauses $ \(Clause name pats expr) -> liftM (Clause name pats) (fixFixity tab expr)
+    return (DefData name params' cons' clauses')
+fixFixityDef _ d@DefImport{} = return d
+fixFixityDef _ d@DefFixity{} = return d
+
+fixFixityTele :: Monad m => [(Name,Fixity)] -> Tele -> WarnT [Error] m Tele
+fixFixityTele tab (VarsTele vars expr) = liftM (VarsTele vars) (fixFixity tab expr)
+fixFixityTele tab (TypeTele      expr) = liftM  TypeTele       (fixFixity tab expr)
diff --git a/src/Syntax/Parser/Lexer.x b/src/Syntax/Parser/Lexer.x
new file mode 100644
--- /dev/null
+++ b/src/Syntax/Parser/Lexer.x
@@ -0,0 +1,164 @@
+{
+module Syntax.Parser.Lexer
+    ( alexScanTokens
+    , Token(..), tokGetPos
+    , Parser, ParserErr
+    , Layout(..)
+    ) where
+
+import Data.Word
+import Data.Char(isAlpha,isSpace)
+import qualified Data.ByteString as B
+import qualified Data.ByteString.Char8 as C
+import Control.Monad.State
+
+import TypeChecking.Monad.Warn
+import Syntax
+}
+
+$alpha      = [a-zA-Z]
+$digit      = [0-9]
+$any        = [\x00-\x10ffff]
+$operator   = [\~\!\@\#\$\%\^\&\*\-\+\=\|\?\<\>\,\.\/\:\;\[\]\{\}]
+@ident      = ($alpha | \_) ($alpha | $digit | \' | \- | \_)*
+@lcomm      = "--".*
+@mcomm      = "{-" ([$any # \-] | \- [$any # \}])* "-}"
+@skip       = $white | @lcomm | @mcomm
+@newline    = \n @skip*
+@with       = "with" @skip*
+@of         = "of" @skip*
+@import     = "import" $white+ @ident ("." @ident)*
+
+:-
+
+[$white # \n]+;
+@lcomm;
+@mcomm;
+
+@import         { \_ s -> TokImport $ breaks '.' $
+                    dropWhile (\c -> not (isAlpha c) && c /= '_') (drop 6 s)        }
+"data"          { \_ _ -> TokData                                                   }
+"case"          { \p _ -> TokCase p                                                 }
+@of             { \_ _ -> TokOf 0                                                   }
+@with           { \_ _ -> TokWith 0                                                 }
+\\              { \p _ -> TokLam p                                                  }
+\(              { \p _ -> TokLParen p                                               }
+\:              { \_ _ -> TokColon                                                  }
+\=              { \_ _ -> TokEquals                                                 }
+\{              { \p _ -> TokLBrace p                                               }
+\}              { \_ _ -> TokRBrace                                                 }
+\;              { \_ _ -> TokSemicolon                                              }
+\)              { \_ _ -> TokRParen                                                 }
+\|              { \_ _ -> TokPipe                                                   }
+\@              { \_ _ -> TokAt                                                     }
+\`              { \_ _ -> TokApos                                                   }
+"->"            { \_ _ -> TokArrow                                                  }
+$operator+      { \p s -> TokOperator (PIdent p s)                                  }
+$digit+         { \p s -> TokInteger (p, read s)                                    }
+"infixl"        { \p _ -> TokInfix (p, InfixL)                                      }
+"infixr"        { \p _ -> TokInfix (p, InfixR)                                      }
+"infix"         { \p _ -> TokInfix (p, InfixNA)                                     }
+@ident          { \p s -> TokIdent (PIdent p s)                                     }
+@newline        { \_ _ -> TokNewLine                                                }
+
+{
+data Token
+    = TokIdent !PIdent
+    | TokOperator !PIdent
+    | TokLam !Posn
+    | TokLParen !Posn
+    | TokImport ![String]
+    | TokData
+    | TokCase !Posn
+    | TokOf !Int
+    | TokColon
+    | TokEquals
+    | TokLBrace !Posn
+    | TokRBrace
+    | TokSemicolon
+    | TokDot
+    | TokRParen
+    | TokPipe
+    | TokAt
+    | TokApos
+    | TokArrow
+    | TokWith !Int
+    | TokNewLine
+    | TokInfix !(Posn, Infix)
+    | TokInteger !(Posn, Int)
+    | TokEOF
+
+tokGetPos :: Token -> Maybe Posn
+tokGetPos (TokIdent (PIdent pos _)) = Just pos
+tokGetPos (TokLam pos) = Just pos
+tokGetPos (TokLParen pos) = Just pos
+tokGetPos (TokOperator (PIdent pos _)) = Just pos
+tokGetPos _ = Nothing
+
+breaks :: Eq a => a -> [a] -> [[a]]
+breaks a as = case break (== a) as of
+    (as1, [])    -> [as1]
+    (as1, _:as2) -> as1 : breaks a as2
+
+type AlexInput = (Posn, B.ByteString)
+
+data Layout = Layout Int | NoLayout deriving Eq
+
+type ParserErr a = WarnT [(Posn, String)] (State [Layout]) a
+type Parser a = AlexInput -> ParserErr a
+
+alexScanTokens :: (Token -> Parser a) -> Parser a
+alexScanTokens cont = go
+  where
+    go inp@(pos,str) = case alexScan inp 0 of
+        AlexEOF             -> cont TokEOF inp
+        AlexError inp'      -> do
+            warn [(pos, "Lexer error")]
+            (go . findAGoodSymbol . skippingTheBadOne) inp'
+        AlexSkip  inp' _    -> go inp'
+        AlexToken inp'@((_, c), _) len act -> case act pos $ C.unpack (B.take len str) of
+            TokNewLine -> do
+                layout:layouts <- lift get
+                case layout of
+                    NoLayout -> go inp'
+                    Layout n -> case compare n c of
+                        LT -> go inp'
+                        EQ -> cont TokSemicolon inp'
+                        GT -> do
+                            lift (put layouts)
+                            cont TokRBrace inp
+            TokRBrace  -> do
+                layout <- lift get
+                if NoLayout `elem` layout
+                then do
+                    lift $ put (tail layout)
+                    cont TokRBrace $ if head layout == NoLayout then inp' else inp
+                else do
+                    warn [(pos, "Misplaced '}'")]
+                    go inp'
+            TokWith{} -> cont (TokWith c) inp'
+            TokOf{} -> cont (TokOf c) inp'
+            tok -> cont tok inp'
+
+findAGoodSymbol :: AlexInput -> AlexInput
+findAGoodSymbol ((l, c), str) =
+    let (f,s) = C.break (\c -> isAlpha c || isSpace c || c `elem` "~!@#$%^&*-+=|?<>,./:l[]{}()\\_") str
+    in ((l, c + B.length f), s)
+
+skippingTheBadOne :: AlexInput -> AlexInput
+skippingTheBadOne inp@((l, c), str) = if B.null str then inp else ((l, c + 1), B.tail str)
+
+alexGetByte :: AlexInput -> Maybe (Word8, AlexInput)
+alexGetByte (pos, str) = fmap (\(h,t) -> (h, (alexMove pos $ C.head str, t))) (B.uncons str)
+
+tabSize :: Int
+tabSize = 4
+
+alexMove :: Posn -> Char -> Posn
+alexMove (l, c) '\t' = (l, ((c + tabSize - 1) `div` tabSize) * tabSize + 1)
+alexMove (l, c) '\n' = (l + 1, 1)
+alexMove (l, c) _    = (l , c + 1)
+
+alexInputPrevChar :: AlexInput -> Char
+alexInputPrevChar = error "alexInputPrevChar"
+}
diff --git a/src/Syntax/Parser/Parser.y b/src/Syntax/Parser/Parser.y
new file mode 100644
--- /dev/null
+++ b/src/Syntax/Parser/Parser.y
@@ -0,0 +1,194 @@
+--
+{
+module Syntax.Parser.Parser
+    ( pDefs, pExpr
+    ) where
+
+import Control.Monad.Trans
+import Control.Monad.State
+import Control.Monad.Error
+import Data.Bifunctor
+import Data.Void
+import Data.Maybe
+
+import Syntax.Parser.Lexer
+import Syntax
+import TypeChecking.Monad.Warn
+}
+
+%name pDefs Defs
+%name pExpr Expr
+%tokentype { Token }
+%error { parseError }
+%monad { Parser } { bind } { return' }
+%lexer { alexScanTokens } { TokEOF }
+
+%token
+    PIdent      { TokIdent    $$    }
+    Import      { TokImport   $$    }
+    Operator    { TokOperator $$    }
+    Infix       { TokInfix    $$    }
+    Integer     { TokInteger  $$    }
+    '\\'        { TokLam      $$    }
+    '('         { TokLParen   $$    }
+    'case'      { TokCase     $$    }
+    'of'        { TokOf       $$    }
+    'data'      { TokData           }
+    ':'         { TokColon          }
+    '='         { TokEquals         }
+    '{'         { TokLBrace   $$    }
+    '}'         { TokRBrace         }
+    ';'         { TokSemicolon      }
+    ')'         { TokRParen         }
+    '|'         { TokPipe           }
+    '@'         { TokAt             }
+    '`'         { TokApos           }
+    '->'        { TokArrow          }
+    'with'      { TokWith     $$    }
+
+%%
+
+Name :: { PName }
+    : PIdent            { (getPos $1, Ident (getName $1))       }
+    | '(' Operator ')'  { (getPos $2, Operator (getName $2))    }
+
+InfixOp :: { PName }
+    : Operator          { (getPos $1, Operator (getName $1))    }
+    | '`' PIdent '`'    { (getPos $2, Ident (getName $2))       }
+
+InfixOps :: { [PName] }
+    : InfixOp           { [$1]  }
+    | InfixOps InfixOp  { $2:$1 }
+
+LBrace :: { Posn }
+    : '{'           {% \_ -> lift  (modify (NoLayout :)) >> return $1 }
+
+with :: { () }
+    : 'with' '{'    {% \_ -> lift $ modify (NoLayout  :) }
+    | 'with' error  {% \_ -> lift $ modify (Layout $1 :) }
+
+of :: { () }
+    : 'of' '{'      {% \_ -> lift $ modify (NoLayout  :) }
+    | 'of' error    {% \_ -> lift $ modify (Layout $1 :) }
+
+Def :: { Def }
+    : Name ':' Expr                                     { DefType $1 $3                                     }
+    | Name Patterns '=' Expr                            { DefFun $1 (reverse $2) (Just $4)                  }
+    | Name Patterns                                     { DefFun $1 (reverse $2) Nothing                    }
+    | 'data' Name Teles                                 { DefData $2 (reverse $3) [] []                     }
+    | 'data' Name Teles '=' Cons                        { DefData $2 (reverse $3) (reverse $5) []           }
+    | 'data' Name Teles '=' Cons with FunClauses '}'    { DefData $2 (reverse $3) (reverse $5) (reverse $7) }
+    | Infix Integer InfixOps                            { DefFixity (fst $1) (snd $1) (snd $2) (map snd $3) }
+    | Import                                            { DefImport $1 }
+
+Defs :: { [Def] }
+    : {- empty -}   { []    }
+    | Def           { [$1]  }
+    | Defs ';'      { $1    }
+    | Defs ';' Def  { $3:$1 }
+
+FunClauses :: { [Clause] }
+    : Name Patterns '=' Expr                { [Clause $1 (reverse $2) $4]       }
+    | FunClauses ';'                        { $1                                }
+    | FunClauses ';' Name Patterns '=' Expr { Clause $3 (reverse $4) $6 : $1    }
+
+Pattern :: { Term PName Void }
+    : PIdent                    { Apply (getPos $1, Ident $ getName $1) []              }
+    | '(' ')'                   { Apply ($1, Operator "") []                            }
+    | '(' PIdent Patterns ')'   { Apply (getPos $2, Ident $ getName $2) (reverse $3)    }
+
+Patterns :: { [Term PName Void] }
+    : {- empty -}       { []    }
+    | Patterns Pattern  { $2:$1 }
+
+Con :: { Con }
+    : PIdent Teles  { ConDef $1 (reverse $2) } 
+
+Cons :: { [Con] }
+    : Con           { [$1]  } 
+    | Cons '|' Con  { $3:$1 }
+
+Tele :: { Tele }
+    : Expr5                     { TypeTele $1                                                               }
+    | '(' Exprs ':' Expr ')'    {% \_ -> mapM exprToVar $2 >>= \vars -> return (VarsTele (reverse vars) $4) }
+
+Teles :: { [Tele] }
+    : {- empty -}   { []    }
+    | Teles Tele    { $2:$1 }
+
+PiTele :: { (Explicit,PiTele) }
+    : '(' Exprs ':' Expr ')'    { (Explicit, PiTele $1 (reverse $2) $4) }
+    | LBrace Exprs ':' Expr '}' { (Implicit, PiTele $1 (reverse $2) $4) }
+
+PiTeles :: { [(Explicit,PiTele)] }
+    : PiTele            { [$1]  }
+    | PiTeles PiTele    { $2:$1 }
+
+PIdents :: { [PIdent] }
+    : PIdent            { [$1]  }
+    | PIdents PIdent    { $2:$1 }
+
+Expr :: { RawExpr }
+    : Expr1                     { $1                                                }
+    | '\\' PIdents '->' Expr    { Apply ($1, Lam $ reverse $ map getName $2) [$4]   }
+
+Expr1 :: { RawExpr }
+    : Expr2                 { $1                                            }
+    | Expr2 '->' Expr1      { Apply (termPos $1, Pi Explicit []) [$1, $3]   }
+    | PiTeles '->' Expr1    {% \_ -> piExpr (reverse $1) $3                 }
+
+Expr2 :: { RawExpr }
+    : Expr3             { $1                                    }
+    | Expr3 '=' Expr3   { Apply (termPos $1, PathImp) [$1,$3]   }
+
+Expr3 :: { RawExpr }
+    : Expr4                 { Apply (termPos $1, Null) [$1]                                 }
+    | Expr3 '@' Expr4       { Apply (termPos $1, At) [$1, $3]                               }
+    | Expr3 InfixOp Expr4   { Apply (termPos $1, Name (Infix InfixL 90) $ snd $2) [$1, $3]  }
+
+Expr4 :: { RawExpr }
+    : Exprs { let e:es = reverse $1 in apps e es }
+
+Exprs :: { [RawExpr] }
+    : Expr5         { [$1]  }
+    | Exprs Expr5   { $2:$1 }
+
+Expr5 :: { RawExpr }
+    : Name                              { Apply (fst $1, Name Prefix $ snd $1) []                                   }
+    | '(' Expr ')'                      { $2                                                                        }
+    | 'case' Expr of CaseClauses '}'    { Apply ($1, Case $ map vacuous $ reverse $ fst $4) ($2 : reverse (snd $4)) }
+
+CaseClauses :: { ([Term PName Void], [RawExpr]) }
+    : Name Patterns '->' Expr                   { ([Apply $1 $2], [$4])                 }
+    | CaseClauses ';'                           { $1                                    }
+    | CaseClauses ';' Name Patterns '->' Expr   { (Apply $3 $4 : fst $1, $6 : snd $1)   }
+
+{
+return' :: a -> Parser a
+return' a _ = return a
+
+bind :: Parser a -> (a -> Parser b) -> Parser b
+bind p k e = p e >>= \a -> k a e
+
+data PiTele = PiTele Posn [RawExpr] RawExpr
+
+piExpr :: [(Explicit,PiTele)] -> RawExpr -> ParserErr RawExpr
+piExpr [] term = return term
+piExpr ((e, PiTele pos t1 t2) : teles) term = do
+    vars <- mapM exprToVar t1
+    term' <- piExpr teles term
+    return $ Apply (pos, Pi e $ map getName vars) [t2,term']
+
+termPos :: RawExpr -> Posn
+termPos (Apply (pos, _) _) = pos
+termPos _ = error "termPos"
+
+exprToVar :: RawExpr -> ParserErr PIdent
+exprToVar (Apply (pos, Name Prefix (Ident v)) []) = return (PIdent pos v)
+exprToVar term = throwError [(termPos term, "Expected a list of identifiers")]
+
+parseError :: Token -> Parser a
+parseError tok (pos,_) = throwError [(maybe pos id (tokGetPos tok), "Syntax error")]
+
+myLexer = alexScanTokens
+}
diff --git a/src/Syntax/Pattern.hs b/src/Syntax/Pattern.hs
deleted file mode 100644
--- a/src/Syntax/Pattern.hs
+++ /dev/null
@@ -1,14 +0,0 @@
-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
diff --git a/src/Syntax/PrettyPrinter.hs b/src/Syntax/PrettyPrinter.hs
--- a/src/Syntax/PrettyPrinter.hs
+++ b/src/Syntax/PrettyPrinter.hs
@@ -1,97 +1,101 @@
+{-# LANGUAGE FlexibleInstances #-}
+
 module Syntax.PrettyPrinter
     ( ppTerm
-    , scopeToTerm
     ) where
 
 import Text.PrettyPrint
-import Data.Foldable
+import Data.Bifunctor
+import Data.Bifoldable
+import Data.Void
 
-import Syntax.Term
+import Syntax
 import qualified Syntax.ErrorDoc as E
 
-instance E.Pretty1 Term where
-    pretty1 t = ppTermCtx (toList $ fmap render t) t
+instance E.Pretty1 (Term Syntax) where
+    pretty1 t = ppTermCtx (freeVars t) t
 
-ppTerm :: Term String -> Doc
-ppTerm t = ppTermCtx (toList t) (fmap text t)
+freeVars :: Term Syntax a -> [String]
+freeVars = biconcatMap (\t -> case t of
+    Name _ (Ident s)    -> [s]
+    _                   -> []) (const [])
 
-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
+ppTerm :: Term Syntax Void -> Doc
+ppTerm t = ppTermCtx (freeVars t) (vacuous t)
 
-ppList :: [String] -> Term Doc -> [Term Doc] -> Doc
-ppList ctx t ts = hsep $ map (ppTermPrec (prec t + 1) ctx) ts
+ppTermCtx :: [String] -> Term Syntax Doc -> Doc
+ppTermCtx ctx (Var d ts) = d <+> ppList ctx ts
+ppTermCtx ctx (Apply s ts) = ppSyntax ctx s ts
+ppTermCtx ctx (Lambda t) = ppTermCtx ctx $ fmap (\v -> case v of
+    Bound -> text "(error: Bound)"
+    Free d -> d) t
 
-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')
+ppSyntax :: [String] -> Syntax -> [Term Syntax Doc] -> Doc
+ppSyntax ctx p@(Pi e vs) (t1:t2:ts) =
+    let r = (if null vs then ppTermPrec (prec p + 1) ctx t1
+            else (if e == Explicit then parens else braces) $ hsep (map text vs) <+> colon <+> ppTermCtx ctx t1)
+            <+> arrow <+> ppBound (prec p) ctx vs t2
+    in if null ts then r else parens r <+> ppList ctx ts
+ppSyntax ctx l@(Lam vs) (t:ts) = bparens (not $ null ts) (text "\\" <> hsep (map text vs) <+> arrow <+> ppBound (prec l) ctx vs t) <+> ppList ctx ts
+ppSyntax ctx t@PathImp [_,t2,t3] = ppTermPrec (prec t + 1) ctx t2 <+> equals <+> ppTermPrec (prec t + 1) ctx t3
+ppSyntax ctx t@At (_:_:t3:t4:ts) = bparens (not $ null ts)
+    (ppTermPrec (prec t) ctx t3 <+> text "@" <+> ppTermPrec (prec t + 1) ctx t4) <+> ppList ctx ts
+ppSyntax ctx t@(Name (Infix ft _) n) (t1:t2:ts) =
+    bparens (not $ null ts) (ppTermPrec (opFixity InfixL ft $ prec t) ctx t1 <+> text (nameToInfix n)
+        <+> ppTermPrec (opFixity InfixR ft $ prec t) ctx t2) <+> ppList ctx ts
+ppSyntax ctx (Name _ n) ts = text (nameToPrefix n) <+> ppList ctx ts
+ppSyntax ctx (Case pats) (expr:terms) = hang (text "case" <+> ppTermCtx ctx expr <+> text "of") 4 $ vcat $
+    map (\(pat,term) -> ppTermCtx ctx (bimap (Name Prefix . snd) text pat) <+> arrow <+>
+        ppBound 0 ctx (bifoldMap (const []) return pat) term) (zip pats terms)
+ppSyntax ctx Null [t] = ppTermCtx ctx t
+ppSyntax _ Null _ = empty
+ppSyntax _ Lam{} [] = error "ppSyntax: Lam"
+ppSyntax _ Pi{} _ = error "ppSyntax: Pi"
+ppSyntax _ PathImp{} _ = error "ppSyntax: PathImp"
+ppSyntax _ At _ = error "ppSyntax: At"
+ppSyntax _ Case{} [] = error "ppSyntax: Case"
 
-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)
+opFixity :: Infix -> Infix -> Int -> Int
+opFixity ft ft' p = if ft == ft' then p else p + 1
 
-ppTermPrec :: Int -> [String] -> Term Doc -> Doc
-ppTermPrec p ctx t = if p > prec t then parens (ppTermCtx ctx t) else ppTermCtx ctx t
+ppList :: [String] -> [Term Syntax Doc] -> Doc
+ppList ctx ts = hsep $ map (ppTermPrec 100 ctx) ts
 
+ppBound :: Int -> [String] -> [String] -> Term Syntax Doc -> Doc
+ppBound p ctx (v:vs) (Lambda t) =
+    let (ctx',v') = renameName2 v ctx (freeVars t)
+    in ppBound p ctx' vs $ instantiate1 (capply $ Name Prefix $ Ident v') t
+ppBound p ctx _ t = ppTermPrec p ctx t
+
+ppTermPrec :: Int -> [String] -> Term Syntax Doc -> Doc
+ppTermPrec p ctx t = bparens (p > precTerm t) (ppTermCtx ctx t)
+
+bparens :: Bool -> Doc -> Doc
+bparens True d = parens d
+bparens False d = d
+
 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
+renameName2 :: String -> [String] -> [String] -> ([String], String)
+renameName2 var ctx ctx' = if var `elem` ctx && var `elem` ctx'
+    then renameName (var ++ "'") ctx'
+    else (var:ctx,var)
+
+prec :: Syntax             -> Int
+prec (Name Prefix _)        = 100
+prec (Name (Infix _ p) _)   = p
+prec At                     = 80
+prec PathImp{}              = 70
+prec Pi{}                   = 60
+prec Lam{}                  = 50
+prec _                      = 0
+
+precTerm :: Term Syntax a -> Int
+precTerm Var{} = 100
+precTerm (Apply Name{} (_:_)) = 90
+precTerm (Apply s _) = prec s
+precTerm (Lambda t) = precTerm t
diff --git a/src/Syntax/Scope.hs b/src/Syntax/Scope.hs
deleted file mode 100644
--- a/src/Syntax/Scope.hs
+++ /dev/null
@@ -1,105 +0,0 @@
-{-# 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)
diff --git a/src/Syntax/Term.hs b/src/Syntax/Term.hs
--- a/src/Syntax/Term.hs
+++ b/src/Syntax/Term.hs
@@ -1,200 +1,96 @@
+{-# LANGUAGE RankNTypes #-}
+
 module Syntax.Term
-    ( Term(..), Type(..)
-    , Level(..), level
-    , Explicit(..), PatternC
-    , module Syntax.Scope, module Syntax.Pattern
-    , POrd(..), lessOrEqual
-    , apps, collect, dropOnePi
+    ( Term(..), Scoped(..)
+    , capply, cvar, bvar, apps
+    , instantiate1
+    , Closed(..), closed
     ) where
 
-import Prelude.Extras
-import Data.Function
-import Data.Traversable hiding (mapM)
-import Data.Foldable hiding (msum)
+import Data.Maybe
+import Data.Monoid
+import Data.Foldable
+import Data.Traversable
+import Data.Bifunctor
+import Data.Bifoldable
+import Data.Bitraversable
 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 p a
+    = Var a [Term p a]
+    | Apply p [Term p a]
+    | Lambda (Term p (Scoped a))
 
-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 Functor  (Term p) where fmap = fmapDefault
+instance Foldable (Term p) where foldMap = foldMapDefault
+instance Bifunctor  Term where bimap = bimapDefault
+instance Bifoldable Term where bifoldMap = bifoldMapDefault
+instance Traversable (Term p) where traverse = bitraverse pure
 
-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 Bitraversable Term where
+    bitraverse f g (Var a ts) = Var <$> g a <*> traverse (bitraverse f g) ts
+    bitraverse f g (Apply p ts) = Apply <$> f p <*> traverse (bitraverse f g) ts
+    bitraverse f g (Lambda t) = Lambda <$> bitraverse f (traverse g) t
 
-instance Eq a => Eq (Type a) where
-    Type t _ == Type t' _ = t == t'
+instance Applicative (Term p) where
+    pure    = cvar
+    (<*>)   = ap
 
-instance Eq1 Term where (==#) = (==)
+instance Monad (Term p) where
+    return           = cvar
+    Var a ts   >>= k = apps (k a) $ map (>>= k) ts
+    Apply p ts >>= k = Apply p $ map (>>= k) ts
+    Lambda s   >>= k = Lambda $ s >>= \v -> case v of
+        Free a -> fmap Free (k a)
+        Bound  -> return Bound
 
-class POrd a where
-    pcompare :: a -> a -> Maybe Ordering
+capply :: p -> Term p a
+capply p = Apply p []
 
-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
+cvar :: a -> Term p a
+cvar a = Var a []
 
-instance Eq a => POrd (Type a) where
-    pcompare (Type t _) (Type t' _) = pcompare t t'
+bvar :: Term p (Scoped a)
+bvar = cvar Bound
 
-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
+apps :: Term s a -> [Term s a] -> Term s a
+apps t [] = t
+apps (Lambda t) (t1:ts) = apps (instantiate1 t1 t) ts
+apps (Apply a as) ts = Apply a (as ++ ts)
+apps (Var a as) ts = Var a (as ++ ts)
 
-lessOrEqual :: POrd a => a -> a -> Bool
-lessOrEqual a b = case pcompare a b of
-    Just r | r == EQ || r == LT -> True
-    _                           -> False
+newtype Closed f = Closed { open :: forall a. f a }
 
-instance Functor  Term where fmap    = fmapDefault
-instance Foldable Term where foldMap = foldMapDefault
+data Scoped a = Free a | Bound
 
-instance Functor  Type where
-    fmap f (Type t l) = Type (fmap f t) l
+instance Eq a => Eq (Scoped a) where
+    Bound == Bound = True
+    Free a == Free a' = a == a'
+    _ == _ = False
 
-instance Applicative Term where
-    pure  = Var
-    (<*>) = ap
+instance Functor Scoped where
+    fmap _ Bound = Bound
+    fmap f (Free a)  = Free (f a)
 
-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 Foldable Scoped where
+    foldMap _ Bound = mempty
+    foldMap f (Free a)  = f a
 
-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
+instance Traversable Scoped where
+    traverse _ Bound = pure Bound
+    traverse f (Free a) = Free <$> f a
 
-apps :: Term a -> [Term a] -> Term a
-apps e [] = e
-apps e1 (e2:es) = apps (App e1 e2) es
+instance Applicative Scoped where
+    pure = Free
+    Bound <*> _ = Bound
+    _ <*> Bound = Bound
+    Free f <*> Free a = Free (f a)
 
-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
+instantiate1 :: Monad f => f a -> f (Scoped a) -> f a
+instantiate1 s t = t >>= \v -> case v of
+    Bound   -> s
+    Free a  -> return a
 
-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
+closed :: Traversable f => f a -> Closed f
+closed t = Closed $ fromJust $ traverse (const Nothing) t
diff --git a/src/TypeChecking/Context.hs b/src/TypeChecking/Context.hs
--- a/src/TypeChecking/Context.hs
+++ b/src/TypeChecking/Context.hs
@@ -4,7 +4,7 @@
 
 import Control.Monad
 
-import Syntax.Scope
+import Syntax.Term
 
 data Ctx s f b a where
     Nil  :: Ctx s f b b
@@ -20,23 +20,37 @@
 
 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'
+lookupCtx b (Snoc ctx s t) = if s == b
     then Just (return Bound, fmap Free t)
-    else fmap (\(te, ty) -> (liftM Free te, fmap Free ty)) (lookupCtx s ctx)
+    else fmap (\(te, ty) -> (liftM Free te, fmap Free ty)) (lookupCtx b ctx)
 
-close :: Monad f => Ctx b g b a -> f a -> f b
+ctxToVars :: Monad g => Ctx s f b a -> [g a]
+ctxToVars = reverse . go
+  where
+    go :: Monad g => Ctx s f b a -> [g a]
+    go Nil = []
+    go (Snoc ctx s _) = return Bound : map (liftM Free) (go ctx)
+
+close :: Functor f => Ctx c g b a -> f (Either c a) -> f (Either c 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
+close (Snoc ctx s _) t = close ctx $ fmap (\v -> case v of
+    Left c          -> Left c
+    Right Bound     -> Left s
+    Right (Free a)  -> Right a) t
 
 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)
+toBase :: Ctx s f b a -> a -> Maybe b
+toBase Nil b = Just b
+toBase Snoc{} Bound = Nothing
+toBase (Snoc ctx _ _) (Free a) = toBase ctx a
+
+ctxVars :: Ctx s f b a -> [s]
+ctxVars Nil = []
+ctxVars (Snoc ctx v _) = v : ctxVars ctx
+
+abstractTerm :: Ctx s f b a -> Term p a -> Term p b
+abstractTerm Nil term = term
+abstractTerm (Snoc ctx v _) term = abstractTerm ctx (Lambda term)
diff --git a/src/TypeChecking/Definitions.hs b/src/TypeChecking/Definitions.hs
--- a/src/TypeChecking/Definitions.hs
+++ b/src/TypeChecking/Definitions.hs
@@ -2,61 +2,47 @@
     ( typeCheckDefs
     ) where
 
-import Control.Monad
-import Control.Monad.Error
+import Control.Monad.Fix
+import Data.Void
 
-import Syntax.Expr as E
-import Syntax.Term as T
+import Syntax
+import Semantics.Value
 import Syntax.ErrorDoc
 import TypeChecking.Expressions
+import TypeChecking.Expressions.Utils
 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) =
+typeCheckDefs (DefImport{} : defs) = typeCheckDefs defs
+typeCheckDefs (DefFixity{} : defs) = typeCheckDefs defs
+typeCheckDefs (DefType p@(pos, name) ty : defs) =
     case span (theSameAs name) defs of
         ([],_) -> do
-            warn [emsgLC lc ("Missing a realization of function " ++ show name) enull]
+            warn [Error Other $ emsgLC pos ("Missing a realization of function " ++ show (nameToString name)) enull]
             typeCheckDefs defs
         (defs1,defs2) -> do
-            typeCheckFunction p ty (map defToPDef defs1)
+            typeCheckFunction p ty (map (\d -> case d of
+                DefFun (pos, _) pats expr -> (pos, pats, expr)
+                _ -> error "typeCheckDefs") defs1)
+                `catchError` \errs -> warn errs >> return ()
             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
+typeCheckDefs (DefFun p@(pos, name) [] (Just expr) : defs) = do
     (term, ty) <- typeCheck expr Nothing
-    addFunctionCheck p (FunSyn name term) ty
+    addFunctionCheck p (SynEval $ closed term) $ Closed (vacuous 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 (DefFun (pos, name) [] Nothing : defs) = do
+    warn [Error Other $ emsgLC pos "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 (DefFun (pos, name) _ _ : defs) = do
+    warn [inferErrorMsg pos "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 (DefData dt ty cons conds : defs) = do
+    typeCheckDataType dt ty cons 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 :: Name -> Def -> Bool
+theSameAs name (DefFun (_, name') _ _) = name == name'
 theSameAs _ _ = False
diff --git a/src/TypeChecking/Definitions/Conditions.hs b/src/TypeChecking/Definitions/Conditions.hs
deleted file mode 100644
--- a/src/TypeChecking/Definitions/Conditions.hs
+++ /dev/null
@@ -1,140 +0,0 @@
-{-# 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]
diff --git a/src/TypeChecking/Definitions/Coverage.hs b/src/TypeChecking/Definitions/Coverage.hs
deleted file mode 100644
--- a/src/TypeChecking/Definitions/Coverage.hs
+++ /dev/null
@@ -1,89 +0,0 @@
-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
diff --git a/src/TypeChecking/Definitions/DataTypes.hs b/src/TypeChecking/Definitions/DataTypes.hs
--- a/src/TypeChecking/Definitions/DataTypes.hs
+++ b/src/TypeChecking/Definitions/DataTypes.hs
@@ -1,4 +1,4 @@
-{-# LANGUAGE RecursiveDo #-}
+{-# LANGUAGE RecursiveDo, ExistentialQuantification #-}
 
 module TypeChecking.Definitions.DataTypes
     ( typeCheckDataType
@@ -7,109 +7,94 @@
 import Control.Monad
 import Control.Monad.Fix
 import Data.List
+import Data.Bifunctor
+import Data.Bifoldable
+import Data.Void
 
-import Syntax.Expr as E
-import Syntax.Term as T
+import Syntax as S
+import Semantics
+import Semantics.Value as V
 import Syntax.ErrorDoc
 import TypeChecking.Monad
 import TypeChecking.Context
 import TypeChecking.Expressions
-import TypeChecking.Definitions.Patterns
-import TypeChecking.Definitions.Conditions
+import TypeChecking.Expressions.Utils
+import TypeChecking.Expressions.Patterns
+import TypeChecking.Expressions.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
+typeCheckDataType :: MonadFix m => PName -> [Tele] -> [S.Con] -> [Clause] -> TCM m ()
+typeCheckDataType p@(pos, 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
+    (SomeEq ctx, dataType@(Type dtTerm _)) <- checkTele Nil params $ universe (Set NoLevel)
+    dtid <- addDataTypeCheck p lcons $ Closed (vacuous dataType)
+    cons' <- forW (zip cons [0..]) $ \(ConDef con@(PIdent pos conName) tele, i) -> do
+        (_, Type conType conSort) <- checkTele ctx tele $ Apply (Semantics (Name Prefix dt) $ DataType dtid lcons) (ctxToVars ctx)
+        case findOccurrence dtid (nf WHNF conType) of
+            Just n | n > 1 -> throwError [Error Other $ emsgLC pos "Data type is not strictly positive" enull]
+            _ -> return ()
+        let conds'' = map snd $ filter (\(c,_) -> c == conName) conds'
+            conTerm = Semantics (Name Prefix $ Ident conName) $ Con $ DCon i lcons (PatEval conds'')
+        return $ Just (con, (i, conds'', conTerm), Type conType conSort)
+    let ks = map (\(_, _, Type _ k) -> k) cons'
+        mk = if null ks then Prop else dmaximum ks
+    forM_ cons' $ \(PIdent pcon con, (i, cs, _), Type ty k) ->
+        addConstructorCheck (pcon, Ident con) dtid i lcons (PatEval cs) $ Closed $ Type (vacuous $ abstractTerm ctx ty) mk
+    conds' <- forW conds $ \(Clause (pos, con) pats expr) ->
+        case find (\((PIdent _ c), _, _) -> Ident c == con) cons' of
+            Just (PIdent _ conName, (i, _, _), 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
+                when bf $ warn [Error Other $ emsgLC pos "Absurd patterns are not allowed in conditions" enull]
+                (term, _) <- typeCheckCtx (ctx +++ ctx') expr $ Just (nfType WHNF ty')
+                let scope = closed (abstractTerm ctx' term)
+                throwErrors $ checkTermination (Left i) pos (map (first snd) rtpats) scope
+                return $ Just (conName, (rtpats, scope))
+            _ -> do
+                warn [notInScope pos "data constructor" (nameToString con)]
+                return Nothing
+    lift $ replaceDataType dt lcons $ Closed $ Type (vacuous $ replaceSort dtTerm mk) mk
+    forM_ cons' $ \(PIdent pos _, (_, conds, con), _) -> warn $
+        checkConditions pos Nil (capply con) $ map (\(p, Closed t) -> (p, t)) conds
 
-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)
+data SomeEq f = forall a. Eq a => SomeEq (f a)
 
-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
+extendCtx :: (Functor t, Eq a) => [s] -> Ctx s t b a -> t a -> SomeEq (Ctx s t b)
+extendCtx [] ctx _ = SomeEq ctx
+extendCtx (x:xs) ctx t = extendCtx xs (Snoc ctx x t) (fmap Free t)
 
-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 ()
+checkTele :: (Monad m, Eq a) => Ctx String (Type Semantics) Void a -> [Tele] -> Term Semantics a
+    -> TCM m (SomeEq (Ctx String (Type Semantics) Void), Type Semantics a)
+checkTele ctx [] term = return (SomeEq ctx, Type term $ Set NoLevel)
+checkTele ctx (VarsTele vars expr : tele) term = do
+    (r1, Type t1 _) <- typeCheckCtx ctx expr Nothing
+    k1 <- checkIsType ctx (termPos expr) (nf WHNF t1)
+    case extendCtx (map getName vars) Nil (Type r1 k1) of
+        SomeEq ctx' -> do
+            (rctx, Type r2 k2) <- checkTele (ctx +++ ctx') tele $ fmap (liftBase ctx') term
+            let sem = Semantics (S.Pi Explicit $ reverse $ ctxVars ctx') (V.Pi k1 k2)
+            return (rctx, Type (Apply sem [r1, abstractTerm ctx' r2]) $ dmax k1 k2)
+checkTele ctx (TypeTele expr : tele) term = do
+    (r1, Type t1 _) <- typeCheckCtx ctx expr Nothing
+    k1 <- checkIsType ctx (termPos expr) (nf WHNF t1)
+    (rctx, Type r2 k2) <- checkTele ctx tele term
+    return (rctx, Type (Apply (Semantics (S.Pi Explicit []) $ V.Pi k1 k2) [r1,r2]) $ dmax k1 k2)
 
-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 ()
+replaceSort :: Term Semantics a -> Sort -> Term Semantics a
+replaceSort (Apply p@(Semantics _ V.Pi{}) [a,b]) k = Apply p [a, replaceSort b k]
+replaceSort (Lambda t) k = Lambda (replaceSort t k)
+replaceSort _ k = universe k
 
-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]
+findOccurrence :: Eq a => ID -> Term Semantics a -> Maybe Int
+findOccurrence dt (Apply (Semantics _ V.Pi{}) [a,b]) = case (findOccurrence dt $ nf WHNF a, findOccurrence dt $ nf WHNF b) of
+        (Nothing, Nothing) -> Nothing
+        (Nothing, Just b') -> Just b'
+        (Just a', Nothing) -> Just (succ a')
+        (Just a', Just b') -> Just $ max (succ a') b'
+findOccurrence dt (Lambda t) = findOccurrence dt (nf WHNF t)
+findOccurrence dt t = if dt `elem` collectDataTypes t then Just 0 else Nothing
 
-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
+collectDataTypes :: Term Semantics a -> [ID]
+collectDataTypes = biconcatMap (\t -> case t of
+    Semantics _ (DataType dt _) -> [dt]
+    _                           -> []) (const [])
diff --git a/src/TypeChecking/Definitions/Functions.hs b/src/TypeChecking/Definitions/Functions.hs
--- a/src/TypeChecking/Definitions/Functions.hs
+++ b/src/TypeChecking/Definitions/Functions.hs
@@ -1,53 +1,64 @@
-{-# LANGUAGE RecursiveDo #-}
-
 module TypeChecking.Definitions.Functions
     ( typeCheckFunction
     ) where
 
-import Control.Monad
-import Control.Monad.Fix
 import Data.Maybe
+import Data.Void
+import Data.Bifunctor
 
-import Syntax.Expr as E
-import Syntax.Term as T
+import Syntax
+import Semantics
+import Semantics.Value
 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.Expressions.Utils
+import TypeChecking.Expressions.Patterns
+import TypeChecking.Expressions.Coverage
+import TypeChecking.Expressions.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
+typeCheckFunction :: Monad m => PName -> Term (Posn, Syntax) Void
+    -> [(Posn, [Term PName Void], Maybe (Term (Posn, Syntax) Void))] -> TCM m ()
+typeCheckFunction p@(pos, name) ety clauses = do
     (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
+    k <- case nf WHNF u of
+            Apply (Semantics _ (Universe k)) _ -> return k
+            u' -> throwError [Error TypeMismatch $ emsgLC (termPos ety) "" $ pretty "Expected a type"
+                                                                          $$ pretty "Actual type:" <+> prettyOpen Nil u']
+    let cty = Closed $ Type (vacuous ty) k
+    fcid <- addFunctionCheck p (PatEval []) cty
+    clausesAndPats <- forW clauses $ \(pos,pats,mexpr) ->  do
+        (bf, TermsInCtx ctx _ ty', rtpats) <- typeCheckPatterns Nil (Type (nf WHNF ty) k) 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]
+                warn [Error Other $ emsgLC pos 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]
+                warn [Error Other $ emsgLC (termPos 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))
+                (term, _) <- typeCheckCtx ctx expr $ Just (nfType WHNF ty')
+                let scope = closed (abstractTerm ctx term)
+                    rtpats' = map (first snd) rtpats
+                throwErrors $ checkTermination (Right fcid) pos rtpats' scope
+                return $ Just ((rtpats, scope), (pos, rtpats'))
     let clauses' = map fst clausesAndPats
+        eval = PatEval $ map (fmap $ \(Closed scope) -> Closed $ replaceFunCalls fcid fc scope) clauses'
+        fc = Closed $ capply $ Semantics (Name Prefix name) (FunCall fcid eval)
+    lift $ replaceFunction name eval cty
     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)
+        Nothing | length clausesAndPats /= length (filter (\(_,_,me) -> isJust me) clauses) -> return ()
+        r -> warn (coverageErrorMsg pos r)
+    warn $ checkConditions pos Nil (open fc) $ map (\((p,Closed t),_) -> (p,t)) clausesAndPats
+
+replaceFunCalls :: ID -> Closed (Term Semantics) -> Term Semantics a -> Term Semantics a
+replaceFunCalls name fc (Var a ts) = Var a $ map (replaceFunCalls name fc) ts
+replaceFunCalls name fc (Apply (Semantics _ (FunCall name' _)) ts) | name == name' = apps (open fc) ts
+replaceFunCalls name fc (Apply s ts) = Apply s $ map (replaceFunCalls name fc) ts
+replaceFunCalls name fc (Lambda t) = Lambda (replaceFunCalls name fc t)
diff --git a/src/TypeChecking/Definitions/Patterns.hs b/src/TypeChecking/Definitions/Patterns.hs
deleted file mode 100644
--- a/src/TypeChecking/Definitions/Patterns.hs
+++ /dev/null
@@ -1,79 +0,0 @@
-{-# 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 _                             = []
diff --git a/src/TypeChecking/Definitions/Termination.hs b/src/TypeChecking/Definitions/Termination.hs
--- a/src/TypeChecking/Definitions/Termination.hs
+++ b/src/TypeChecking/Definitions/Termination.hs
@@ -6,42 +6,43 @@
 
 import Control.Monad.State
 
-import Syntax.Term
+import qualified Syntax as S
+import Semantics.Value
+import Semantics
 import Syntax.ErrorDoc
 import TypeChecking.Context
+import TypeChecking.Expressions.Utils
 
-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]
+checkTermination :: Either Int ID -> S.Posn -> [Term (Con t) String] -> Closed (Term Semantics) -> [Error]
+checkTermination name pos pats (Closed scope) = map msg $ case scopeToCtx Nil scope of
+    TermInCtx ctx term -> collectFunCalls ctx name term >>= \mts -> case mts of
+        TermsInCtx ctx' terms -> if evalState (checkTerms ctx' pats terms) 0 == LT then [] else [pos]
   where
-    msg :: (Int,Int) -> EMsg Term
-    msg lc = emsgLC lc "Termination check failed" enull
+    msg :: S.Posn -> Error
+    msg pos = Error Other $ emsgLC pos "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
+checkTerm :: Ctx String (Term Semantics) String a -> Term (Con t) String -> Term Semantics a -> State Int Ordering
+checkTerm _ (Apply (ICon con) _) (Apply (Semantics _ (Con (ICon con'))) []) | con == con' = return EQ
+checkTerm ctx Var{} (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 :: Ctx String (Term Semantics) 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
+checkTerm ctx (Apply (DCon 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
+    if minimum (GT:results) /= GT then return LT else case term of
+        Apply (Semantics _ (Con (DCon 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 :: Ctx String (Term Semantics) String a -> [Term (Con t) String] -> [Term Semantics a] -> State Int Ordering
 checkTerms _ [] _ = return EQ
 checkTerms _ _ [] = return EQ
 checkTerms ctx (pat:pats) (term:terms) = do
@@ -53,35 +54,15 @@
 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 []
+scopeToCtx :: Ctx s (Term Semantics) b a -> Term Semantics a -> TermInCtx s (Term Semantics) b
+scopeToCtx ctx (Lambda t) = scopeToCtx (Snoc ctx (error "") $ error "") t
+scopeToCtx ctx t = TermInCtx ctx t
 
-scopedToMaybe :: Scoped a -> Maybe a
-scopedToMaybe Bound = Nothing
-scopedToMaybe (Free a) = Just a
+collectFunCalls :: Ctx String (Term Semantics) b a -> Either Int ID
+    -> Term Semantics a -> [TermsInCtx String (Term Semantics) b]
+collectFunCalls ctx name (Lambda t) = collectFunCalls (Snoc ctx (error "") $ error "") name t
+collectFunCalls ctx name (Var _ as) = as >>= collectFunCalls ctx name
+collectFunCalls ctx name (Apply a as) = (case a of
+    Semantics _ (Con (DCon name' _ _)) | name == Left name' -> [TermsInCtx ctx as]
+    Semantics _ (FunCall name' _) | name == Right name' -> [TermsInCtx ctx as]
+    _ -> []) ++ (as >>= collectFunCalls ctx name)
diff --git a/src/TypeChecking/Expressions.hs b/src/TypeChecking/Expressions.hs
--- a/src/TypeChecking/Expressions.hs
+++ b/src/TypeChecking/Expressions.hs
@@ -1,306 +1,416 @@
-{-# 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.Either
 import Data.Maybe
+import Data.Void
+import Data.Bifunctor
+import Data.Bitraversable
+import Data.Traversable(sequenceA)
 
-import Syntax.Expr as E
-import Syntax.Term as T
+import Syntax as S
+import Semantics
+import Semantics.Value as V
 import Syntax.ErrorDoc
 import TypeChecking.Monad
 import TypeChecking.Context
+import TypeChecking.Expressions.Utils
+import TypeChecking.Expressions.Patterns
+import TypeChecking.Expressions.Conditions
+import TypeChecking.Expressions.Coverage
 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
+type Context = Ctx String (Type Semantics) Void
 
-inferParamsErrorMsg :: Show a => (Int,Int) -> a -> EMsg f
-inferParamsErrorMsg lc d = emsgLC lc ("Cannot infer parameters of data constructor " ++ show d) enull
+intType :: Type Semantics a
+intType = Type interval (TypeK NoLevel)
 
-expectedArgErrorMsg :: Show a => (Int,Int) -> a -> EMsg f
-expectedArgErrorMsg lc d = emsgLC lc ("Expected an argument to " ++ show d) enull
+pathExp :: Sort -> Semantics
+pathExp k = Semantics (Name Prefix $ Ident "Path") (Path k)
 
-prettyOpen :: (Pretty b f, Monad f) => Ctx b g b a -> f a -> EDoc f
-prettyOpen ctx term = epretty $ liftM pretty (close ctx term)
+pathImp :: Sort -> Semantics
+pathImp k = Semantics PathImp (Path k)
 
-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]
+sortPred :: Sort -> Sort
+sortPred Prop = Contr
+sortPred Set{} = Prop
+sortPred k = k
 
-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]
+prettyOpen' :: Ctx String (Type Semantics) Void a -> Term Semantics (Either k a) -> EDoc (Term Syntax)
+prettyOpen' ctx term = epretty $ fmap (pretty . either id absurd) $ close ctx $
+    first syntax term >>= fmap Right . either (const $ capply $ Name Prefix $ Ident "?") return
 
-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]
+typeCheck :: Monad m => Term (Posn, Syntax) Void -> Maybe (Type Semantics Void) -> TCM m (Term Semantics Void, Type Semantics Void)
+typeCheck = typeCheckCtx Nil
 
-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
+typeCheckCtx :: (Monad m, Eq a) => Context a -> Term (Posn, Syntax) Void
+    -> Maybe (Type Semantics a) -> TCM m (Term Semantics a, Type Semantics a)
+typeCheckCtx ctx term mty = do
+    (te, ty, _) <- typeCheckCtx' ctx term $ fmap (\(Type t k) -> Type (fmap Right t) k) mty
+    return (te, ty)
 
-intType :: Type a
-intType = Type T.Interval NoLevel
+typeCheckCtx' :: (Monad m, Eq a) => Context a -> Term (Posn, Syntax) Void -> Maybe (Type Semantics (Either Argument a))
+    -> TCM m (Term Semantics a, Type Semantics a, [(Argument, Term Semantics a)])
+typeCheckCtx' ctx (Apply (pos, Name ft var) ts) mty = typeCheckName ctx pos ft var ts mty
+typeCheckCtx' ctx (Apply (_, S.Lam []) [te]) mty = typeCheckCtx' ctx te mty
+typeCheckCtx' ctx (Apply (pos, S.Lam (v:vs)) [te]) (Just (Type (Apply p@(Semantics (S.Pi e _) (V.Pi k1 k2)) [a,b]) k3)) =
+    case bitraverse Right id a of
+        Left{} -> throwError [inferErrorMsg pos "the argument"]
+        Right a' -> do
+            (te', Type b' k2', tab) <- typeCheckCtx' (Snoc ctx v $ Type a' k1) (Apply (pos, S.Lam vs) [te]) $
+                Just $ Type (nf WHNF $ fmap sequenceA $ snd $ dropOnePi p a b) k2
+            let te'' = case te' of
+                    Apply (Semantics (S.Lam vs') _) [t] -> Apply (Semantics (S.Lam $ v:vs') V.Lam) [Lambda t]
+                    _                                   -> Apply (Semantics (S.Lam [v]) V.Lam) [Lambda te']
+                tab' = tab >>= \(kp, term) -> case sequenceA term of
+                                                    Bound -> []
+                                                    Free t -> [(kp, t)]
+            return (te'', Type (Apply (Semantics (S.Pi e [v]) $ V.Pi k1 k2') [a', Lambda b']) k3, tab')
+typeCheckCtx' ctx (Apply (pos, S.Lam{}) [_]) (Just (Type (Var Left{} _) _)) =
+    throwError [inferErrorMsg pos "lambda expressions"]
+typeCheckCtx' ctx (Apply (pos, S.Lam{}) [_]) (Just (Type ty _)) =
+    throwError [Error TypeMismatch $ emsgLC pos "" $ pretty "Expected type:" <+> prettyOpen' ctx ty
+                                                  $$ pretty "But lambda expression has pi type"]
+typeCheckCtx' ctx (Apply (pos, S.Lam{}) _) _ = throwError [inferErrorMsg pos "the argument"]
+typeCheckCtx' ctx (Apply (pos, S.Pi e vs) (a:b:ts)) Nothing = do
+    (a', Type ty1 _) <- typeCheckCtx ctx a Nothing
+    k1 <- checkIsType ctx (termPos a) ty1
+    (b', k2) <- extend ctx vs (Type a' k1)
+    unless (null ts) $ warn [argsErrorMsg pos "A type"]
+    let k = case (k1, k2) of
+                (_, Contr) -> Contr
+                (_, Prop) -> Prop
+                (Set l1, Set l2) -> Set (max l1 l2)
+                (TypeK l1, Set l2) -> Set (max l1 l2)
+                (_, Set l) -> Set l
+                (Set l1, TypeK l2) -> TypeK (max l1 l2)
+                (TypeK l1, TypeK l2) -> TypeK (max l1 l2)
+                (_, TypeK l) -> TypeK l
+    return (Apply (Semantics (S.Pi e vs) (V.Pi k1 k2)) [a', b'], Type (universe k) $ succ k, [])
+  where
+    extend :: (Monad m, Eq a) => Context a -> [String] -> Type Semantics a -> TCM m (Term Semantics a, Sort)
+    extend ctx [] _ = do
+        (te, Type ty _) <- typeCheckCtx ctx b Nothing
+        k <- checkIsType ctx (termPos b) ty
+        return (te, k)
+    extend ctx (v:vs) a = do
+        (te, k) <- extend (Snoc ctx v a) vs (fmap Free a)
+        return (Lambda te, k)
+typeCheckCtx' ctx (Apply (pos, PathImp) (a1:a2:ts)) Nothing = do
+    unless (null ts) $ warn [argsErrorMsg pos "A type"]
+    (r1, Type t1 k) <- typeCheckCtx ctx a1 Nothing
+    (r2, _) <- typeCheckCtx ctx a2 $ Just $ Type (nf WHNF t1) k
+    return (Apply (pathImp k) [Apply (Semantics (S.Lam ["_"]) V.Lam)
+            [Lambda $ fmap Free t1], r1, r2], Type (universe $ sortPred k) $ succ $ sortPred k, [])
+typeCheckCtx' ctx (Apply (pos, S.At) (b:c:ts)) mty = do
+    (r1, Type t1 k) <- typeCheckCtx ctx b Nothing
+    (r2, _) <- typeCheckCtx ctx c (Just intType)
+    case nf WHNF t1 of
+        Apply (Semantics _ Path{}) [a,b',c'] -> do
+            (tes, ty, tab) <- typeCheckApps pos (Just $ Operator "@") ctx ts (Type (apps a [r2]) k) mty
+            return (Apply (Semantics S.At V.At) (b':c':r1:r2:tes), ty, tab)
+        t1' -> throwError [Error TypeMismatch $ emsgLC pos "" $ pretty "Expected type: Path"
+                                                             $$ pretty "Actual type:" <+> prettyOpen ctx t1']
+typeCheckCtx' ctx (Apply (pos, (S.Case (pat:pats))) (expr:terms)) mty = do
+    (exprTerm, exprType) <- typeCheckCtx ctx expr Nothing
+    let (term1:terms1,terms2) = splitAt (length pats + 1) terms
+        typeCheckClause mtype (pat,term) = do
+            (bf, mt, pat') <- typeCheckPattern ctx exprType pat
+            when bf $ warn [Error Other $ emsgLC (termPos pat) "Absurd patterns are not allowed in case constructions" enull]
+            case fromMaybe (TermInCtx (Snoc Nil "_" exprType) $ error "") mt of
+                TermInCtx ctx' _ -> do
+                    (te, Type ty k, tab) <- typeCheckCtx' (ctx +++ ctx') term $ fmap (fmap $ fmap $ liftBase ctx') mtype
+                    let tab' = tab >>= \(kp, t) -> case sequenceA $ fmap (toBase ctx') t of
+                                                    Nothing -> []
+                                                    Just t' -> [(kp, t')]
+                    return (pat', abstractTerm ctx' te, Type (abstractTerm ctx' ty) k, tab')
+    (pat', term1', Type type1 k, tab1) <- typeCheckClause (if null terms2 then mty else Nothing) (pat,term1)
+    type1' <- case isStationary type1 of
+                Nothing -> throwError [Error Other $
+                    emsgLC pos "Type of expressions in case constructions cannot be dependent" enull]
+                Just r  -> return (Type r k)
+    patsAndTerms <- mapM (liftM (\(p,t,_,_) -> (p,t)) . typeCheckClause (Just $ nfType WHNF $ fmap Right type1')) (zip pats terms1)
+    (terms2', ty, tab2) <- if null terms2
+        then return ([], type1', [])
+        else typeCheckApps pos Nothing ctx terms2 type1' mty
+    let (pats',terms1') = unzip patsAndTerms
+        sem = Semantics (S.Case $ map (first $ \(s,_) -> ((0,0), Ident s)) $ pat':pats') $ V.Case (pat':pats')
+        terms' = term1' : terms1' ++ terms2'
+    warn $ coverageErrorMsg pos $ checkCoverage $ zipWith (\p1 p2 -> (termPos p1, [first snd p2])) (pat:pats) (pat':pats')
+    warn $ checkConditions pos ctx (Lambda $ Apply sem $ bvar : map (fmap Free) terms') $
+        map (\(p,t) -> ([p],t)) $ (pat',term1'):patsAndTerms
+    return (Apply sem $ exprTerm:terms', ty, tab1 ++ tab2)
+  where
+    isStationary :: Term a b -> Maybe (Term a b)
+    isStationary (Lambda t) = case sequenceA t of
+        Bound -> Nothing
+        Free t' -> isStationary t'
+    isStationary t = Just t
+typeCheckCtx' ctx te (Just (Type ty _)) = do
+    (te', Type ty' k') <- typeCheckCtx ctx te Nothing
+    tab <- actExpType True ctx (fmap Right ty') ty (termPos te)
+    return (te', Type ty' k', tab)
+typeCheckCtx' _ _ _ = error "typeCheckCtx"
 
-data SomeEq f = forall a. Eq a => SomeEq (f a)
+typeCheckName :: (Monad m, Eq a) => Context a -> Posn -> Fixity -> Name -> [Term (Posn, Syntax) Void]
+    -> Maybe (Type Semantics (Either Argument a)) -> TCM m (Term Semantics a, Type Semantics a, [(Argument, Term Semantics a)])
+typeCheckName ctx pos ft var ts mty = do
+    when (nameToString var == "_") $ throwError [inferExprErrorMsg pos]
+    eres <- case lookupCtx (nameToString var) ctx of
+        Just r -> return (Left r)
+        Nothing -> do
+            let mdt = case mty of
+                        Just (Type (Apply (Semantics _ (DataType dti _)) params) _) -> Just (dti,params)
+                        _ -> Nothing
+            mt <- lift $ getEntry var mdt
+            case mt of
+                [] -> liftM Right (typeCheckKeyword ctx pos (nameToString var) ts mty)
+                [(s, ty)] ->
+                    let s' = case syntax s of
+                                Name ft' _ | ft == ft'  -> s
+                                _                       -> s { syntax = Name ft var }
+                    in case sequenceA ty of
+                        Left kp -> throwError (inferArgErrorMsg kp)
+                        Right ty' -> return $ Left (capply s', ty')
+                _ -> throwError [Error Other $ emsgLC pos ("Ambiguous identifier: " ++ show (nameToString var)) enull]
+    case eres of
+        Left (te, ty) -> do
+            (tes, ty', tab) <- typeCheckApps pos (Just var) ctx ts ty mty
+            return (apps te tes, ty', tab)
+        Right res -> return res
 
-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)
+typeCheckKeyword :: (Monad m, Eq a) => Context a -> Posn -> String -> [Term (Posn, Syntax) Void]
+    -> Maybe (Type Semantics (Either Argument a)) -> TCM m (Term Semantics a, Type Semantics a, [(Argument, Term Semantics a)])
+typeCheckKeyword _ pos u as Nothing | (k,""):_ <- reads u = do
+    unless (null as) $ warn [argsErrorMsg pos "A type"]
+    return (universe k, Type (universe $ succ k) $ succ $ succ k, [])
+typeCheckKeyword ctx pos "contr" [] (Just (Type ty k)) = do
+    case k of
+        Contr   -> return ()
+        _       -> warn [Error TypeMismatch $ emsgLC pos "" $ pretty "Expected a contractible type"
+                                                           $$ pretty "Actual type:" <+> prettyOpen' ctx ty]
+    case sequenceA ty of
+        Left kp -> throwError (inferArgErrorMsg kp)
+        Right ty' -> return (capply $ Semantics (Name Prefix $ Ident "contr") CCon, Type ty' k, [])
+typeCheckKeyword _ pos "contr" _ _ = throwError [inferErrorMsg pos "contr"]
+typeCheckKeyword _ pos "I" as Nothing = do
+    unless (null as) $ warn [argsErrorMsg pos "A type"]
+    return (interval, Type (universe $ TypeK NoLevel) $ TypeK $ Level 1, [])
+typeCheckKeyword _ pos "left" as Nothing = do
+    unless (null as) $ warn [argsErrorMsg pos $ show "left"]
+    return (iCon ILeft, intType, [])
+typeCheckKeyword _ pos "right" as Nothing = do
+    unless (null as) $ warn [argsErrorMsg pos $ show "right"]
+    return (iCon IRight, intType, [])
+typeCheckKeyword _ pos "Path" [] _ = throwError [expectedArgErrorMsg pos "Path"]
+typeCheckKeyword ctx pos "Path" (a:as) Nothing = do
+    (r1, _, (v, t1)) <- typeCheckLambda ctx a intType
+    k <- checkIsType (Snoc ctx v $ error "") (termPos a) t1
+    let r1' c = apps r1 [iCon c]
+        k' = sortPred k
+        mkType t = Type t (succ k')
+    case as of
+        [] -> return (Apply (pathExp k) [r1], mkType $ Apply (Semantics (S.Pi Explicit []) $ V.Pi k $ succ k)
+            [r1' ILeft, Apply (Semantics (S.Pi Explicit []) $ V.Pi k $ succ k) [r1' IRight, universe k']], [])
+        [a2] -> do
+            (r2, _) <- typeCheckCtx ctx a2 $ Just $ Type (nf WHNF $ r1' ILeft) k
+            return (Apply (pathExp k) [r1,r2], mkType $ Apply (Semantics (S.Pi Explicit []) $ V.Pi k $ succ k) [r1' IRight, universe k'], [])
+        a2:a3:as' -> do
+            unless (null as') $ warn [argsErrorMsg pos "A type"]
+            (r2, _) <- typeCheckCtx ctx a2 $ Just $ Type (nf WHNF $ r1' ILeft) k
+            (r3, _) <- typeCheckCtx ctx a3 $ Just $ Type (nf WHNF $ r1' IRight) k
+            return (Apply (pathExp k) [r1,r2,r3], mkType $ universe k', [])
+typeCheckKeyword _ pos "path" [] _ = throwError [expectedArgErrorMsg pos "path"]
+typeCheckKeyword ctx pos "path" (a:as) mty = do
+    unless (null as) $ warn [argsErrorMsg pos "A path"]
+    case mty of
+        Nothing -> do
+            (te, Type _ k, (_, ty)) <- typeCheckLambda ctx a intType
+            return (path [te], Type (Apply (pathImp k) [Apply (Semantics (S.Lam ["_"]) V.Lam) [Lambda ty], apps te [iCon ILeft], apps te [iCon IRight]]) k, [])
+        Just (Type (Var (Left kp) _) _) -> do
+            (te, Type _ k, (_, ty)) <- typeCheckLambda ctx a intType
+            let ty' = Apply (pathImp k) [Apply (Semantics (S.Lam ["_"]) V.Lam) [Lambda ty], apps te [iCon ILeft], apps te [iCon IRight]]
+            return (path [te], Type ty' k, [(kp,ty')])
+        Just (Type ety@(Apply (Semantics _ (Path k1)) [t1,_,_]) k) -> do
+            let sem = Semantics (S.Pi Explicit ["i"]) $ V.Pi (TypeK NoLevel) k1
+                aty = Apply sem [interval, Lambda $ apps (fmap Free t1) [bvar]]
+            (r, Type ty' _, tab1) <- typeCheckCtx' ctx a $ Just (Type aty k1)
+            case nf WHNF ty' of
+                Apply (Semantics (S.Pi e vs) p) [ta, tb] -> do
+                    let tb' = case tb of
+                                Lambda t@Lambda{} -> Apply (Semantics (S.Lam ["i"]) V.Lam)
+                                    [Lambda $ Apply (Semantics (S.Pi e $ tail vs) p) [fmap Free ta, t]]
+                                Lambda{} -> Apply (Semantics (S.Lam ["i"]) V.Lam) [tb]
+                                _ -> Apply (Semantics (S.Lam ["_"]) V.Lam) [Lambda $ fmap Free tb]
+                        aty = Apply (pathImp k1) [tb', apps r [iCon ILeft], apps r [iCon IRight]]
+                    tab2 <- actExpType True ctx (fmap Right aty) ety pos
+                    return (path [r], Type aty k, tab1 ++ tab2)
+                _ -> error "typeCheckKeyword: path"
+        Just (Type ty _) -> throwError [Error TypeMismatch $ emsgLC pos "" $ pretty "Expected type:" <+> prettyOpen' ctx ty
+                                                                          $$ pretty "Actual type: Path"]
+typeCheckKeyword _ pos "coe" [] _ = throwError [expectedArgErrorMsg pos "coe"]
+typeCheckKeyword ctx pos "coe" (a1:as) Nothing = do
+    (r1, _, (v, t1)) <- typeCheckLambda ctx a1 intType
+    k <- checkIsType (Snoc ctx v $ error "") (termPos a1) t1
+    let res = Apply (Semantics (S.Pi Explicit ["r"]) $ V.Pi (TypeK NoLevel) k) [interval, Lambda $ apps (fmap Free r1) [bvar]]
+        coe = Semantics (Name Prefix $ Ident "coe") Coe
+    case as of
+        [] -> return (Apply coe [r1], Type (Apply (Semantics (S.Pi Explicit ["l"]) $ V.Pi (TypeK NoLevel) k) [interval, Lambda $
+            Apply (Semantics (S.Pi Explicit []) $ V.Pi k k) [apps (fmap Free r1) [bvar], fmap Free res]]) k, [])
+        a2:as1 -> do
+            (r2, _) <- typeCheckCtx ctx a2 (Just intType)
+            case as1 of
+                [] -> return (Apply coe [r1,r2], Type (Apply (Semantics (S.Pi Explicit []) $ V.Pi k k) [apps r1 [r2], res]) k, [])
+                a3:as2 -> do
+                    (r3, _) <- typeCheckCtx ctx a3 $ Just $ Type (nf WHNF $ apps r1 [r2]) k
+                    case as2 of
+                        [] -> return (Apply coe [r1,r2,r3], Type res k, [])
+                        a4:as3 -> do
+                            (r4, _) <- typeCheckCtx ctx a4 (Just intType)
+                            (tes, ty, _) <- typeCheckApps pos Nothing ctx as3 (Type (apps r1 [r4]) k) Nothing
+                            return (Apply coe $ [r1,r2,r3,r4] ++ tes, ty, [])
+typeCheckKeyword ctx pos "iso" (a1:a2:a3:a4:a5:a6:as) Nothing = do
+    (r1, Type t1 _) <- typeCheckCtx ctx a1 Nothing
+    (r2, Type t2 _) <- typeCheckCtx ctx a2 Nothing
+    let t1' = nf WHNF t1
+        t2' = nf WHNF t2
+    k1 <- checkIsType ctx (termPos a1) t1'
+    k2 <- checkIsType ctx (termPos a2) t2'
+    let k = dmax k1 k2
+    (r3, _) <- typeCheckCtx ctx a3 $ Just $ Type (Apply (Semantics (S.Pi Explicit []) $ V.Pi k1 k2) [r1,r2]) k
+    (r4, _) <- typeCheckCtx ctx a4 $ Just $ Type (Apply (Semantics (S.Pi Explicit []) $ V.Pi k2 k1) [r2,r1]) k
+    let h e s1 s3 s4 tk = typeCheckCtx ctx e $ Just $ Type (Apply (Semantics (S.Pi Explicit ["x"]) $ V.Pi tk tk) [s1, Lambda $
+            Apply (pathImp tk) [Apply (Semantics (S.Lam ["_"]) V.Lam) [Lambda $ fmap (Free . Free) s1],
+                apps (fmap Free s4) [apps (fmap Free s3) [bvar]], bvar]]) tk
+        iso = Semantics (Name Prefix $ Ident "iso") Iso
+    (r5, _) <- h a5 r1 r3 r4 k1
+    (r6, _) <- h a6 r2 r4 r3 k2
+    case as of
+        [] -> return (Apply iso [r1,r2,r3,r4,r5,r6],
+            Type (Apply (Semantics (S.Pi Explicit []) $ V.Pi (TypeK NoLevel) $ succ k) [interval, universe k]) $ succ k, [])
+        a7:as' -> do
+            unless (null as') $ warn [argsErrorMsg pos "A type"]
+            (r7, _) <- typeCheckCtx ctx a7 (Just intType)
+            return (Apply iso [r1,r2,r3,r4,r5,r6,r7], Type (universe k) $ succ k, [])
+typeCheckKeyword _ pos "iso" _ Nothing =
+    throwError [Error NotEnoughArgs $ emsgLC pos "Expected at least 6 arguments to \"iso\"" enull]
+typeCheckKeyword ctx pos "squeeze" as Nothing =
+    let mkType t = Apply (Semantics (S.Pi Explicit []) $ V.Pi (TypeK NoLevel) $ TypeK NoLevel) [interval, t]
+        squeeze = Semantics (Name Prefix $ Ident "squeeze") Squeeze
+    in case as of
+        [] -> return (capply squeeze, Type (mkType $ mkType interval) $ TypeK NoLevel, [])
+        [a1] -> do
+            (r1, _) <- typeCheckCtx ctx a1 (Just intType)
+            return (Apply squeeze [r1], Type (mkType interval) $ TypeK NoLevel, [])
+        [a1,a2] -> do
+            (r1, _) <- typeCheckCtx ctx a1 (Just intType)
+            (r2, _) <- typeCheckCtx ctx a2 (Just intType)
+            return (Apply squeeze [r1,r2], intType, [])
+        _ -> throwError [argsErrorMsg pos "squeeze _ _"]
+typeCheckKeyword ctx pos var ts (Just (Type ty _)) = do
+    (te', Type ty' k', _) <- typeCheckKeyword ctx pos var ts Nothing
+    tab <- actExpType True ctx (fmap Right ty') ty pos
+    return (te', Type ty' k', tab)
+typeCheckKeyword _ pos var _ _ = throwError [notInScope pos "" var]
 
-typeCheck :: Monad m => Expr -> Maybe (Type String) -> TCM m (Term String, Type String)
-typeCheck = typeCheckCtx Nil
+actExpType :: (Monad m, Eq a) => Bool -> Context a -> Term Semantics (Either Argument a)
+    -> Term Semantics (Either Argument a) -> Posn -> EDocM m [(Argument, Term Semantics a)]
+actExpType w ctx act exp pos = do
+    let act' = nf NF act
+        exp' = nf NF exp
+        (mo,(l1,l2)) = pcmpTerms act' exp'
+        l = if w then l2 else l1
+    unless (mo == Just EQ || mo == Just LT) $
+        throwError [Error TypeMismatch $ emsgLC pos "" $ pretty "Expected type:" <+> prettyOpen' ctx exp'
+                                                      $$ pretty "Actual type:"   <+> prettyOpen' ctx act']
+    return l
 
-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
+typeCheckApps :: (Monad m, Eq a) => Posn -> Maybe Name -> Context a -> [Term (Posn, Syntax) Void]
+    -> Type Semantics a -> Maybe (Type Semantics (Either Argument a))
+    -> TCM m ([Term Semantics a], Type Semantics a, [(Argument, Term Semantics a)])
+typeCheckApps pos mname ctx allTerms ty mety = go 0 [] [] (map (\t -> (Explicit, Left t)) allTerms) nty
   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)
+    nty = nfType WHNF (fmap Right ty)
+    
+    go n acc rest ((e1, term@(Left (Apply (pos', Name _ (Ident "_")) []))) : terms) (Type (Apply p@(Semantics (S.Pi e2 _) (V.Pi _ k2)) [a,b]) _) | e1 == e2 =
+        go (n + 1) (Left (inferArgErrorMsg $ Argument n pos' mname) : acc) ((e1,term):rest) terms $
+        Type (nf WHNF $ instantiate1 (cvar $ Left (Argument n pos' mname)) $ snd $ dropOnePi p a b) k2
+    go n acc rest ((e1,term):terms) (Type (Apply p@(Semantics (S.Pi e2 _) (V.Pi k1 k2)) [a,b]) _) | e1 == e2 = do
+        mres <- case term of
+                    Left t -> let catchErrs = catchErrorType [Inference]
+                              in liftM (\(a,b,c) -> Right (a, Just b, c))
+                                (typeCheckCtx' ctx t $ Just $ Type (nf WHNF a) k1) `catchErrs` (return . Left)
+                    Right (te, maty) -> do
+                        case maty of
+                            Just (Type aty _) -> actExpType True ctx (fmap Right aty) a pos
+                            Nothing -> return []
+                        return $ Right (te, maty, [])
+        case mres of
+            Left errs -> go (n + 1) (Left errs : acc) ((e1,term):rest) terms $
+                Type (nf WHNF $ instantiate1 (cvar $ Left $ NoArgument errs) $ snd $ dropOnePi p a b) k2
+            Right (term', mty, tab) ->
+                let ty' = Right (term', mty)
+                in if useful tab
+                    then go 0 [] [] (replaceTerms (reverse rest ++ [(e1, ty')] ++ terms) tab) nty
+                    else go (n + 1) (ty' : acc) ((e1, ty') : rest) terms $ Type (nf WHNF $ case b of
+                        Lambda{} -> instantiate1 (fmap Right term') $ snd (dropOnePi p a b)
+                        _        -> b) k2
+    go n acc rest terms (Type (Apply p@(Semantics (S.Pi Implicit _) (V.Pi _ k2)) [a,b]) _) =
+        go (n + 1) (Left (inferArgErrorMsg $ Argument n pos mname) : acc)
+            ((Implicit, Left (capply (pos, Name Prefix $ Ident "_"))) : rest) terms $
+            Type (nf WHNF $ instantiate1 (cvar $ Left (Argument n pos mname)) $ snd $ dropOnePi p a b) k2
+    go _ acc rest [] (Type aty k) =
+        let checkAty = case sequenceA aty of
+                        Left kp -> throwError (inferArgErrorMsg kp)
+                        Right aty' -> case partitionEithers (reverse acc) of
+                                        ([], rights) -> return (map fst rights, Type aty' k, [])
+                                        (left:_, _)  -> throwError left
+        in case mety of
+            Just (Type ety _) -> do
+                tab <- actExpType False ctx aty ety pos
+                if useful tab
+                then go 0 [] [] (replaceTerms (reverse rest) tab) nty
+                else do
+                    (acc', Type aty' k', _) <- checkAty
+                    tab' <- actExpType True ctx (fmap Right aty') ety pos
+                    return (acc', Type aty' k', tab')
+            Nothing -> checkAty
+    go _ _ _ _ (Type (Var (Left kp) _) _) = throwError (inferArgErrorMsg kp)
+    go _ _ _ _ (Type ty _) = throwError [Error TypeMismatch $ emsgLC pos "" $ pretty "Expected pi type"
+                                                                           $$ pretty "Actual type:" <+> prettyOpen' ctx ty]
+    
+    replaceTerms :: [(e, Either t (s, Maybe u))] -> [(Argument, s)] -> [(e, Either t (s, Maybe u))]
+    replaceTerms ts [] = ts
+    replaceTerms ts ((Argument k _ _, t):tab) =
+        let (ts1,ts2) = splitAt k (replaceTerms ts tab)
+        in if null ts2 then ts1 else ts1 ++ [(fst $ head ts2, Right (t, Nothing))] ++ tail ts2
+    replaceTerms ts ((NoArgument{},_):tab) = replaceTerms ts tab
 
-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
+useful :: [(Argument,a)] -> Bool
+useful = not . null . filter (\(arg,_) -> case arg of
+    Argument{}   -> True
+    NoArgument{} -> False)
+
+typeCheckLambda :: (Monad m, Eq a) => Context a -> Term (Posn, Syntax) Void -> Type Semantics a
+    -> TCM m (Term Semantics a, Type Semantics a, (String, Term Semantics (Scoped a)))
+typeCheckLambda ctx (Apply (pos, S.Lam (v:vs)) [te]) (Type ty k) = do
+    (te', Type ty' k') <- typeCheckCtx (Snoc ctx v $ Type ty k) (if null vs then te else Apply (pos, S.Lam vs) [te]) Nothing
+    let te'' = case te' of
+                Apply (Semantics (S.Lam vs') _) [te''] -> Apply (Semantics (S.Lam $ v:vs') V.Lam) [Lambda te'']
+                _ -> Apply (Semantics (S.Lam [v]) V.Lam) [Lambda te']
+    return (te'', Type (Apply (Semantics (S.Pi Explicit [v]) (V.Pi k k')) [ty, Lambda ty']) $ dmax k k', (v, ty'))
+typeCheckLambda ctx te ty = do
+    (te', Type ty' k') <- typeCheckCtx ctx te Nothing
     case nf WHNF ty' of
-        T.Pi a b lvlb ->
-            let Type na lvla = nfType NF a
-                Type nty lvlty = nfType NF ty
+        ty''@(Apply p@(Semantics sp (V.Pi ka kb)) [a,b]) ->
+            let na = nf NF a
+                Type nty kty = 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]
+                then return (te', Type ty'' k', dropOnePi p a b)
+                else throwError [Error TypeMismatch $ emsgLC (termPos te) "" $
+                        pretty "Expected type:" <+> prettyOpen ctx (Apply (Semantics sp $ V.Pi kty kb) [nty,b]) $$
+                        pretty "Actual type:"   <+> prettyOpen ctx (Apply p [na,b])]
+        _ -> throwError [Error TypeMismatch $ emsgLC (termPos te) "" $ pretty "Expected pi type"
+                                                                    $$ pretty "Actual type:" <+> prettyOpen ctx ty']
diff --git a/src/TypeChecking/Expressions/Conditions.hs b/src/TypeChecking/Expressions/Conditions.hs
new file mode 100644
--- /dev/null
+++ b/src/TypeChecking/Expressions/Conditions.hs
@@ -0,0 +1,138 @@
+{-# LANGUAGE GADTs, ExistentialQuantification, FlexibleInstances #-}
+
+module TypeChecking.Expressions.Conditions
+    ( checkConditions
+    ) where
+
+import Control.Monad
+import Control.Monad.State
+import Data.Maybe
+import Data.Bifunctor
+import Data.Void
+
+import qualified Syntax as S
+import Semantics
+import Semantics.Value
+import Syntax.ErrorDoc
+import TypeChecking.Context
+import TypeChecking.Expressions.Utils
+import Normalization
+
+instance Eq (Term (s, Con t) a) where
+    Apply (_,s) _ == Apply (_,s') _ = s == s'
+    Var{} == Var{} = True
+    _ == _ = False
+
+checkConditions :: Eq a => S.Posn -> Ctx String f Void a => Term Semantics a
+    -> [([Term (String,SCon) String], Term Semantics a)] -> [Error]
+checkConditions pos ctx func cs =
+    maybeToList $ msum $ map (\(p, scope) -> fmap (msg ctx) $ checkPatterns func (map fst cs) p scope) cs
+  where
+    msg :: Ctx String f Void a -> ([String], Term Semantics a, Term Semantics a) -> Error
+    msg ctx (vs, t1, t2) = Error Conditions $ emsgLC pos "Conditions check failed:" $
+        scopeToEDoc ctx vs t1 <+> pretty "is not equal to" <+> scopeToEDoc ctx vs t2
+    
+    scopeToEDoc :: Ctx String f Void a -> [String] -> Term Semantics a -> EDoc (Term S.Syntax)
+    scopeToEDoc ctx vs t = epretty $ bimap syntax pretty $ apps (vacuous $ abstractTerm ctx t) $ map cvar (ctxVars ctx ++ vs)
+
+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 :: Eq a => Term Semantics a -> [[Term (String,SCon) String]] -> [Term (String,SCon) String]
+    -> Term Semantics a -> Maybe ([String], Term Semantics a, Term Semantics a)
+checkPatterns func cs pats scope = listToMaybe $ findSuspiciousPairs cs pats >>= \(TermsInCtx2 ctx terms terms') ->
+    let nscope1 = nfApps $ abstractTerm ctx $ apps (fmap (liftBase ctx) func) terms
+        nscope2 = abstractTerm ctx $ apps (fmap (liftBase ctx) scope) terms'
+    in if nf NF nscope1 == nf NF nscope2 then [] else [(reverse $ ctxVars ctx, nscope1, nscope2)]
+  where
+    nfApps :: Eq a => Term Semantics a -> Term Semantics a
+    nfApps (Apply a as) = Apply a $ map (nf WHNF) as
+    nfApps (Lambda t) = Lambda (nfApps t)
+    nfApps t = t
+
+findSuspiciousPairs :: [[Term (String,SCon) String]] -> [Term (String,SCon) String] -> [TermsInCtx2 (Term Semantics) b]
+findSuspiciousPairs _ [] = []
+findSuspiciousPairs cs (pat@(Var var _) : pats) =
+    check ILeft ++ check IRight ++ map ext (findSuspiciousPairs (mapTail pat cs) pats)
+  where
+    ext (TermsInCtx2 ctx terms1 terms2) = TermsInCtx2 (Snoc ctx var $ error "") (bvar : map (fmap Free) terms1)
+                                                                                (bvar : map (fmap Free) terms2)
+    check con = if null $ filter (== Apply ("", ICon con) []) (mapHead cs)
+        then []
+        else case patternsToTerms pats of
+            TermsInCtx ctx terms -> [TermsInCtx2 ctx (iCon con : terms) (iCon con : ctxToVars ctx)]
+findSuspiciousPairs cs (pat@(Apply (name, con) args) : pats) =
+    (case con of
+        DCon _ _ (PatEval conds) -> 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
+            Apply (_, con') args' : _ | con == con' -> [args']
+            _ -> []
+    
+    ext0 :: [Term (String,SCon) String] -> TermsInCtx (Term Semantics) b -> TermsInCtx2 (Term Semantics) b
+    ext0 args (TermsInCtx ctx terms) = case patternsToTerms pats of
+        TermsInCtx ctx' terms' -> TermsInCtx2 (ctx +++ ctx')
+            (fmap (liftBase ctx') (Apply (Semantics (S.Name S.Prefix $ S.Ident name) (Con con)) $ substPatterns args terms) : terms')
+            (map (fmap $ liftBase ctx') terms ++ ctxToVars ctx')
+    
+    ext1 :: TermsInCtx2 (Term Semantics) b -> TermsInCtx2 (Term Semantics) b
+    ext1 (TermsInCtx2 ctx terms1 terms2) = case patternsToTerms pats of
+        TermsInCtx ctx' terms' -> TermsInCtx2 (ctx +++ ctx') (fmap (liftBase ctx') (Apply (Semantics (S.Name S.Prefix $ S.Ident name) (Con con)) terms1) : terms')
+                                                             (map (fmap $ liftBase ctx') terms2 ++ ctxToVars ctx')
+    
+    ext2 :: Ctx String (Term Semantics) a b -> [Term Semantics b] -> TermsInCtx2 (Term Semantics) b -> TermsInCtx2 (Term Semantics) a
+    ext2 ctx terms (TermsInCtx2 ctx' terms1 terms2) =
+        TermsInCtx2 (ctx +++ ctx') (fmap (liftBase ctx') (Apply (Semantics (S.Name S.Prefix $ S.Ident name) (Con con)) terms) : terms1)
+                                   (map (fmap $ liftBase ctx') (ctxToVars ctx) ++ terms2)
+findSuspiciousPairs _ (Lambda{} : _) = error "findSuspiciousPairs"
+
+unifyPatterns :: Term (String,SCon) String -> Term (String,SCon) String -> Maybe [Term (String,SCon) String]
+unifyPatterns (Apply (_,con) pats) (Apply (_,con') pats') | con == con' = unifyPatternLists pats pats'
+unifyPatterns Var{} p = Just [p]
+unifyPatterns p Var{} = Just (varList p)
+unifyPatterns _ _ = Nothing
+
+unifyPatternLists :: [Term (String,SCon) String] -> [Term (String,SCon) String] -> Maybe [Term (String,SCon) String]
+unifyPatternLists pats pats' = fmap concat $ sequence (zipWith unifyPatterns pats pats')
+
+varList :: Term (String,SCon) String -> [Term (String,SCon) String]
+varList pat@Var{} = [pat]
+varList (Apply _ pats) = pats >>= varList
+varList _ = []
+
+substPatterns :: [Term (String,SCon) String] -> [Term Semantics a] -> [Term Semantics a]
+substPatterns pats terms = evalState (mapM substPattern pats) terms
+  where
+    substPattern :: Term (String,SCon) String -> State [Term Semantics a] (Term Semantics a)
+    substPattern Var{} = do
+        term:terms <- get
+        put terms
+        return term
+    substPattern (Apply (name, con) pats) = do
+        terms <- mapM substPattern pats
+        return $ Apply (Semantics (S.Name S.Prefix $ S.Ident name) (Con con)) terms
+    substPattern Lambda{} = error "substPattern"
+
+patternToTerm :: Term (String,SCon) String -> TermInCtx (Term Semantics) a
+patternToTerm (Var var _) = TermInCtx (Snoc Nil var $ error "") bvar
+patternToTerm (Apply (name, con) pats) = case patternsToTerms pats of
+    TermsInCtx ctx' terms -> TermInCtx ctx' $ Apply (Semantics (S.Name S.Prefix $ S.Ident name) (Con con)) terms
+patternToTerm Lambda{} = error "patternToTerm"
+
+patternsToTerms :: [Term (String,SCon) String] -> TermsInCtx (Term Semantics) 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
+
+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 || head as /= a then [] else [tail as]
diff --git a/src/TypeChecking/Expressions/Coverage.hs b/src/TypeChecking/Expressions/Coverage.hs
new file mode 100644
--- /dev/null
+++ b/src/TypeChecking/Expressions/Coverage.hs
@@ -0,0 +1,100 @@
+module TypeChecking.Expressions.Coverage
+    ( checkCoverage
+    ) where
+
+import Data.List
+import Data.Bifunctor
+
+import Syntax.Term
+import Semantics.Value hiding (Value(..))
+
+instance Eq s => Eq (Term s a) where
+    Apply s _ == Apply s' _ = s == s'
+    Var{} == Var{} = True
+    _ == _ = False
+
+data PatternType t = Interval | DataType Int [(Int, [Term (Con t) String])] | Path | Unknown
+
+data OK = OK | Incomplete deriving Eq
+data Result = Result OK [Int]
+
+checkCoverage :: [((Int,Int),[Term (Con t) String])] -> 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 :: [[Term (Con t) String]] -> 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 t -> [[Term (Con t) String]] ->
+    (PatternType t, [(Term (Con t) String, [Term (Con t) String])], 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
+                Var{}                -> t1
+                Apply ICon{} _       -> Interval
+                Apply PCon _         -> Path
+                Apply (DCon _ n _) _ ->
+                    let heads = pat : concatMap (\c -> if null c then [] else [head c]) cs
+                    in DataType n $ heads >>= \p -> case p of
+                        Apply (DCon i _ (PatEval conds)) _ -> map (\(cond,_) -> (i, map (first snd) cond)) conds
+                        _ -> []
+                Lambda{} -> error "checkNull"
+    in (t2, (pat, pats) : cs', b)
+
+checkNonEmptyClauses :: PatternType t -> [(Term (Con t) String, [Term (Con t) String])] -> Result
+checkNonEmptyClauses _                  []      = Result Incomplete []
+checkNonEmptyClauses Interval           clauses = checkIntervalClauses clauses
+checkNonEmptyClauses (DataType n conds) clauses = checkDataTypeClauses n conds clauses
+checkNonEmptyClauses Path               clauses = checkClauses (map snd clauses)
+checkNonEmptyClauses Unknown            clauses = checkClauses (map snd clauses)
+
+checkIntervalClauses :: [(Term (Con t) String, [Term (Con t) String])] -> Result
+checkIntervalClauses clauses =
+    let get con = map (\(i,(_,ps)) -> (i,ps)) $ filterWithIndex (\(c,_) -> c == con) clauses
+        lefts   = get $ Apply (ICon ILeft) []
+        rights  = get $ Apply (ICon IRight) []
+        vars    = get $ Var (error "") []
+        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, [Term (Con t) String])] -> [(Term (Con t) String, [Term (Con t) String])] -> Result
+checkDataTypeClauses n conds clauses = getResults $ flip map [0 .. n-1] $ \j ->
+    let getLength [] = 0
+        getLength (Apply (DCon i _ _) args : _) | i == j = length args
+        getLength (_ : pats) = getLength pats
+        len = getLength (map fst clauses)
+        
+        getPatterns (Apply _ pats) = pats
+        getPatterns _              = replicate len $ Var (error "") []
+    in map (\(i,(p,ps)) -> (i, getPatterns p ++ ps))
+           (filterWithIndex (\(c,_) -> c == Apply (DCon j n $ PatEval []) [] || c == Var (error "") []) clauses)
+       ++ (conds >>= \(c,ps) -> if j == c then [(-1, ps)] else [])
+  where
+    getResults :: [[(Int, [Term (Con t) String])]] -> 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
diff --git a/src/TypeChecking/Expressions/Patterns.hs b/src/TypeChecking/Expressions/Patterns.hs
new file mode 100644
--- /dev/null
+++ b/src/TypeChecking/Expressions/Patterns.hs
@@ -0,0 +1,81 @@
+{-# LANGUAGE ExistentialQuantification #-}
+
+module TypeChecking.Expressions.Patterns
+    ( typeCheckPatterns, typeCheckPattern
+    , TermsInCtx(..), TermInCtx(..)
+    ) where
+
+import Data.Void
+import Control.Monad
+
+import Semantics
+import Semantics.Value as V
+import Syntax as S
+import Syntax.ErrorDoc
+import TypeChecking.Context
+import TypeChecking.Monad
+import TypeChecking.Expressions.Utils
+import Normalization
+
+data TermInCtx b  = forall a. Eq a => TermInCtx  (Ctx String (Type Semantics) b a) (Term Semantics a)
+data TermsInCtx b = forall a. Eq a => TermsInCtx (Ctx String (Type Semantics) b a) [Term Semantics a] (Type Semantics a)
+
+typeCheckPattern :: (Monad m, Eq a) => Ctx String (Type Semantics) Void a -> Type Semantics a
+    -> Term PName b -> TCM m (Bool, Maybe (TermInCtx a), Term (String,SCon) String)
+typeCheckPattern ctx (Type (Apply (Semantics _ Interval) _) _) (Apply (pos, Ident "left") pats) = do
+    unless (null pats) $ warn [tooManyArgs pos]
+    return (False, Just $ TermInCtx Nil $ iCon ILeft, Apply ("left", ICon ILeft) [])
+typeCheckPattern ctx (Type (Apply (Semantics _ Interval) _) _) (Apply (pos, Ident "right") pats) = do
+    unless (null pats) $ warn [tooManyArgs pos]
+    return (False, Just $ TermInCtx Nil $ iCon IRight, Apply ("right", ICon IRight) [])
+typeCheckPattern ctx (Type (Apply (Semantics _ (DataType _ 0)) _) _) (Apply (_, Operator "") _) =
+    return (True, Nothing, Var "_" [])
+typeCheckPattern ctx (Type ty _) (Apply (pos, Operator "") _) =
+    throwError [Error Other $ emsgLC pos "" $ pretty "Expected non-empty type:" <+> prettyOpen ctx ty]
+typeCheckPattern ctx _ (Apply (_, Ident "_") []) = return (False, Nothing, Var "_" [])
+typeCheckPattern ctx (Type ty@(Apply (Semantics _ (DataType dt _)) _) k) (Apply (pos, Ident var) []) = do
+    cons <- lift $ getConstructor (Ident var) (Just dt)
+    case cons of
+        (con@(Semantics _ (Con (DCon i n conds))), Closed (Type conType _)):_ -> if isDataType conType
+            then return (False, Just $ TermInCtx Nil $ capply con, Apply (var, DCon i n conds) [])
+            else throwError [notEnoughArgs pos var]
+        _ -> return (False, Just $ TermInCtx (Snoc Nil var $ Type ty k) bvar, Var var [])
+  where
+    isDataType :: Term Semantics a -> Bool
+    isDataType (Lambda t) = isDataType t
+    isDataType (Apply (Semantics _ DataType{}) _) = True
+    isDataType _ = False
+typeCheckPattern ctx (Type ty k) (Apply (pos, Ident var) []) =
+    return (False, Just $ TermInCtx (Snoc Nil var $ Type ty k) bvar, cvar var)
+typeCheckPattern ctx (Type (Apply (Semantics _ (DataType dt _)) params) _) (Apply (pos, Ident conName) pats) = do
+    cons <- lift $ getConstructor (Ident conName) (Just dt)
+    case cons of
+        (con@(Semantics _ (Con (DCon i n conds))), Closed (Type conType k)):_ -> do
+            let conType' = Type (nf WHNF $ apps conType params) k
+            (bf, TermsInCtx ctx' terms (Type ty' _), rtpats) <- typeCheckPatterns ctx conType' pats
+            case nf WHNF ty' of
+                Apply (Semantics _ DataType{}) _ ->
+                    return (bf, Just $ TermInCtx ctx' (Apply con terms), Apply (conName, DCon i n conds) rtpats)
+                _ -> throwError [notEnoughArgs pos conName]
+        _ -> throwError [notInScope pos "data constructor" conName]
+typeCheckPattern ctx (Type ty _) (Apply (pos, _) _) =
+    throwError [Error TypeMismatch $ emsgLC pos "" $ pretty "Unexpected pattern"
+                                                  $$ pretty "Expected type:" <+> prettyOpen ctx ty]
+typeCheckPattern _ _ _ = error "typeCheckPattern"
+
+typeCheckPatterns :: (Monad m, Eq a) => Ctx String (Type Semantics) Void a -> Type Semantics a
+    -> [Term PName b] -> TCM m (Bool, TermsInCtx a, [Term (String,SCon) String])
+typeCheckPatterns _ ty [] = return (False, TermsInCtx Nil [] ty, [])
+typeCheckPatterns ctx (Type (Apply p@(Semantics _ (V.Pi k1 k2)) [a, b]) _) (pat:pats) = do
+    let a' = Type (nf WHNF a) k1
+    (bf1, mte, rtpat) <- typeCheckPattern ctx a' pat
+    TermInCtx ctx' te <- case mte of
+                            Nothing -> return $ TermInCtx (Snoc Nil "_" a') bvar
+                            Just te -> return te
+    let b' = case b of
+                Lambda{} -> instantiate1 te $ fmap (fmap $ liftBase ctx') $ snd (dropOnePi p a b)
+                _        -> fmap (liftBase ctx') b
+    (bf2, TermsInCtx ctx'' tes ty, rtpats) <- typeCheckPatterns (ctx +++ ctx') (Type (nf WHNF b') k2) pats
+    return (bf1 || bf2, TermsInCtx (ctx' +++ ctx'') (fmap (liftBase ctx'') te : tes) ty, rtpat:rtpats)
+typeCheckPatterns _ _ (Apply (pos, _) _ : _) = throwError [tooManyArgs pos]
+typeCheckPatterns _ _ _ = error "typeCheckPatterns"
diff --git a/src/TypeChecking/Expressions/Utils.hs b/src/TypeChecking/Expressions/Utils.hs
new file mode 100644
--- /dev/null
+++ b/src/TypeChecking/Expressions/Utils.hs
@@ -0,0 +1,86 @@
+module TypeChecking.Expressions.Utils where
+
+import Data.Bifunctor
+import Data.Void
+
+import Syntax
+import Syntax.ErrorDoc
+import Semantics
+import Semantics.Value
+import TypeChecking.Context
+import TypeChecking.Monad.Warn
+
+data Error = Error { errorType :: ErrorType, errorMsg :: EMsg (Term Syntax) }
+
+instance Eq Error where
+    Error e _ == Error e' _ = e == e'
+
+data ErrorType
+    = NotInScope
+    | Inference
+    | TooManyArgs
+    | NotEnoughArgs
+    | Coverage
+    | TypeMismatch
+    | Conditions
+    | Other
+    deriving Eq
+
+data Argument = Argument Int Posn (Maybe Name) | NoArgument [Error]
+
+instance Eq Argument where
+    Argument k p _ == Argument k' p' _ = k == k' && p == p'
+    _ == _ = False
+
+notInScope :: Show a => Posn -> String -> a -> Error
+notInScope pos s a = Error NotInScope $ emsgLC pos ("Not in scope: " ++ (if null s then "" else s ++ " ") ++ show a) enull
+
+inferErrorMsg :: Posn -> String -> Error
+inferErrorMsg pos s = Error Inference $ emsgLC pos ("Cannot infer type of " ++ s) enull
+
+inferExprErrorMsg :: Posn -> Error
+inferExprErrorMsg pos = Error Inference $ emsgLC pos "Cannot infer an expressions" enull
+
+inferArgErrorMsg :: Argument -> [Error]
+inferArgErrorMsg (Argument k pos mname) = [Error Inference $ emsgLC pos
+    ("Cannot infer " ++ nth (k + 1) ++ " argument" ++ maybe "" (\name -> " for " ++ nameToPrefix name) mname) enull]
+  where
+    nth 1 = "first"
+    nth 2 = "second"
+    nth 3 = "third"
+    nth n = show n ++ "th"
+inferArgErrorMsg (NoArgument errs) = errs
+
+inferParamsErrorMsg :: Show a => Posn -> a -> Error
+inferParamsErrorMsg pos d = Error Inference $ emsgLC pos ("Cannot infer parameters of data constructor " ++ show d) enull
+
+argsErrorMsg :: Posn -> String -> Error
+argsErrorMsg pos s = Error TooManyArgs $ emsgLC pos (s ++ " is applied to arguments") enull
+
+expectedArgErrorMsg :: Show a => Posn -> a -> Error
+expectedArgErrorMsg lc d = Error NotEnoughArgs $ emsgLC lc ("Expected an argument to " ++ show d) enull
+
+coverageErrorMsg :: Posn -> Maybe [Posn] -> [Error]
+coverageErrorMsg pos Nothing = [Error Coverage $ emsgLC pos "Incomplete pattern matching" enull]
+coverageErrorMsg _ (Just uc) = map (\pos -> Error Coverage $ emsgLC pos "Unreachable clause" enull) uc
+
+notEnoughArgs :: Show a => Posn -> a -> Error
+notEnoughArgs pos a = Error NotEnoughArgs $ emsgLC pos ("Not enough arguments to " ++ show a) enull
+
+tooManyArgs :: Posn -> Error
+tooManyArgs pos = Error TooManyArgs $ emsgLC pos "Too many arguments" enull
+
+prettyOpen :: Ctx String (Type Semantics) Void a -> Term Semantics a -> EDoc (Term Syntax)
+prettyOpen ctx term = epretty $ fmap (pretty . either id absurd) $ close ctx (bimap syntax Right term)
+
+checkIsType :: Monad m => Ctx String (Type Semantics) Void a -> Posn -> Term Semantics a -> WarnT [Error] m Sort
+checkIsType _ _ (Apply (Semantics _ (Universe k)) _) = return k
+checkIsType ctx pos t = throwError [Error TypeMismatch $ emsgLC pos "" $ pretty "Expected type: Type"
+                                                                      $$ pretty "Actual type:" <+> prettyOpen ctx t]
+
+termPos :: Term (Posn, s) a -> Posn
+termPos (Apply (pos, _) _) = pos
+termPos _ = error "termPos"
+
+catchErrorType :: Monad m => [ErrorType] -> WarnT [Error] m a -> ([Error] -> WarnT [Error] m a) -> WarnT [Error] m a
+catchErrorType errs = catchErrorBy $ \(Error err _) -> err `elem` errs
diff --git a/src/TypeChecking/Monad.hs b/src/TypeChecking/Monad.hs
--- a/src/TypeChecking/Monad.hs
+++ b/src/TypeChecking/Monad.hs
@@ -1,5 +1,5 @@
 module TypeChecking.Monad
-    ( EDocM, ScopeM, TCM, runTCM
+    ( EDocM, TCM, runTCM
     , addFunctionCheck, addDataTypeCheck, addConstructorCheck
     , module TypeChecking.Monad.Warn
     , module TypeChecking.Monad.Scope
@@ -9,42 +9,36 @@
 import Control.Monad
 import Control.Monad.Trans(lift)
 
+import TypeChecking.Expressions.Utils
 import TypeChecking.Monad.Warn
 import TypeChecking.Monad.Scope
-import Syntax.Term
-import Syntax.Expr
+import Syntax
+import Semantics
+import Semantics.Value
 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)
+type EDocM = WarnT [Error]
+type TCM m = EDocM (ScopeT 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
+multipleDeclaration :: Posn -> Name -> Error
+multipleDeclaration pos var = Error Other $ emsgLC pos ("Multiple declarations of " ++ show (nameToString var)) enull
 
-addFunctionCheck :: Monad m => PIdent -> Term String -> Type String -> TCM m ()
-addFunctionCheck (PIdent (lc,var)) te ty = do
+addFunctionCheck :: Monad m => PName -> SEval -> Closed (Type Semantics) -> TCM m ID
+addFunctionCheck (pos, var) e ty = do
     mr <- lift (getEntry var Nothing)
-    case mr of
-        [] -> lift (addFunction var te ty)
-        _  -> warn [multipleDeclaration lc var]
+    if null mr then lift (addFunction var e ty) else throwError [multipleDeclaration pos 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)
+addDataTypeCheck :: Monad m => PName -> Int -> Closed (Type Semantics) -> TCM m ID
+addDataTypeCheck (pos, var) n ty = do
+    mf <- lift (getFunction var)
+    md <- lift (getDataType var)
+    if null mf && null md then lift (addDataType var n ty) else throwError [multipleDeclaration pos var]
 
-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)
+addConstructorCheck :: Monad m => PName -> ID -> Int -> Int -> SEval -> Closed (Type Semantics) -> TCM m ()
+addConstructorCheck (pos, var) dt i n e ty = do
+    mf <- lift (getFunction var)
+    mc <- lift $ getConstructor var (Just dt)
+    if null mf && null mc then lift (addConstructor var dt i n e ty) else warn [multipleDeclaration pos var]
diff --git a/src/TypeChecking/Monad/Scope.hs b/src/TypeChecking/Monad/Scope.hs
--- a/src/TypeChecking/Monad/Scope.hs
+++ b/src/TypeChecking/Monad/Scope.hs
@@ -3,57 +3,94 @@
 module TypeChecking.Monad.Scope
     ( ScopeT, runScopeT
     , addFunction, addConstructor, addDataType
-    , deleteDataType
-    , getConstructor, getConstructorDataTypes
-    , Entry(..), getEntry
+    , replaceDataType, replaceFunction
+    , getDataType, getFunction
+    , getConstructor, 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
+import Syntax
+import Semantics
+import Semantics.Value
 
-data ScopeState a b c d = ScopeState
-    { functions    :: [(String, (a, b))]
-    , dataTypes    :: [(String, (b, Int))]
-    , constructors :: [((String, String), (Int, c, d))]
+data ScopeState = ScopeState
+    { functions    :: [(Name, (Semantics, Closed (Type Semantics)))]
+    , dataTypes    :: [(Name, (Semantics, Closed (Type Semantics)))]
+    , constructors :: [((Name, ID), (Semantics, Closed (Type Semantics)))]
+    , counter      :: ID
     }
 
-newtype ScopeT a b c d m a' = ScopeT { unScopeT :: StateT (ScopeState a b c d) m a' }
+newtype ScopeT m a = ScopeT { unScopeT :: StateT ScopeState 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 }
+addFunction :: Monad m => Name -> SEval -> Closed (Type Semantics) -> ScopeT m ID
+addFunction v e ty = ScopeT $ do
+    scope <- get
+    let (fc,scope') = updScopeFunction v e ty scope
+    put scope'
+    return fc
 
-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 }
+replaceFunction :: Monad m => Name -> SEval -> Closed (Type Semantics) -> ScopeT m ()
+replaceFunction v e ty = ScopeT $ modify $ \scope -> case lookupDelete v (functions scope) of
+    Just ((Semantics s (FunCall i _),_), functions') -> scope { functions = (v, (Semantics s (FunCall i e), ty)) : functions' }
+    _ -> snd (updScopeFunction v e ty 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 }
+updScopeFunction :: Name -> SEval -> Closed (Type Semantics) -> ScopeState -> (ID, ScopeState)
+updScopeFunction v e ty scope = (counter scope, scope
+    { functions = (v, (Semantics (Name Prefix v) (FunCall (counter scope) e), ty)) : functions scope
+    , counter = counter scope + 1
+    })
 
-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) }
+getFunction :: Monad m => Name -> ScopeT m [(Semantics, Closed (Type Semantics))]
+getFunction v = ScopeT $ liftM (map snd . filter (\(v',_) -> v == v') . functions) get
 
-getConstructor :: Monad m => String -> Maybe String -> ScopeT a b c d m [(Int, c, d)]
+addDataType :: Monad m => Name -> Int -> Closed (Type Semantics) -> ScopeT m ID
+addDataType v n ty = ScopeT $ do
+    scope <- get
+    let (dt,scope') = updScopeDataType v n ty scope
+    put scope'
+    return dt
+
+replaceDataType :: Monad m => Name -> Int -> Closed (Type Semantics) -> ScopeT m ()
+replaceDataType v n ty = ScopeT $ modify $ \scope -> case lookupDelete v (dataTypes scope) of
+    Just ((Semantics s (DataType i _), _), dataTypes') -> scope { dataTypes = (v, (Semantics s (DataType i n), ty)) : dataTypes' }
+    _ -> snd (updScopeDataType v n ty scope)
+
+updScopeDataType :: Name -> Int -> Closed (Type Semantics) -> ScopeState -> (ID, ScopeState)
+updScopeDataType v n ty scope = (counter scope, scope
+    { dataTypes = (v, (Semantics (Name Prefix v) (DataType (counter scope) n), ty)) : dataTypes scope
+    , counter = counter scope + 1
+    })
+
+getDataType :: Monad m => Name -> ScopeT m [(Semantics, Closed (Type Semantics))]
+getDataType v = ScopeT $ liftM (map snd . filter (\(v',_) -> v == v') . dataTypes) get
+
+lookupDelete :: Eq a => a -> [(a,b)] -> Maybe (b, [(a,b)])
+lookupDelete _ [] = Nothing
+lookupDelete a' ((a,b):xs) | a == a' = Just (b, xs)
+                           | otherwise = fmap (\(b',xs') -> (b', (a,b):xs')) (lookupDelete a' xs)
+
+addConstructor :: Monad m => Name -> ID -> Int -> Int -> SEval -> Closed (Type Semantics) -> ScopeT m ()
+addConstructor con dt i n e ty = ScopeT $ modify $ \scope -> scope
+    { constructors = ((con, dt), (Semantics (Name Prefix con) (Con $ DCon i n e), ty)) : constructors scope
+    }
+
+getConstructor :: Monad m => Name -> Maybe ID -> ScopeT m [(Semantics, Closed (Type Semantics))]
 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 :: Monad m => Name -> Maybe (ID, [Term Semantics a]) -> ScopeT m [(Semantics, Type Semantics a)]
 getEntry v dt = ScopeT $ do
-    cons  <- unScopeT (getConstructor v dt)
+    cons  <- unScopeT $ getConstructor v (fmap fst 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
+    let dts = if isNothing dt then maybeToList $ lookup v $ dataTypes scope else []
+    return $ map (\(s,t) -> (s, open t)) (maybeToList (lookup v $ functions scope) ++ dts)
+            ++ if null dts then (map (\(s, Closed (Type t l)) -> (s, Type (apps t (maybe [] snd dt)) l)) cons) else []
 
-runScopeT :: Monad m => ScopeT a b c d m a' -> m a'
-runScopeT (ScopeT f) = evalStateT f $ ScopeState [] [] []
+runScopeT :: Monad m => ScopeT m a -> m a
+runScopeT (ScopeT f) = evalStateT f $ ScopeState [] [] [] 0
diff --git a/src/TypeChecking/Monad/Warn.hs b/src/TypeChecking/Monad/Warn.hs
--- a/src/TypeChecking/Monad/Warn.hs
+++ b/src/TypeChecking/Monad/Warn.hs
@@ -3,7 +3,9 @@
 module TypeChecking.Monad.Warn
     ( WarnT, warn, runWarnT
     , throwError, catchError
+    , catchErrorBy
     , forW, throwErrors
+    , mapWarnT
     ) where
 
 import Control.Monad
@@ -13,6 +15,7 @@
 import Control.Applicative
 import Data.Monoid hiding ((<>))
 import Data.Maybe
+import Data.Either
 
 newtype WarnT w m a = WarnT { runWarnT :: m (w, Maybe a) }
 
@@ -55,3 +58,12 @@
 throwErrors :: Monad m => [w] -> WarnT [w] m ()
 throwErrors [] = return ()
 throwErrors ws = throwError ws
+
+catchErrorBy :: Monad m => (w -> Bool) -> WarnT [w] m a -> ([w] -> WarnT [w] m a) -> WarnT [w] m a
+catchErrorBy p m h = WarnT $ runWarnT m >>= \(errs, ma) ->
+    case partitionEithers $ map (\err -> if p err then Left err else Right err) errs of
+        ([],_) -> return (errs,ma)
+        (errs1,errs2) -> runWarnT $ warn errs2 >> h errs1
+
+mapWarnT :: Monad m => (w -> w') -> WarnT w m a -> WarnT w' m a
+mapWarnT f (WarnT m) = WarnT $ liftM (\(w,a) -> (f w, a)) m