diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,20 @@ +Copyright (c) 2017 Anonymous + +Permission is hereby granted, free of charge, to any person obtaining +a copy of this software and associated documentation files (the +"Software"), to deal in the Software without restriction, including +without limitation the rights to use, copy, modify, merge, publish, +distribute, sublicense, and/or sell copies of the Software, and to +permit persons to whom the Software is furnished to do so, subject to +the following conditions: + +The above copyright notice and this permission notice shall be +included in all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF +MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. +IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY +CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, +TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE +SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. diff --git a/Makefile b/Makefile new file mode 100644 --- /dev/null +++ b/Makefile @@ -0,0 +1,10 @@ +# Makefile for Sit + +default : + cabal install --only-dependencies + cabal configure + cabal build + dist/build/Sit.bin/Sit.bin test/Test.agda + +install : + cabal install diff --git a/README.md b/README.md new file mode 100644 --- /dev/null +++ b/README.md @@ -0,0 +1,88 @@ +# Sit: size-irrelevant types +A prototype dependently-typed language with sized natural numbers + +Sit parses and typechecks `.agda` that conform to the Sit language syntax. + +Syntax (excerpt): +```agda +--- Lexical stuff + +--- Single line comment +{- Block comment -} +--; --- End of declaration (mandatory) +f_x'1 --- identifiers start with a letter, then have letters, digits, _ and ' + +--- Declarations + +x : T --; --- type signature +x = t --; --- definition +open import M --; --- ignored, for Agda compatibility + +--- Sit specifics + +oo --- infinity size +i + 1 --- successor size + +Nat a --- type of natural numbers below size a +zero a --- number zero (a is size annotation) +suc a n --- successor of n (a is size annotation) + +forall .i -> T --- irrelevant size quantification +forall ..i -> T --- relevant size quantification + +fix T t n --- recursive function over natural numbers + --- T: return type + --- t: functional + --- n: natural number argument + +\{ (zero _) -> t; (suc _ x) -> u } --- case distinction function + +--- Inherited Agda syntax + +U -> T --- non-dependent function type +(x y z : U) -> T --- dependent function type +\ x y z -> t --- lambda-abstraction +t u --- application + +Set --- first universe +Set1 --- second universe +Set a --- universe of level a + +``` + +## Limitations + +Sit only understands a tiny subset of the Agda language. +Sit does not understand layout, instead each declaration has to be terminated with +comment `--;`. + +## Installation + +Requires GHC and cabal, for instance via the Haskell Platform. +In a shell, type +``` + cabal install +``` + +## Test + +In a shell, type +``` + Sit.bin test/Test.agda +``` + +## Example + +This is the addition function in Sit: +``` +--- Addition of natural numbers + +plus : forall .i -> Nat i -> Nat oo -> Nat oo --; +plus = \ i x y -> + fix (\ i x -> Nat oo) + (\ _ f -> \ + { (zero _) -> y + ; (suc _ x) -> suc oo (f x) + }) + x +``` diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/Sit.cabal b/Sit.cabal new file mode 100644 --- /dev/null +++ b/Sit.cabal @@ -0,0 +1,75 @@ +name: Sit +version: 0.2017.02.26 +build-type: Simple +cabal-version: >= 1.8 +license: OtherLicense +license-file: LICENSE +author: Anonymous +maintainer: Anonymous +homepage: NONE +category: Dependent types +synopsis: Prototypical type checker for Type Theory with Sized Natural Numbers +description: + Sit = Size-irrelevant types + . + Sit is a prototypical language with an Agda-compatible syntax. + It has dependent function types, universes, sized natural numbers, + and case and recursion over natural numbers. + There is a relevant and an irrelevant quantifier over sizes. + For an example, see file test/Test.agda + +tested-with: GHC == 7.8.4 + GHC == 7.10.3 + GHC == 8.0.1 + +data-files: test/Makefile + test/Base.agda + test/Test.agda + README.md + +extra-source-files: Makefile + src/Makefile + src/Sit.cf + src/undefined.h + +source-repository head + type: git + location: NONE + +executable Sit.bin + ghc-options: -rtsopts + hs-source-dirs: src + + build-depends: array >= 0.3 && < 1.0, + base >= 4.2 && < 5.0, + containers >= 0.3 && < 1.0, + data-lens-light >= 0.1.2.2 && < 0.2, + mtl >= 2.2.1 && < 3.0 + +-- -- The lexer and parser are shipped as .hs files, thus, no tools necessary. +-- build-tools: happy >= 1.15 && < 2, +-- alex >= 3.0 && < 4 + + extensions: MultiParamTypeClasses + FunctionalDependencies + TypeSynonymInstances + FlexibleInstances + FlexibleContexts + GeneralizedNewtypeDeriving + LambdaCase + TupleSections + + main-is: Sit.hs + + other-modules: Abstract + Evaluation + Impossible + Internal + Lens + Substitute + TypeChecker + Sit.Abs + Sit.ErrM + Sit.Lex + Sit.Par + Sit.Print diff --git a/dist/build/Sit.bin/Sit.bin-tmp/Sit/Lex.hs b/dist/build/Sit.bin/Sit.bin-tmp/Sit/Lex.hs new file mode 100644 --- /dev/null +++ b/dist/build/Sit.bin/Sit.bin-tmp/Sit/Lex.hs @@ -0,0 +1,423 @@ +{-# OPTIONS_GHC -fno-warn-unused-binds -fno-warn-missing-signatures #-} +{-# LANGUAGE CPP,MagicHash #-} +{-# LINE 3 "src/Sit/Lex.x" #-} + +{-# OPTIONS -fno-warn-incomplete-patterns #-} +{-# OPTIONS_GHC -w #-} +module Sit.Lex where + + + +import qualified Data.Bits +import Data.Word (Word8) +import Data.Char (ord) + +#if __GLASGOW_HASKELL__ >= 603 +#include "ghcconfig.h" +#elif defined(__GLASGOW_HASKELL__) +#include "config.h" +#endif +#if __GLASGOW_HASKELL__ >= 503 +import Data.Array +import Data.Array.Base (unsafeAt) +#else +import Array +#endif +#if __GLASGOW_HASKELL__ >= 503 +import GHC.Exts +#else +import GlaExts +#endif +alex_tab_size :: Int +alex_tab_size = 8 +alex_base :: AlexAddr +alex_base = AlexA# "\xf8\xff\xff\xff\xd9\xff\xff\xff\x47\x00\x00\x00\xc7\x00\x00\x00\x9a\x01\x00\x00\x1a\x02\x00\x00\x1a\x03\x00\x00\xb6\xff\xff\xff\x00\x00\x00\x00\x0b\x03\x00\x00\x00\x00\x00\x00\x09\x01\x00\x00\x8b\x03\x00\x00\xdb\xff\xff\xff\x4b\x04\x00\x00\x0b\x04\x00\x00\x00\x00\x00\x00\x01\x05\x00\x00\x00\x00\x00\x00\x02\x00\x00\x00\xda\xff\xff\xff\x00\x00\x00\x00\xdc\xff\xff\xff\xda\x05\x00\x00\xd9\x01\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\x04\x00\xff\xff\x04\x00\xff\xff\x04\x00\x04\x00\x0a\x00\x0a\x00\x10\x00\x10\x00\xff\xff\xff\xff\x11\x00\x11\x00\x11\x00\x11\x00\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"# + +alex_accept = listArray (0::Int,24) [AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccSkip,AlexAccSkip,AlexAccSkip,AlexAcc (alex_action_3),AlexAcc (alex_action_3),AlexAcc (alex_action_3),AlexAcc (alex_action_4),AlexAcc (alex_action_5)] +{-# LINE 39 "src/Sit/Lex.x" #-} + + +tok :: (Posn -> String -> Token) -> (Posn -> String -> Token) +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 + + deriving (Eq,Show,Ord) + +data Token = + PT Posn Tok + | Err Posn + deriving (Eq,Show,Ord) + +printPosn :: Posn -> String +printPosn (Pn _ l c) = "line " ++ show l ++ ", column " ++ show c + +tokenPos :: [Token] -> String +tokenPos (t:_) = printPosn (tokenPosn t) +tokenPos [] = "end of file" + +tokenPosn :: Token -> Posn +tokenPosn (PT p _) = p +tokenPosn (Err p) = p + +tokenLineCol :: Token -> (Int, Int) +tokenLineCol = posLineCol . tokenPosn + +posLineCol :: Posn -> (Int, Int) +posLineCol (Pn _ l c) = (l,c) + +mkPosToken :: Token -> ((Int, Int), String) +mkPosToken t@(PT p _) = (posLineCol p, prToken t) + +prToken :: Token -> String +prToken t = case t of + PT _ (TS s _) -> s + PT _ (TL s) -> show s + PT _ (TI s) -> s + PT _ (TV s) -> s + PT _ (TD s) -> s + PT _ (TC s) -> s + Err _ -> "#error" + + +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 :: BTree +resWords = b "\\" 16 (b ":" 8 (b "--;" 4 (b ")" 2 (b "(" 1 N N) (b "+" 3 N N)) (b "." 6 (b "->" 5 N N) (b ".." 7 N N))) (b "Set" 12 (b "=" 10 (b ";" 9 N N) (b "Nat" 11 N N)) (b "Set2" 14 (b "Set1" 13 N N) (b "Size" 15 N N)))) (b "of" 24 (b "forall" 20 (b "case" 18 (b "_" 17 N N) (b "fix" 19 N N)) (b "lsuc" 22 (b "import" 21 N N) (b "lzero" 23 N N))) (b "suc" 28 (b "open" 26 (b "oo" 25 N N) (b "return" 27 N N)) (b "{" 30 (b "zero" 29 N N) (b "}" 31 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 (TV . share) s)) +alex_action_5 = tok (\p s -> PT p (TI $ share s)) +{-# LINE 1 "templates/GenericTemplate.hs" #-} +{-# LINE 1 "templates/GenericTemplate.hs" #-} +{-# LINE 1 "" #-} +{-# LINE 1 "" #-} +{-# LINE 9 "" #-} +# 1 "/usr/include/stdc-predef.h" 1 3 4 + +# 17 "/usr/include/stdc-predef.h" 3 4 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +{-# LINE 9 "" #-} +{-# 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 21 "templates/GenericTemplate.hs" #-} + + + + + +-- Do not remove this comment. Required to fix CPP parsing when using GCC and a clang-compiled alex. +#if __GLASGOW_HASKELL__ > 706 +#define GTE(n,m) (tagToEnum# (n >=# m)) +#define EQ(n,m) (tagToEnum# (n ==# m)) +#else +#define GTE(n,m) (n >=# m) +#define EQ(n,m) (n ==# m) +#endif +{-# LINE 51 "templates/GenericTemplate.hs" #-} + + +data AlexAddr = AlexA# Addr# +-- Do not remove this comment. Required to fix CPP parsing when using GCC and a clang-compiled alex. +#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 GTE(offset,0#) && EQ(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 198 "templates/GenericTemplate.hs" #-} + +data AlexLastAcc a + = AlexNone + | AlexLastAcc a !AlexInput !Int + | AlexLastSkip !AlexInput !Int + +instance Functor AlexLastAcc where + fmap _ AlexNone = AlexNone + fmap f (AlexLastAcc x y z) = AlexLastAcc (f x) y z + fmap _ (AlexLastSkip x y) = AlexLastSkip x y + +data AlexAcc a user + = AlexAccNone + | AlexAcc a + | AlexAccSkip diff --git a/dist/build/Sit.bin/Sit.bin-tmp/Sit/Par.hs b/dist/build/Sit.bin/Sit.bin-tmp/Sit/Par.hs new file mode 100644 --- /dev/null +++ b/dist/build/Sit.bin/Sit.bin-tmp/Sit/Par.hs @@ -0,0 +1,995 @@ +{-# OPTIONS_GHC -w #-} +{-# OPTIONS -fglasgow-exts -cpp #-} +{-# OPTIONS_GHC -fno-warn-incomplete-patterns -fno-warn-overlapping-patterns #-} +module Sit.Par where +import Sit.Abs +import Sit.Lex +import Sit.ErrM +import qualified Data.Array as Happy_Data_Array +import qualified GHC.Exts as Happy_GHC_Exts +import Control.Applicative(Applicative(..)) +import Control.Monad (ap) + +-- parser produced by Happy Version 1.19.5 + +newtype HappyAbsSyn = HappyAbsSyn HappyAny +#if __GLASGOW_HASKELL__ >= 607 +type HappyAny = Happy_GHC_Exts.Any +#else +type HappyAny = forall a . a +#endif +happyIn15 :: (Ident) -> (HappyAbsSyn ) +happyIn15 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn15 #-} +happyOut15 :: (HappyAbsSyn ) -> (Ident) +happyOut15 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut15 #-} +happyIn16 :: (Integer) -> (HappyAbsSyn ) +happyIn16 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn16 #-} +happyOut16 :: (HappyAbsSyn ) -> (Integer) +happyOut16 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut16 #-} +happyIn17 :: (Prg) -> (HappyAbsSyn ) +happyIn17 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn17 #-} +happyOut17 :: (HappyAbsSyn ) -> (Prg) +happyOut17 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut17 #-} +happyIn18 :: (Decl) -> (HappyAbsSyn ) +happyIn18 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn18 #-} +happyOut18 :: (HappyAbsSyn ) -> (Decl) +happyOut18 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut18 #-} +happyIn19 :: (QualId) -> (HappyAbsSyn ) +happyIn19 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn19 #-} +happyOut19 :: (HappyAbsSyn ) -> (QualId) +happyOut19 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut19 #-} +happyIn20 :: ([Decl]) -> (HappyAbsSyn ) +happyIn20 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn20 #-} +happyOut20 :: (HappyAbsSyn ) -> ([Decl]) +happyOut20 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut20 #-} +happyIn21 :: (IdU) -> (HappyAbsSyn ) +happyIn21 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn21 #-} +happyOut21 :: (HappyAbsSyn ) -> (IdU) +happyOut21 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut21 #-} +happyIn22 :: (Bind) -> (HappyAbsSyn ) +happyIn22 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn22 #-} +happyOut22 :: (HappyAbsSyn ) -> (Bind) +happyOut22 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut22 #-} +happyIn23 :: ([Bind]) -> (HappyAbsSyn ) +happyIn23 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn23 #-} +happyOut23 :: (HappyAbsSyn ) -> ([Bind]) +happyOut23 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut23 #-} +happyIn24 :: ([Ident]) -> (HappyAbsSyn ) +happyIn24 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn24 #-} +happyOut24 :: (HappyAbsSyn ) -> ([Ident]) +happyOut24 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut24 #-} +happyIn25 :: ([IdU]) -> (HappyAbsSyn ) +happyIn25 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn25 #-} +happyOut25 :: (HappyAbsSyn ) -> ([IdU]) +happyOut25 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut25 #-} +happyIn26 :: (Exp) -> (HappyAbsSyn ) +happyIn26 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn26 #-} +happyOut26 :: (HappyAbsSyn ) -> (Exp) +happyOut26 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut26 #-} +happyIn27 :: (Exp) -> (HappyAbsSyn ) +happyIn27 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn27 #-} +happyOut27 :: (HappyAbsSyn ) -> (Exp) +happyOut27 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut27 #-} +happyIn28 :: (Exp) -> (HappyAbsSyn ) +happyIn28 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn28 #-} +happyOut28 :: (HappyAbsSyn ) -> (Exp) +happyOut28 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut28 #-} +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# "\x7f\x00\x7f\x00\xf0\x00\x7f\x00\xf0\xff\x04\x00\x04\x00\xf0\x00\xf0\xff\x52\x00\x1a\x00\x52\x00\xf0\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x01\x00\x1a\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\xeb\x00\x3b\x00\x1a\x00\xf3\xff\x1a\x00\x04\x00\xeb\x00\xf0\xff\xeb\x00\xea\x00\xe6\x00\x04\x00\xe6\x00\xe7\x00\xe7\x00\xe7\x00\xe4\x00\xe4\x00\x43\x00\x01\x01\xe2\x00\xe1\x00\x00\x00\xfd\xff\xd2\x00\xd2\x00\x00\x00\xd1\x00\xd1\x00\x7f\x00\x1a\x00\x1a\x00\x00\x00\x00\x00\xdd\x00\x00\x00\x00\x00\x00\x00\xee\x00\xc5\x00\xe9\x00\xdc\x00\xf9\x00\x00\x00\xc2\x00\x1a\x00\xe0\x00\x00\x00\x00\x00\x00\x00\x1a\x00\xb7\x00\x1a\x00\x1a\x00\x1a\x00\x1a\x00\x00\x00\x00\x00\x00\x00\xc9\x00\x00\x00\xd0\x00\x00\x00\xb4\x00\x00\x00\xc0\x00\xbf\x00\xbe\x00\xae\x00\x1a\x00\x00\x00\x00\x00\xad\x00\x1a\x00\x00\x00\x1a\x00\x98\x00\x9d\x00\x80\x00\x66\x00\xf0\xff\x6b\x00\x54\x00\x1a\x00\xe8\xff\x00\x00\x00\x00"# + +happyGotoOffsets :: HappyAddr +happyGotoOffsets = HappyA# "\x8b\x00\x06\x00\x3f\x00\xbb\x00\x82\x00\x5f\x00\xfb\x00\x38\x00\x50\x00\x61\x00\xec\x00\xef\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x44\x00\xde\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\x44\x00\xdb\x00\x2f\x00\xcd\x00\xf8\x00\x00\x00\x16\x00\x00\x00\x34\x00\x00\x00\xf6\x00\x00\x00\x29\x00\x55\x00\x42\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x24\x00\x15\x00\xaa\x00\xca\x00\xbc\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\x07\x00\xb9\x00\x00\x00\x00\x00\x00\x00\x00\x00\xab\x00\x00\x00\xa8\x00\x9a\x00\x97\x00\x89\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\x86\x00\x00\x00\x00\x00\x00\x00\x78\x00\x00\x00\x74\x00\x00\x00\x00\x00\x00\x00\x00\x00\x64\x00\x00\x00\x00\x00\x70\x00\x00\x00\x00\x00\x00\x00"# + +happyDefActions :: HappyAddr +happyDefActions = HappyA# "\xed\xff\xed\xff\x00\x00\xed\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf3\xff\xe8\xff\xdc\xff\xdd\xff\xc7\xff\x00\x00\x00\x00\xda\xff\xd9\xff\xd8\xff\xd7\xff\xe7\xff\xd4\xff\xd2\xff\xd3\xff\xdb\xff\xd5\xff\xd6\xff\xf2\xff\x00\x00\xc9\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xdf\xff\x00\x00\xe1\xff\x00\x00\xe3\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xea\xff\x00\x00\x00\x00\xec\xff\x00\x00\x00\x00\x00\x00\xf1\xff\x00\x00\x00\x00\xed\xff\x00\x00\x00\x00\xe5\xff\xe6\xff\x00\x00\xe2\xff\xe0\xff\xde\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xc8\xff\x00\x00\x00\x00\x00\x00\xd1\xff\xcd\xff\xcb\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xef\xff\xf0\xff\xe9\xff\xee\xff\xeb\xff\x00\x00\xcf\xff\x00\x00\xd0\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xe4\xff\xcc\xff\x00\x00\x00\x00\xce\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xca\xff"# + +happyCheck :: HappyAddr +happyCheck = HappyA# "\xff\xff\x11\x00\x01\x00\x06\x00\x11\x00\x01\x00\x00\x00\x1f\x00\x01\x00\x03\x00\x06\x00\x07\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x20\x00\x1e\x00\x11\x00\x20\x00\x13\x00\x00\x00\x00\x00\x16\x00\x17\x00\x04\x00\x19\x00\x01\x00\x06\x00\x1c\x00\x1d\x00\x22\x00\x0a\x00\x20\x00\x21\x00\x22\x00\x00\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x00\x00\x10\x00\x11\x00\x12\x00\x13\x00\x14\x00\x00\x00\x16\x00\x17\x00\x09\x00\x19\x00\x00\x00\x06\x00\x1c\x00\x1d\x00\x00\x00\x0a\x00\x20\x00\x21\x00\x01\x00\x09\x00\x03\x00\x00\x00\x05\x00\x09\x00\x00\x00\x04\x00\x00\x00\x01\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x06\x00\x08\x00\x11\x00\x0a\x00\x13\x00\x0b\x00\x00\x00\x16\x00\x17\x00\x01\x00\x19\x00\x00\x00\x06\x00\x1c\x00\x1d\x00\x05\x00\x0a\x00\x20\x00\x21\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x00\x00\x01\x00\x11\x00\x00\x00\x13\x00\x07\x00\x06\x00\x16\x00\x17\x00\x06\x00\x19\x00\x0b\x00\x02\x00\x1c\x00\x1d\x00\x00\x00\x01\x00\x20\x00\x21\x00\x00\x00\x01\x00\x06\x00\x11\x00\x00\x00\x01\x00\x06\x00\x0b\x00\x0c\x00\x0d\x00\x06\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x06\x00\x00\x00\x01\x00\x00\x00\x06\x00\x02\x00\x03\x00\x06\x00\x05\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x1a\x00\x00\x00\x01\x00\x1c\x00\x06\x00\x01\x00\x20\x00\x06\x00\x09\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x00\x00\x00\x00\x01\x00\x03\x00\x06\x00\x05\x00\x02\x00\x06\x00\x05\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x00\x00\x00\x00\x01\x00\x03\x00\x06\x00\x05\x00\x02\x00\x06\x00\x05\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x18\x00\x00\x00\x01\x00\x06\x00\x06\x00\x11\x00\x02\x00\x06\x00\x1d\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x01\x00\x00\x00\x01\x00\x1b\x00\x06\x00\x02\x00\x21\x00\x06\x00\x08\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x05\x00\x00\x00\x01\x00\x20\x00\x06\x00\x05\x00\x22\x00\x06\x00\x15\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x02\x00\x0d\x00\x07\x00\x08\x00\x07\x00\x08\x00\x08\x00\x07\x00\x08\x00\x22\x00\x04\x00\x22\x00\x20\x00\x22\x00\xff\xff\x20\x00\xff\xff\xff\xff\x22\x00\xff\xff\xff\xff\x20\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"# + +happyTable :: HappyAddr +happyTable = HappyA# "\x00\x00\x19\x00\x14\x00\x3c\x00\x19\x00\x2e\x00\x32\x00\x76\x00\x51\x00\x38\x00\x2f\x00\x30\x00\x15\x00\x16\x00\x17\x00\x18\x00\x0e\x00\x4a\x00\x19\x00\x0e\x00\x1a\x00\x36\x00\x0e\x00\x1b\x00\x1c\x00\x5b\x00\x1d\x00\x23\x00\x27\x00\x1e\x00\x1f\x00\xff\xff\x45\x00\x0e\x00\x20\x00\xff\xff\x5c\x00\x15\x00\x16\x00\x17\x00\x18\x00\x29\x00\x24\x00\x19\x00\x25\x00\x1a\x00\x26\x00\x0e\x00\x1b\x00\x1c\x00\x42\x00\x1d\x00\x29\x00\x27\x00\x1e\x00\x1f\x00\x29\x00\x48\x00\x0e\x00\x20\x00\x14\x00\x44\x00\x4d\x00\x36\x00\x4e\x00\x2a\x00\x40\x00\x37\x00\x0e\x00\x0f\x00\x15\x00\x16\x00\x17\x00\x18\x00\x10\x00\x3f\x00\x19\x00\x40\x00\x1a\x00\x4b\x00\x0e\x00\x1b\x00\x1c\x00\x14\x00\x1d\x00\x41\x00\x27\x00\x1e\x00\x1f\x00\x74\x00\x28\x00\x0e\x00\x20\x00\x15\x00\x16\x00\x17\x00\x18\x00\x0e\x00\x0f\x00\x19\x00\x0e\x00\x1a\x00\x30\x00\x10\x00\x1b\x00\x1c\x00\x71\x00\x1d\x00\x26\x00\x73\x00\x1e\x00\x1f\x00\x0e\x00\x0f\x00\x0e\x00\x20\x00\x0e\x00\x0f\x00\x10\x00\x71\x00\x0e\x00\x0f\x00\x10\x00\x11\x00\x74\x00\x21\x00\x10\x00\x11\x00\x6c\x00\x21\x00\x0e\x00\x11\x00\x6a\x00\x21\x00\x0e\x00\x0f\x00\x31\x00\x0e\x00\x0f\x00\x32\x00\x10\x00\x39\x00\x33\x00\x10\x00\x3a\x00\x11\x00\x67\x00\x21\x00\x11\x00\x5d\x00\x21\x00\x0e\x00\x0f\x00\x36\x00\x0e\x00\x0f\x00\x70\x00\x10\x00\x6f\x00\x0e\x00\x10\x00\x6e\x00\x11\x00\x5e\x00\x21\x00\x11\x00\x5f\x00\x21\x00\x0e\x00\x0f\x00\x32\x00\x0e\x00\x0f\x00\x33\x00\x10\x00\x5a\x00\x69\x00\x10\x00\x6c\x00\x11\x00\x60\x00\x21\x00\x11\x00\x62\x00\x21\x00\x0e\x00\x0f\x00\x32\x00\x0e\x00\x0f\x00\x33\x00\x10\x00\x34\x00\x64\x00\x10\x00\x6a\x00\x11\x00\x50\x00\x21\x00\x11\x00\x58\x00\x21\x00\x0e\x00\x0f\x00\x66\x00\x0e\x00\x0f\x00\x3c\x00\x10\x00\x65\x00\x67\x00\x10\x00\x62\x00\x11\x00\x59\x00\x21\x00\x11\x00\x47\x00\x21\x00\x0e\x00\x0f\x00\x54\x00\x0e\x00\x0f\x00\x56\x00\x10\x00\x50\x00\x20\x00\x10\x00\x58\x00\x11\x00\x4a\x00\x21\x00\x11\x00\x4e\x00\x21\x00\x0e\x00\x0f\x00\x55\x00\x0e\x00\x0f\x00\x0e\x00\x10\x00\x57\x00\xff\xff\x10\x00\x3d\x00\x11\x00\x20\x00\x21\x00\x11\x00\x50\x00\x12\x00\x2b\x00\x43\x00\x2b\x00\x46\x00\x53\x00\x2b\x00\x2c\x00\xff\xff\x3e\x00\xff\xff\x0e\x00\xff\xff\x00\x00\x0e\x00\x00\x00\x00\x00\xff\xff\x00\x00\x00\x00\x0e\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 (12, 56) [ + (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) + ] + +happy_n_terms = 35 :: Int +happy_n_nonterms = 14 :: Int + +happyReduce_12 = happySpecReduce_1 0# happyReduction_12 +happyReduction_12 happy_x_1 + = case happyOutTok happy_x_1 of { (PT _ (TV happy_var_1)) -> + happyIn15 + (Ident happy_var_1 + )} + +happyReduce_13 = happySpecReduce_1 1# happyReduction_13 +happyReduction_13 happy_x_1 + = case happyOutTok happy_x_1 of { (PT _ (TI happy_var_1)) -> + happyIn16 + ((read ( happy_var_1)) :: Integer + )} + +happyReduce_14 = happySpecReduce_1 2# happyReduction_14 +happyReduction_14 happy_x_1 + = case happyOut20 happy_x_1 of { happy_var_1 -> + happyIn17 + (Sit.Abs.Prg happy_var_1 + )} + +happyReduce_15 = happySpecReduce_3 3# happyReduction_15 +happyReduction_15 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut15 happy_x_1 of { happy_var_1 -> + case happyOut27 happy_x_3 of { happy_var_3 -> + happyIn18 + (Sit.Abs.Sig happy_var_1 happy_var_3 + )}} + +happyReduce_16 = happySpecReduce_3 3# happyReduction_16 +happyReduction_16 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut15 happy_x_1 of { happy_var_1 -> + case happyOut27 happy_x_3 of { happy_var_3 -> + happyIn18 + (Sit.Abs.Def happy_var_1 happy_var_3 + )}} + +happyReduce_17 = happySpecReduce_3 3# happyReduction_17 +happyReduction_17 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut19 happy_x_3 of { happy_var_3 -> + happyIn18 + (Sit.Abs.Open happy_var_3 + )} + +happyReduce_18 = happySpecReduce_0 3# happyReduction_18 +happyReduction_18 = happyIn18 + (Sit.Abs.Blank + ) + +happyReduce_19 = happySpecReduce_1 4# happyReduction_19 +happyReduction_19 happy_x_1 + = case happyOut15 happy_x_1 of { happy_var_1 -> + happyIn19 + (Sit.Abs.Sg happy_var_1 + )} + +happyReduce_20 = happySpecReduce_3 4# happyReduction_20 +happyReduction_20 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut19 happy_x_1 of { happy_var_1 -> + case happyOut15 happy_x_3 of { happy_var_3 -> + happyIn19 + (Sit.Abs.Cons happy_var_1 happy_var_3 + )}} + +happyReduce_21 = happySpecReduce_1 5# happyReduction_21 +happyReduction_21 happy_x_1 + = case happyOut18 happy_x_1 of { happy_var_1 -> + happyIn20 + ((:[]) happy_var_1 + )} + +happyReduce_22 = happySpecReduce_3 5# happyReduction_22 +happyReduction_22 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut18 happy_x_1 of { happy_var_1 -> + case happyOut20 happy_x_3 of { happy_var_3 -> + happyIn20 + ((:) happy_var_1 happy_var_3 + )}} + +happyReduce_23 = happySpecReduce_1 6# happyReduction_23 +happyReduction_23 happy_x_1 + = case happyOut15 happy_x_1 of { happy_var_1 -> + happyIn21 + (Sit.Abs.Id happy_var_1 + )} + +happyReduce_24 = happySpecReduce_1 6# happyReduction_24 +happyReduction_24 happy_x_1 + = happyIn21 + (Sit.Abs.Under + ) + +happyReduce_25 = happySpecReduce_2 7# happyReduction_25 +happyReduction_25 happy_x_2 + happy_x_1 + = case happyOut15 happy_x_2 of { happy_var_2 -> + happyIn22 + (Sit.Abs.BIrrel happy_var_2 + )} + +happyReduce_26 = happySpecReduce_2 7# happyReduction_26 +happyReduction_26 happy_x_2 + happy_x_1 + = case happyOut15 happy_x_2 of { happy_var_2 -> + happyIn22 + (Sit.Abs.BRel happy_var_2 + )} + +happyReduce_27 = happyReduce 5# 7# happyReduction_27 +happyReduction_27 (happy_x_5 `HappyStk` + happy_x_4 `HappyStk` + happy_x_3 `HappyStk` + happy_x_2 `HappyStk` + happy_x_1 `HappyStk` + happyRest) + = case happyOut24 happy_x_2 of { happy_var_2 -> + case happyOut27 happy_x_4 of { happy_var_4 -> + happyIn22 + (Sit.Abs.BAnn happy_var_2 happy_var_4 + ) `HappyStk` happyRest}} + +happyReduce_28 = happySpecReduce_1 8# happyReduction_28 +happyReduction_28 happy_x_1 + = case happyOut22 happy_x_1 of { happy_var_1 -> + happyIn23 + ((:[]) happy_var_1 + )} + +happyReduce_29 = happySpecReduce_2 8# happyReduction_29 +happyReduction_29 happy_x_2 + happy_x_1 + = case happyOut22 happy_x_1 of { happy_var_1 -> + case happyOut23 happy_x_2 of { happy_var_2 -> + happyIn23 + ((:) happy_var_1 happy_var_2 + )}} + +happyReduce_30 = happySpecReduce_1 9# happyReduction_30 +happyReduction_30 happy_x_1 + = case happyOut15 happy_x_1 of { happy_var_1 -> + happyIn24 + ((:[]) happy_var_1 + )} + +happyReduce_31 = happySpecReduce_2 9# happyReduction_31 +happyReduction_31 happy_x_2 + happy_x_1 + = case happyOut15 happy_x_1 of { happy_var_1 -> + case happyOut24 happy_x_2 of { happy_var_2 -> + happyIn24 + ((:) happy_var_1 happy_var_2 + )}} + +happyReduce_32 = happySpecReduce_1 10# happyReduction_32 +happyReduction_32 happy_x_1 + = case happyOut21 happy_x_1 of { happy_var_1 -> + happyIn25 + ((:[]) happy_var_1 + )} + +happyReduce_33 = happySpecReduce_2 10# happyReduction_33 +happyReduction_33 happy_x_2 + happy_x_1 + = case happyOut21 happy_x_1 of { happy_var_1 -> + case happyOut25 happy_x_2 of { happy_var_2 -> + happyIn25 + ((:) happy_var_1 happy_var_2 + )}} + +happyReduce_34 = happySpecReduce_1 11# happyReduction_34 +happyReduction_34 happy_x_1 + = case happyOut21 happy_x_1 of { happy_var_1 -> + happyIn26 + (Sit.Abs.Var happy_var_1 + )} + +happyReduce_35 = happySpecReduce_1 11# happyReduction_35 +happyReduction_35 happy_x_1 + = case happyOut16 happy_x_1 of { happy_var_1 -> + happyIn26 + (Sit.Abs.Int happy_var_1 + )} + +happyReduce_36 = happySpecReduce_1 11# happyReduction_36 +happyReduction_36 happy_x_1 + = happyIn26 + (Sit.Abs.Infty + ) + +happyReduce_37 = happySpecReduce_1 11# happyReduction_37 +happyReduction_37 happy_x_1 + = happyIn26 + (Sit.Abs.Nat + ) + +happyReduce_38 = happySpecReduce_1 11# happyReduction_38 +happyReduction_38 happy_x_1 + = happyIn26 + (Sit.Abs.Set + ) + +happyReduce_39 = happySpecReduce_1 11# happyReduction_39 +happyReduction_39 happy_x_1 + = happyIn26 + (Sit.Abs.Set1 + ) + +happyReduce_40 = happySpecReduce_1 11# happyReduction_40 +happyReduction_40 happy_x_1 + = happyIn26 + (Sit.Abs.Set2 + ) + +happyReduce_41 = happySpecReduce_1 11# happyReduction_41 +happyReduction_41 happy_x_1 + = happyIn26 + (Sit.Abs.Zero + ) + +happyReduce_42 = happySpecReduce_1 11# happyReduction_42 +happyReduction_42 happy_x_1 + = happyIn26 + (Sit.Abs.Suc + ) + +happyReduce_43 = happySpecReduce_1 11# happyReduction_43 +happyReduction_43 happy_x_1 + = happyIn26 + (Sit.Abs.Fix + ) + +happyReduce_44 = happySpecReduce_1 11# happyReduction_44 +happyReduction_44 happy_x_1 + = happyIn26 + (Sit.Abs.LZero + ) + +happyReduce_45 = happySpecReduce_1 11# happyReduction_45 +happyReduction_45 happy_x_1 + = happyIn26 + (Sit.Abs.LSuc + ) + +happyReduce_46 = happySpecReduce_3 11# happyReduction_46 +happyReduction_46 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut27 happy_x_2 of { happy_var_2 -> + happyIn26 + (happy_var_2 + )} + +happyReduce_47 = happyReduce 4# 12# happyReduction_47 +happyReduction_47 (happy_x_4 `HappyStk` + happy_x_3 `HappyStk` + happy_x_2 `HappyStk` + happy_x_1 `HappyStk` + happyRest) + = case happyOut25 happy_x_2 of { happy_var_2 -> + case happyOut27 happy_x_4 of { happy_var_4 -> + happyIn27 + (Sit.Abs.Lam happy_var_2 happy_var_4 + ) `HappyStk` happyRest}} + +happyReduce_48 = happyReduce 4# 12# happyReduction_48 +happyReduction_48 (happy_x_4 `HappyStk` + happy_x_3 `HappyStk` + happy_x_2 `HappyStk` + happy_x_1 `HappyStk` + happyRest) + = case happyOut23 happy_x_2 of { happy_var_2 -> + case happyOut27 happy_x_4 of { happy_var_4 -> + happyIn27 + (Sit.Abs.Forall happy_var_2 happy_var_4 + ) `HappyStk` happyRest}} + +happyReduce_49 = happyReduce 7# 12# happyReduction_49 +happyReduction_49 (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 happyOut27 happy_x_2 of { happy_var_2 -> + case happyOut27 happy_x_4 of { happy_var_4 -> + case happyOut27 happy_x_7 of { happy_var_7 -> + happyIn27 + (Sit.Abs.Pi happy_var_2 happy_var_4 happy_var_7 + ) `HappyStk` happyRest}}} + +happyReduce_50 = happySpecReduce_3 12# happyReduction_50 +happyReduction_50 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut28 happy_x_1 of { happy_var_1 -> + case happyOut27 happy_x_3 of { happy_var_3 -> + happyIn27 + (Sit.Abs.Arrow happy_var_1 happy_var_3 + )}} + +happyReduce_51 = happyReduce 6# 12# happyReduction_51 +happyReduction_51 (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 happyOut27 happy_x_2 of { happy_var_2 -> + case happyOut27 happy_x_4 of { happy_var_4 -> + case happyOut27 happy_x_6 of { happy_var_6 -> + happyIn27 + (Sit.Abs.Case happy_var_2 happy_var_4 happy_var_6 + ) `HappyStk` happyRest}}} + +happyReduce_52 = happySpecReduce_3 12# happyReduction_52 +happyReduction_52 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut28 happy_x_1 of { happy_var_1 -> + case happyOut16 happy_x_3 of { happy_var_3 -> + happyIn27 + (Sit.Abs.Plus happy_var_1 happy_var_3 + )}} + +happyReduce_53 = happyReduce 17# 12# happyReduction_53 +happyReduction_53 (happy_x_17 `HappyStk` + happy_x_16 `HappyStk` + happy_x_15 `HappyStk` + happy_x_14 `HappyStk` + happy_x_13 `HappyStk` + happy_x_12 `HappyStk` + happy_x_11 `HappyStk` + happy_x_10 `HappyStk` + 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 happyOut27 happy_x_8 of { happy_var_8 -> + case happyOut21 happy_x_13 of { happy_var_13 -> + case happyOut27 happy_x_16 of { happy_var_16 -> + happyIn27 + (Sit.Abs.ELam happy_var_8 happy_var_13 happy_var_16 + ) `HappyStk` happyRest}}} + +happyReduce_54 = happySpecReduce_1 12# happyReduction_54 +happyReduction_54 happy_x_1 + = case happyOut28 happy_x_1 of { happy_var_1 -> + happyIn27 + (happy_var_1 + )} + +happyReduce_55 = happySpecReduce_2 13# happyReduction_55 +happyReduction_55 happy_x_2 + happy_x_1 + = case happyOut28 happy_x_1 of { happy_var_1 -> + case happyOut26 happy_x_2 of { happy_var_2 -> + happyIn28 + (Sit.Abs.App happy_var_1 happy_var_2 + )}} + +happyReduce_56 = happySpecReduce_1 13# happyReduction_56 +happyReduction_56 happy_x_1 + = case happyOut26 happy_x_1 of { happy_var_1 -> + happyIn28 + (happy_var_1 + )} + +happyNewToken action sts stk [] = + happyDoAction 34# 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 _ (TS _ 12) -> cont 12#; + PT _ (TS _ 13) -> cont 13#; + PT _ (TS _ 14) -> cont 14#; + PT _ (TS _ 15) -> cont 15#; + PT _ (TS _ 16) -> cont 16#; + PT _ (TS _ 17) -> cont 17#; + PT _ (TS _ 18) -> cont 18#; + PT _ (TS _ 19) -> cont 19#; + PT _ (TS _ 20) -> cont 20#; + PT _ (TS _ 21) -> cont 21#; + PT _ (TS _ 22) -> cont 22#; + PT _ (TS _ 23) -> cont 23#; + PT _ (TS _ 24) -> cont 24#; + PT _ (TS _ 25) -> cont 25#; + PT _ (TS _ 26) -> cont 26#; + PT _ (TS _ 27) -> cont 27#; + PT _ (TS _ 28) -> cont 28#; + PT _ (TS _ 29) -> cont 29#; + PT _ (TS _ 30) -> cont 30#; + PT _ (TS _ 31) -> cont 31#; + PT _ (TV happy_dollar_dollar) -> cont 32#; + PT _ (TI happy_dollar_dollar) -> cont 33#; + _ -> happyError' (tk:tks) + } + +happyError_ 34# 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 + +pPrg tks = happySomeParser where + happySomeParser = happyThen (happyParse 0# tks) (\x -> happyReturn (happyOut17 x)) + +pDecl tks = happySomeParser where + happySomeParser = happyThen (happyParse 1# tks) (\x -> happyReturn (happyOut18 x)) + +pQualId tks = happySomeParser where + happySomeParser = happyThen (happyParse 2# tks) (\x -> happyReturn (happyOut19 x)) + +pListDecl tks = happySomeParser where + happySomeParser = happyThen (happyParse 3# tks) (\x -> happyReturn (happyOut20 x)) + +pIdU tks = happySomeParser where + happySomeParser = happyThen (happyParse 4# tks) (\x -> happyReturn (happyOut21 x)) + +pBind tks = happySomeParser where + happySomeParser = happyThen (happyParse 5# tks) (\x -> happyReturn (happyOut22 x)) + +pListBind tks = happySomeParser where + happySomeParser = happyThen (happyParse 6# tks) (\x -> happyReturn (happyOut23 x)) + +pListIdent tks = happySomeParser where + happySomeParser = happyThen (happyParse 7# tks) (\x -> happyReturn (happyOut24 x)) + +pListIdU tks = happySomeParser where + happySomeParser = happyThen (happyParse 8# tks) (\x -> happyReturn (happyOut25 x)) + +pExp2 tks = happySomeParser where + happySomeParser = happyThen (happyParse 9# tks) (\x -> happyReturn (happyOut26 x)) + +pExp tks = happySomeParser where + happySomeParser = happyThen (happyParse 10# tks) (\x -> happyReturn (happyOut27 x)) + +pExp1 tks = happySomeParser where + happySomeParser = happyThen (happyParse 11# tks) (\x -> happyReturn (happyOut28 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" + t:_ -> " before `" ++ id(prToken t) ++ "'" + +myLexer = tokens +{-# LINE 1 "templates/GenericTemplate.hs" #-} +{-# LINE 1 "templates/GenericTemplate.hs" #-} +{-# LINE 1 "" #-} +{-# LINE 1 "" #-} +{-# LINE 10 "" #-} +# 1 "/usr/include/stdc-predef.h" 1 3 4 + +# 17 "/usr/include/stdc-predef.h" 3 4 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +{-# LINE 10 "" #-} +{-# LINE 1 "templates/GenericTemplate.hs" #-} +-- Id: GenericTemplate.hs,v 1.26 2005/01/14 14:47:22 simonmar Exp + +{-# LINE 13 "templates/GenericTemplate.hs" #-} + + + + + +-- Do not remove this comment. Required to fix CPP parsing when using GCC and a clang-compiled alex. +#if __GLASGOW_HASKELL__ > 706 +#define LT(n,m) ((Happy_GHC_Exts.tagToEnum# (n Happy_GHC_Exts.<# m)) :: Bool) +#define GTE(n,m) ((Happy_GHC_Exts.tagToEnum# (n Happy_GHC_Exts.>=# m)) :: Bool) +#define EQ(n,m) ((Happy_GHC_Exts.tagToEnum# (n Happy_GHC_Exts.==# m)) :: Bool) +#else +#define LT(n,m) (n Happy_GHC_Exts.<# m) +#define GTE(n,m) (n Happy_GHC_Exts.>=# m) +#define EQ(n,m) (n Happy_GHC_Exts.==# m) +#endif +{-# LINE 46 "templates/GenericTemplate.hs" #-} + + +data Happy_IntList = HappyCons Happy_GHC_Exts.Int# Happy_IntList + + + + + +{-# LINE 67 "templates/GenericTemplate.hs" #-} + +{-# LINE 77 "templates/GenericTemplate.hs" #-} + +{-# LINE 86 "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 | LT(n,(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 GTE(off_i,(0# :: Happy_GHC_Exts.Int#)) + then EQ(indexShortOffAddr happyCheck off_i, i) + else False + action + | check = indexShortOffAddr happyTable off_i + | otherwise = indexShortOffAddr happyDefActions st + + +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 170 "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 = + case happyDrop k (HappyCons (st) (sts)) of + sts1@((HappyCons (st1@(action)) (_))) -> + let drop_stk = happyDropStk k stk in + happyThen1 (fn stk tk) (\r -> happyGoto nt j tk st1 sts1 (r `HappyStk` drop_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 = + case happyDrop k (HappyCons (st) (sts)) of + sts1@((HappyCons (st1@(action)) (_))) -> + let drop_stk = happyDropStk k stk + + off = indexShortOffAddr happyGotoOffsets st1 + off_i = (off Happy_GHC_Exts.+# nt) + new_state = indexShortOffAddr happyTable off_i + + + + in + happyThen1 (fn stk tk) (\r -> happyNewToken new_state sts1 (r `HappyStk` drop_stk)) + +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/src/Abstract.hs b/src/Abstract.hs new file mode 100644 --- /dev/null +++ b/src/Abstract.hs @@ -0,0 +1,84 @@ +{-# LANGUAGE LambdaCase #-} + +{-# OPTIONS_GHC -fno-warn-typed-holes #-} +{-# OPTIONS_GHC -fwarn-incomplete-patterns #-} + +-- | Auxiliary functions for abstract syntax. + +module Abstract where + +import Control.Monad + +import Sit.Abs as A + +import Lens + +-- data AppView +-- = FixV [Exp] +-- | SetV [Exp] +-- | VarV [Exp] +-- | ZeroV [Exp] +-- | SucV [Exp] + +-- | Gather applications to expose head. + +appView :: Exp -> (Exp, [Exp]) +appView = \case + App f e -> over _2 (++ [e]) $ appView f + e -> (e, []) + +-- | Can this expression only denote a type? + +mustBeType :: Exp -> Bool +mustBeType = \case + Nat -> True + Set -> True + Set1 -> True + Set2 -> True + Forall{} -> True + Pi{} -> True + Arrow{} -> True + App f _ -> mustBeType f + _ -> False + +-- | Is this expression an introduction? + +introduction :: Exp -> Bool +introduction = \case + Var{} -> False + App{} -> False + Case{} -> False + Int{} -> True + Infty -> True + Size -> True + Nat -> True + Set -> True + Set1 -> True + Set2 -> True + Zero -> True + Suc -> True + Fix -> True + LZero -> True + LSuc -> True + Lam{} -> True + Forall{} -> True + Pi{} -> True + Arrow{} -> True + Plus{} -> True + ELam{} -> True + +-- | Convert "identifier-or-underscore" to string. + +fromIdU :: A.IdU -> String +fromIdU = \case + A.Id (A.Ident x) -> x + A.Under -> "_" + +-- | Try to convert an expression to a list of A.IdU + +parseIdUs :: A.Exp -> Maybe [A.IdU] +parseIdUs e = do + let (f, es) = appView e + forM (f : es) $ \case + A.Var x -> Just x + _ -> Nothing diff --git a/src/Evaluation.hs b/src/Evaluation.hs new file mode 100644 --- /dev/null +++ b/src/Evaluation.hs @@ -0,0 +1,393 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE LambdaCase #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TemplateHaskell #-} +{-# LANGUAGE TypeSynonymInstances, FlexibleInstances, MultiParamTypeClasses #-} +-- {-# LANGUAGE FunctionalDependencies, UndecidableInstances #-} + +-- | Values and weak head evaluation + +module Evaluation where + +import Control.Applicative +import Control.Monad +import Control.Monad.Identity +import Control.Monad.Reader + +import Data.Maybe +import Data.Traversable (traverse) + +import Debug.Trace + +import Internal +import Substitute + +import Lens +import Impossible +#include "undefined.h" + +-- * Values + +-- | Generic values are de Bruijn levels. +type VGen = Int + +-- | We have just a single type of values, including size values. +type VSize = Val +type VLevel = VSize + +type VType = Val +type VElim = Elim' Val +type VElims = [VElim] + +data Val + = VType VLevel + | VSize + | VNat VSize + | VZero VSize + | VSuc VSize Val + | VInfty + | VPi (Dom VType) VClos + -- Functions + | -- | Lambda abstraction + VLam VClos + | -- | @\ x -> x e@ for internal use in fix. + VElimBy VElim + -- -- | -- | Constant function + -- -- VConst Val + | -- | Neutrals. + VUp VType VNe + | -- | Type annotation for readback (normal form). + VDown VType Val + deriving (Eq, Show) + +data VNe = VNe + { _neVar :: VGen + , _neElims :: VElims + } + deriving (Eq, Show) + +data VClos = VClos + { closBody :: Abs Term + , closEnv :: Env + } + deriving (Eq, Show) + +-- | An environment maps de Bruijn indices to values. +-- The first entry in the list is the binding for index 0. + +type Env = [Val] + +makeLens ''VNe + +-- | Variable + +vVar :: VType -> VGen -> Val +vVar t x = VUp t $ VNe x [] + +-- * Size arithmetic + +-- | Zero size. + +vsZero :: VSize +vsZero = VZero VInfty + +-- | Successor size. + +vsSuc :: VSize -> VSize +vsSuc = VSuc VInfty + +-- | Variable size. + +vsVar :: VGen -> VSize +vsVar = vVar VSize + +-- | Size increment. + +vsPlus :: Int -> VSize -> VSize +vsPlus n v = iterate vsSuc v !! n + +-- | Constant size. + +vsConst :: Int -> VSize +vsConst n = vsPlus n vsZero + +-- | View a value as a size expression. + +data SizeView + = SVConst Int + -- ^ @n@ + | SVVar VGen Int + -- ^ @i + n@ + | SVInfty + -- ^ @oo@ + deriving (Eq, Show) + +-- | Successor size on view. + +svSuc :: SizeView -> SizeView +svSuc = \case + SVConst n -> SVConst $ succ n + SVVar x n -> SVVar x $ succ n + SVInfty -> SVInfty + +-- | View a value as a size expression. + +sizeView :: Val -> Maybe SizeView +sizeView = \case + VZero _ -> return $ SVConst 0 + VSuc _ v -> svSuc <$> sizeView v + VInfty -> return $ SVInfty + VUp VSize (VNe k []) -> return $ SVVar k 0 + _ -> Nothing + +unSizeView :: SizeView -> Val +unSizeView = \case + SVInfty -> VInfty + SVConst n -> vsConst n + SVVar x n -> vsPlus n $ vsVar x + +-- | Compute the maximum of two sizes. + +maxSize :: VSize -> VSize -> VSize +maxSize v1 v2 = + case ( fromMaybe __IMPOSSIBLE__ $ sizeView v1 + , fromMaybe __IMPOSSIBLE__ $ sizeView v2) of + (SVConst n, SVConst m) -> unSizeView $ SVConst $ max n m + (SVVar x n, SVVar y m) | x == y -> unSizeView $ SVVar x $ max n m + (SVConst n, SVVar y m) | n <= m -> unSizeView $ SVVar y m + (SVVar x n, SVConst m) | n >= m -> unSizeView $ SVVar x n + _ -> VInfty + +-- * Evaluation + +-- | Evaluation monad. + +class (Functor m, Applicative m, Monad m) => MonadEval m where + getDef :: Id -> m Val + +instance MonadEval Identity where + getDef x = __IMPOSSIBLE__ + +evaluateClosed :: Term -> Val +evaluateClosed t = runIdentity $ evalIn t [] + +-- | Evaluation. + +evalIn :: MonadEval m => Term -> Env -> m Val +evalIn t rho = runReaderT (eval t) rho + +class Evaluate a b where -- -- | a -> b where + eval :: MonadEval m => a -> ReaderT Env m b + +instance Evaluate Index Val where + eval (Index i) = (!! i) <$> ask + +instance Evaluate Term Val where + eval = \case + Type l -> VType <$> eval l + Nat a -> VNat <$> eval a + Size -> pure VSize + Infty -> pure VInfty + Zero a -> VZero <$> eval (unArg a) + Suc a t -> liftA2 VSuc (eval $ unArg a) (eval t) + Pi u t -> liftA2 VPi (eval u) (eval t) + -- Lam ai (NoAbs x t) -> VConst <$> eval t + Lam ai t -> VLam <$> eval t + Var x -> eval x + Def f -> lift $ getDef f + App t e -> do + h <- eval t + e <- eval e + lift $ applyE h e + +instance Evaluate (Abs Term) VClos where + eval t = VClos t <$> ask + +instance Evaluate a b => Evaluate [a] [b] where + eval = traverse eval + +instance Evaluate a b => Evaluate (Dom a) (Dom b) where + eval = traverse eval + +instance Evaluate a b => Evaluate (Elim' a) (Elim' b) where + eval = traverse eval + +applyEs :: MonadEval m => Val -> VElims -> m Val +applyEs v [] = return v +applyEs v (e : es) = applyE v e >>= (`applyEs` es) + +applyE :: MonadEval m => Val -> VElim -> m Val +applyE v e = + case (v, e) of + (_ , Apply u ) -> apply v u + (VZero _ , Case _ u _ _) -> return u + (VSuc _ n , Case _ _ _ f) -> apply f $ defaultArg n + (VZero a , Fix t tf f ) -> unfoldFix t tf f a v -- apply f $ e : map (Apply . defaultArg) [ v , VZero ] + (VSuc a n , Fix t tf f ) -> unfoldFix t tf f a v + (VUp (VNat a) n , _) -> elimNeNat a n e + _ -> __IMPOSSIBLE__ + +-- | Apply a function to an argument. + +apply :: MonadEval m => Val -> Arg Val -> m Val +apply v arg@(Arg ai u) = case v of + VPi _ cl -> applyClos cl u -- we also allow instantiation of Pi-types by apply + VLam cl -> applyClos cl u + VElimBy e -> applyE u e + -- VConst f -> return f + VUp (VPi a b) (VNe x es) -> do + t' <- applyClos b u + return $ VUp t' $ VNe x $ es ++ [ Apply $ Arg ai $ VDown (unDom a) u ] + _ -> do + traceM $ "apply " ++ show v ++ " to " ++ show u + __IMPOSSIBLE__ + +-- | Apply a closure to a value. + +applyClos :: MonadEval m => VClos -> Val -> m Val +applyClos (VClos b rho) u = case b of + NoAbs _ t -> evalIn t rho + Abs _ t -> evalIn t $ u : rho + +-- | Unfold a fixed-point. + +unfoldFix :: MonadEval m => VType -> VType -> Val -> VSize -> Val -> m Val +unfoldFix t tf f a v = applyEs f $ map Apply + [ Arg Irrelevant a + , defaultArg $ VElimBy $ Fix t tf f + , defaultArg v + ] + +-- | Eliminate a neutral natural number. +-- Here we need to compute the correct type of the elimination + +elimNeNat :: MonadEval m => VSize -> VNe -> VElim -> m Val +elimNeNat a n e = case e of + Apply{} -> __IMPOSSIBLE__ + + Case t u tf f -> do + -- Compute the type of the result of the elimination application + tr <- apply t $ Arg Relevant $ VUp (VNat a) n + -- Compute the type of the zero branch + tz <- apply t $ Arg Relevant u + -- Compute the type of the suc branch + ts <- return t -- TODO: must be (x : Nat a) -> t (suc a x) + -- Assemble the elimination + let e = Case (VDown (VType VInfty) t) (VDown tz u) (VDown (VType VInfty) tf) (VDown tf f) + -- Assemble the result + return $ VUp tr $ over neElims (++ [e]) n + + Fix t tf f -> do + -- Compute the type of the result of the elimination application + tr <- applyEs t $ map Apply [ Arg ShapeIrr a, Arg Relevant $ VUp (VNat a) n ] + -- Assemble the elimination + let e = Fix (VDown fixKindV t) (VDown (VType VInfty) tf) (VDown tf f) + -- Assemble the result + return $ VUp tr $ over neElims (++ [e]) n + +-- | Type of type of fix motive. +-- @fixKind = ..(i : Size) -> Nat i -> Setω@ + +fixKindV :: VType +fixKindV = evaluateClosed fixKind + +-- * Readback + +-- | Readback. + +class Readback a b where + readback :: MonadEval m => a -> ReaderT Int m b + +instance Readback VGen Index where + readback k = Index . (\ n -> n - (k + 1)) <$> ask + +instance Readback Val Term where + readback = \case + VDown VSize d -> readbackSize d + VDown (VType _) d -> readbackType d + VDown (VNat _ ) d -> readbackNat d + + VDown (VPi a b) d -> do + v0 <- vVar (unDom a) <$> ask + c <- lift $ applyClos b v0 + Lam (_domInfo a) . Abs "x" <$> do + local succ . readback . VDown c =<< do + lift $ apply d $ Arg (_domInfo a) v0 + + VDown (VUp _ _) (VUp _ n) -> readbackNe n + +instance Readback a b => Readback [a] [b] where + readback = traverse readback + +instance Readback a b => Readback (Dom a) (Dom b) where + readback = traverse readback + +instance Readback a b => Readback (Arg a) (Arg b) where + readback = traverse readback + +instance Readback a b => Readback (Elim' a) (Elim' b) where + readback = traverse readback + +readbackType :: MonadEval m => Val -> ReaderT Int m Term +readbackType = \case + VSize -> pure Size + VType a -> Type <$> readbackSize a + VNat a -> Nat <$> readbackSize a + VPi a b -> do + u <- traverse readbackType a + v0 <- vVar (unDom a) <$> ask + Pi u . Abs "x" <$> do + local succ . readbackType =<< do + lift $ applyClos b v0 + VUp _ n -> readbackNe n + _ -> __IMPOSSIBLE__ + +readbackNat :: MonadEval m => Val -> ReaderT Int m Term +readbackNat = \case + VZero a -> zero <$> readbackSize a + VSuc a t -> liftA2 suc (readbackSize a) (readbackNat t) + VUp (VNat _) n -> readbackNe n + _ -> __IMPOSSIBLE__ + +readbackNe :: MonadEval m => VNe -> ReaderT Int m Term +readbackNe (VNe x es) = do + i <- readback x + es' :: Elims <- readback es + return $ foldl App (Var i) es' + +readbackSize :: MonadEval m => Val -> ReaderT Int m Term +readbackSize = \case + VInfty -> pure Infty + VZero _ -> pure sZero + VSuc _ a -> sSuc <$> readbackSize a + VUp VSize (VNe x []) -> Var <$> readback x + _ -> __IMPOSSIBLE__ + +-- * Comparison + +-- | Size values are partially ordered + +cmpSizes :: VSize -> VSize -> Maybe Ordering +cmpSizes v1 v2 = do + s1 <- sizeView v1 + s2 <- sizeView v2 + case (s1, s2) of + (a,b) | a == b -> return EQ + (SVInfty, _) -> return GT + (_, SVInfty) -> return LT + (SVConst n, SVConst m) -> return $ compare n m + (SVVar x n, SVVar y m) | x == y -> return $ compare n m + (SVConst n, SVVar y m) | n <= m -> __IMPOSSIBLE__ -- Here, LT is too strong. + _ -> __IMPOSSIBLE__ -- TODO + +leqSize :: VSize -> VSize -> Bool +leqSize a b = maxSize a b == b + +-- | Compute predecessor size, if possible. +sizePred :: VSize -> Maybe VSize +sizePred v = do + sizeView v >>= \case + SVInfty -> return $ VInfty + SVConst n | n > 0 -> return $ unSizeView $ SVConst $ n-1 + SVVar x n | n > 0 -> return $ unSizeView $ SVVar x $ n-1 + _ -> Just v diff --git a/src/Impossible.hs b/src/Impossible.hs new file mode 100644 --- /dev/null +++ b/src/Impossible.hs @@ -0,0 +1,27 @@ +{-# LANGUAGE DeriveDataTypeable #-} + +module Impossible where + +import Control.Exception +import Data.Typeable ( Typeable ) + + +data Impossible + = Impossible String Integer + -- ^ We reached a program point which should be unreachable. + + deriving Typeable + +instance Show Impossible where + show (Impossible file line) = unlines + [ "An internal error has occurred. Please report this as a bug." + , "Location of the error: " ++ file ++ ":" ++ show line + ] + +instance Exception Impossible + +-- | Abort by throwing an \"impossible\" error. You should not use +-- this function directly. Instead use the macro in @undefined.h@. + +throwImpossible :: Impossible -> a +throwImpossible = throw diff --git a/src/Internal.hs b/src/Internal.hs new file mode 100644 --- /dev/null +++ b/src/Internal.hs @@ -0,0 +1,167 @@ +{-# LANGUAGE GeneralizedNewtypeDeriving #-} +{-# LANGUAGE DeriveFunctor #-} +{-# LANGUAGE DeriveFoldable #-} +{-# LANGUAGE DeriveTraversable #-} +{-# LANGUAGE TemplateHaskell #-} + +-- | Internal Syntax. + +module Internal where + +import Data.Foldable (Foldable) +import Data.Traversable (Traversable) + +import Lens + +-- | Definition names are strings. + +type Id = String + +-- | Variables are de Bruijn indices. + +newtype Index = Index { dbIndex :: Int } + deriving (Eq, Ord, Show, Enum, Num) + +-- | Size expressions. + +type Size = Term +type Level = Size + +-- | Terms/types + +type Type = Term + +data Term + = -- | Universe with level. + Type Level + | -- | Type of sizes (internal use only). + Size + | -- | Sized natural number type. + Nat Size + | -- | Zero constructor, or zero size (then @Size@ is ignored). + Zero (Arg Size) + | -- | Successor constructor, or successor size (then @Size@ is ignored). + Suc (Arg Size) Term + | -- | Infinity size. + Infty + | -- ^ (Dependent) function type. + Pi (Dom Type) (Abs Term) + | -- ^ Lambda abstraction + Lam ArgInfo (Abs Term) + | -- ^ Variable. + Var Index + | -- ^ Function call. + Def Id + | -- ^ Application/eliminiation. + App Term Elim + deriving (Eq, Ord, Show) + +-- | Eliminations. + +type Elims = [ Elim ] +type Elim = Elim' Term + +data Elim' a + = -- | Function application. + Apply (Arg a) + | -- | Case distinction + Case + { caseReturn :: a -- ^ @T : Nat (b + 1) -> Setω@ + , caseZero :: a -- ^ @tz : T zero@ + , caseTySuc :: a -- ^ Type of @caseSuc@. Stored here for convenience, must be + -- @(t : Nat b) -> T (suc t)@ + , caseSuc :: a -- ^ @ts : (t : Nat b) -> T (suc t)@ + } + | -- | Recursion + Fix + { fixReturn :: a + -- ^ @T : ..(i : Size) -> Nat i -> Setω@ + , fixTyBody :: a + -- ^ Type of @fixBody@. Stored here for convenience, must be + -- @.(i : Size) (f : (x : Nat i) -> T i x) (x : Nat (i + 1)) -> T (i + 1) x@. + , fixBody :: a + -- ^ @t : .(i : Size) (f : (x : Nat i) -> T i x) (x : Nat (i + 1)) -> T (i + 1) x@ + } + deriving (Eq, Ord, Show, Functor, Foldable, Traversable) + +-- | Abstraction. + +type AbsName = String + +data Abs a + = -- | Actual abstraction (body contains one more index). + Abs { absName :: AbsName, absBody :: a } + | -- | No abstraction (argument will be ignored). + NoAbs { absName :: AbsName, absBody :: a } + deriving (Eq, Ord, Show) + +-- | Function domain decoration. + +data Dom a = Dom { _domInfo :: ArgInfo, unDom :: a } + deriving (Eq, Ord, Show, Functor, Foldable, Traversable) + +-- | Argument decoration. + +data Arg a = Arg { argInfo :: ArgInfo, unArg :: a } + deriving (Ord, Show, Functor, Foldable, Traversable) + +instance Eq a => Eq (Arg a) where + Arg Irrelevant _ == Arg Irrelevant _ = True + Arg r a == Arg r' a' = r == r' && a == a' + +type ArgInfo = Relevance + +-- | Relevance lattice (order matters) +data Relevance + = Relevant + | ShapeIrr + | Irrelevant + deriving (Eq, Ord, Show) + +makeLens ''Dom + +-- * Smart constructor. + +zero :: Size -> Term +zero = Zero . Arg Irrelevant + +suc :: Size -> Term -> Term +suc = Suc . Arg Irrelevant + +-- var :: Index -> Term +-- var i = Var i [] + +-- app :: Term -> Arg Term -> Maybe Term +-- app t u = case t of +-- Var x es -> Just $ Var x $ es ++ [ Apply u ] +-- Def f es -> Just $ Def f $ es ++ [ Apply u ] +-- _ -> Nothing + +defaultArg :: a -> Arg a +defaultArg = Arg Relevant + +defaultDom :: a -> Dom a +defaultDom = Dom Relevant + +-- | Zero size. + +sZero :: Term +sZero = zero Infty + +-- | Successor size. + +sSuc :: Term -> Term +sSuc = suc Infty + +-- | Size increment. + +sPlus :: Term -> Integer -> Term +sPlus t n = iterate sSuc t !! fromInteger n + +-- | @fixKind = ..(i : Size) -> Nat i -> Setω@ + +fixKind :: Type +fixKind = + Pi (Dom ShapeIrr Size) $ Abs "i" $ + Pi (Dom Relevant (Nat $ Var 0)) $ Abs "x" $ + Type Infty diff --git a/src/Lens.hs b/src/Lens.hs new file mode 100644 --- /dev/null +++ b/src/Lens.hs @@ -0,0 +1,15 @@ +{-# LANGUAGE NoMonomorphismRestriction #-} + +-- | Wrapper module for lens functionality + +module Lens + ( module Data.Lens.Light + , module Lens + ) where + +import Data.Lens.Light + +over = modL +set = setL +use = access +_2 = lens snd $ \ y (x, _) -> (x, y) diff --git a/src/Makefile b/src/Makefile new file mode 100644 --- /dev/null +++ b/src/Makefile @@ -0,0 +1,34 @@ +.PHONY: test +.PRECIOUS : %.hs %.x %.y +all : test + +test : Sit.bin ../test/Test.agda + Sit.bin ../test/Test.agda + +loop : Sit.bin ../test/Loop.agda + Sit.bin ../test/Loop.agda + +Sit.bin : Sit.hs Sit/Abs.hs Sit/Lex.hs Sit/Par.hs \ + undefined.h Impossible.hs \ + Abstract.hs Internal.hs Substitute.hs Evaluation.hs TypeChecker.hs + ghc --make $< -o Sit.bin + +Sit/Lex.x Sit/Par.y Sit/Abs.hs : Sit.cf + bnfc --haskell -d $< + touch $@ + +Sit/Par.hs: Sit/Par.y + happy -gcai $< + +Sit/Lex.hs: Sit/Lex.x + alex -g $< + +Sit/Test: Sit/Test.hs Sit/Par.hs Sit/Lex.hs + ghc --make $< -o $@ + +clean: + -rm -f Sit/*.log Sit/*.aux Sit/*.hi Sit/*.o Sit/*.dvi + +distclean: clean + -rm -f Sit/Doc.* Sit/Lex.* Sit/Par.* Sit/Layout.* Sit/Skel.* Sit/Print.* Sit/Test.* Sit/Abs.* Sit/Test Sit/ErrM.* Sit/SharedString.* Sit/ComposOp.* Sit/Sit.dtd Sit/XML.* + -rmdir -p Sit/ diff --git a/src/Sit.cf b/src/Sit.cf new file mode 100644 --- /dev/null +++ b/src/Sit.cf @@ -0,0 +1,82 @@ +-- Type theory with sized natural numbers and a irrelevant +-- size quantifier. + +-- Types: T ::= Nat a | Set a | (x : T) -> T | T -> T | forall Bs -> T +-- Binding: B ::= (x : T) | .i | ..i + +-- Terms: t ::= x | t t | \ xs -> t | zero | suc t | fix l T t n | case n return T of \{ zero -> tz; suc x -> ts } +-- +-- Sizes: a ::= Integer | x | x + Integer | w + +-- SizeVar. SizeExp ::= Ident; +-- SizeInf. SizeExp ::= "oo"; +-- SizeConst. SizeExp ::= Integer; +-- SizeInc. SizeExp1 ::= Ident "+" Integer; +-- +-- coercions Exp 1; + +Prg. Prg ::= [Decl]; + +-- Declarations. + +Sig. Decl ::= Ident ":" Exp; +Def. Decl ::= Ident "=" Exp; +Open. Decl ::= "open" "import" QualId; +Blank. Decl ::= ; + +Sg. QualId ::= Ident; +Cons. QualId ::= QualId "." Ident; + +separator nonempty Decl "--;" ; + +-- Identifier which can be _ + +Id. IdU ::= Ident; +Under. IdU ::= "_"; + +-- Binder: + +BIrrel. Bind ::= "." Ident; +BRel. Bind ::= ".." Ident; +BAnn. Bind ::= "(" [Ident] ":" Exp ")"; + +terminator nonempty Bind ""; +terminator nonempty Ident ""; +terminator nonempty IdU ""; + +-- Atoms: + +Var. Exp2 ::= IdU; +Int. Exp2 ::= Integer; +Infty. Exp2 ::= "oo"; +Nat. Exp2 ::= "Nat"; +Set. Exp2 ::= "Set"; +Set1. Exp2 ::= "Set1"; +Set2. Exp2 ::= "Set2"; +Zero. Exp2 ::= "zero"; +Suc. Exp2 ::= "suc"; +Fix. Exp2 ::= "fix"; +LZero. Exp2 ::= "lzero"; +LSuc. Exp2 ::= "lsuc"; + +internal +Size. Exp ::= "Size"; + +-- Applications: + +App. Exp1 ::= Exp1 Exp2; + +-- Abstraction etc. + +Lam. Exp ::= "\\" [IdU] "->" Exp; +Forall. Exp ::= "forall" [Bind] "->" Exp; +Pi. Exp ::= "(" Exp ":" Exp ")" "->" Exp; -- The first Exp should be [IdU], but this conflicts +Arrow. Exp ::= Exp1 "->" Exp; +Case. Exp ::= "case" Exp "return" Exp "of" Exp; +Plus. Exp ::= Exp1 "+" Integer; +ELam. Exp ::= "\\" "{" "(" "zero" "_" ")" "->" Exp ";" "(" "suc" "_" IdU ")" "->" Exp "}"; + +coercions Exp 2; + +comment "---"; +comment "{-" "-}"; diff --git a/src/Sit.hs b/src/Sit.hs new file mode 100644 --- /dev/null +++ b/src/Sit.hs @@ -0,0 +1,45 @@ +{-# LANGUAGE LambdaCase #-} + +import System.Environment (getArgs) +import System.Exit (exitFailure) + +import Data.Foldable + +import Sit.Abs +import Sit.ErrM +import Sit.Lex +import Sit.Par +import Sit.Print + +import TypeChecker + +main :: IO () +main = getArgs >>= \case + [file] -> check =<< readFile file + _ -> usage + +usage :: IO () +usage = do + putStrLn "Usage: Sit " + exitFailure + +-- | Handle error by failing hard. + +failOnErr :: String -> Err a -> IO a +failOnErr msg = \case + Ok a -> return a + Bad err -> exitMsg $ unlines [ msg , err ] + +exitMsg :: String -> IO a +exitMsg msg = do + putStrLn msg + exitFailure + +-- | Run the type checker on file contents +check :: String -> IO () +check txt = do + Prg decls <- failOnErr "PARSE ERROR" $ pPrg $ myLexer txt + -- putStrLn "Parsed the following declarations" + -- forM_ decls $ \ d -> do + -- putStrLn $ printTree d + either (\ err -> exitMsg $ unlines [ "TYPE ERROR" , err ]) return $ typeCheck decls diff --git a/src/Sit/Abs.hs b/src/Sit/Abs.hs new file mode 100644 --- /dev/null +++ b/src/Sit/Abs.hs @@ -0,0 +1,49 @@ + + +module Sit.Abs where + +-- Haskell module generated by the BNF converter + + + + +newtype Ident = Ident String deriving (Eq, Ord, Show, Read) +data Prg = Prg [Decl] + deriving (Eq, Ord, Show, Read) + +data Decl = Sig Ident Exp | Def Ident Exp | Open QualId | Blank + deriving (Eq, Ord, Show, Read) + +data QualId = Sg Ident | Cons QualId Ident + deriving (Eq, Ord, Show, Read) + +data IdU = Id Ident | Under + deriving (Eq, Ord, Show, Read) + +data Bind = BIrrel Ident | BRel Ident | BAnn [Ident] Exp + deriving (Eq, Ord, Show, Read) + +data Exp + = Var IdU + | Int Integer + | Infty + | Nat + | Set + | Set1 + | Set2 + | Zero + | Suc + | Fix + | LZero + | LSuc + | Size + | App Exp Exp + | Lam [IdU] Exp + | Forall [Bind] Exp + | Pi Exp Exp Exp + | Arrow Exp Exp + | Case Exp Exp Exp + | Plus Exp Integer + | ELam Exp IdU Exp + deriving (Eq, Ord, Show, Read) + diff --git a/src/Sit/ErrM.hs b/src/Sit/ErrM.hs new file mode 100644 --- /dev/null +++ b/src/Sit/ErrM.hs @@ -0,0 +1,37 @@ +-- BNF Converter: Error Monad +-- Copyright (C) 2004 Author: Aarne Ranta + +-- This file comes with NO WARRANTY and may be used FOR ANY PURPOSE. +module Sit.ErrM where + +-- the Error monad: like Maybe type with error msgs + +import Control.Monad (MonadPlus(..), liftM) +import Control.Applicative (Applicative(..), Alternative(..)) + +data Err a = Ok a | Bad String + deriving (Read, Show, Eq, Ord) + +instance Monad Err where + return = Ok + fail = Bad + Ok a >>= f = f a + Bad s >>= _ = Bad s + +instance Applicative Err where + pure = Ok + (Bad s) <*> _ = Bad s + (Ok f) <*> o = liftM f o + + +instance Functor Err where + fmap = liftM + +instance MonadPlus Err where + mzero = Bad "Err.mzero" + mplus (Bad _) y = y + mplus x _ = x + +instance Alternative Err where + empty = mzero + (<|>) = mplus diff --git a/src/Sit/Lex.hs b/src/Sit/Lex.hs new file mode 100644 --- /dev/null +++ b/src/Sit/Lex.hs @@ -0,0 +1,423 @@ +{-# OPTIONS_GHC -fno-warn-unused-binds -fno-warn-missing-signatures #-} +{-# LANGUAGE CPP,MagicHash #-} +{-# LINE 3 "Sit/Lex.x" #-} + +{-# OPTIONS -fno-warn-incomplete-patterns #-} +{-# OPTIONS_GHC -w #-} +module Sit.Lex where + + + +import qualified Data.Bits +import Data.Word (Word8) +import Data.Char (ord) + +#if __GLASGOW_HASKELL__ >= 603 +#include "ghcconfig.h" +#elif defined(__GLASGOW_HASKELL__) +#include "config.h" +#endif +#if __GLASGOW_HASKELL__ >= 503 +import Data.Array +import Data.Array.Base (unsafeAt) +#else +import Array +#endif +#if __GLASGOW_HASKELL__ >= 503 +import GHC.Exts +#else +import GlaExts +#endif +alex_tab_size :: Int +alex_tab_size = 8 +alex_base :: AlexAddr +alex_base = 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\x04\x00\xff\xff\x04\x00\xff\xff\x04\x00\x04\x00\x0a\x00\x0a\x00\x10\x00\x10\x00\xff\xff\xff\xff\x11\x00\x11\x00\x11\x00\x11\x00\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"# + +alex_accept = listArray (0::Int,24) [AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccSkip,AlexAccSkip,AlexAccSkip,AlexAcc (alex_action_3),AlexAcc (alex_action_3),AlexAcc (alex_action_3),AlexAcc (alex_action_4),AlexAcc (alex_action_5)] +{-# LINE 39 "Sit/Lex.x" #-} + + +tok :: (Posn -> String -> Token) -> (Posn -> String -> Token) +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 + + deriving (Eq,Show,Ord) + +data Token = + PT Posn Tok + | Err Posn + deriving (Eq,Show,Ord) + +printPosn :: Posn -> String +printPosn (Pn _ l c) = "line " ++ show l ++ ", column " ++ show c + +tokenPos :: [Token] -> String +tokenPos (t:_) = printPosn (tokenPosn t) +tokenPos [] = "end of file" + +tokenPosn :: Token -> Posn +tokenPosn (PT p _) = p +tokenPosn (Err p) = p + +tokenLineCol :: Token -> (Int, Int) +tokenLineCol = posLineCol . tokenPosn + +posLineCol :: Posn -> (Int, Int) +posLineCol (Pn _ l c) = (l,c) + +mkPosToken :: Token -> ((Int, Int), String) +mkPosToken t@(PT p _) = (posLineCol p, prToken t) + +prToken :: Token -> String +prToken t = case t of + PT _ (TS s _) -> s + PT _ (TL s) -> show s + PT _ (TI s) -> s + PT _ (TV s) -> s + PT _ (TD s) -> s + PT _ (TC s) -> s + Err _ -> "#error" + + +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 :: BTree +resWords = b "\\" 16 (b ":" 8 (b "--;" 4 (b ")" 2 (b "(" 1 N N) (b "+" 3 N N)) (b "." 6 (b "->" 5 N N) (b ".." 7 N N))) (b "Set" 12 (b "=" 10 (b ";" 9 N N) (b "Nat" 11 N N)) (b "Set2" 14 (b "Set1" 13 N N) (b "Size" 15 N N)))) (b "of" 24 (b "forall" 20 (b "case" 18 (b "_" 17 N N) (b "fix" 19 N N)) (b "lsuc" 22 (b "import" 21 N N) (b "lzero" 23 N N))) (b "suc" 28 (b "open" 26 (b "oo" 25 N N) (b "return" 27 N N)) (b "{" 30 (b "zero" 29 N N) (b "}" 31 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 (TV . share) s)) +alex_action_5 = tok (\p s -> PT p (TI $ share s)) +{-# LINE 1 "templates/GenericTemplate.hs" #-} +{-# LINE 1 "templates/GenericTemplate.hs" #-} +{-# LINE 1 "" #-} +{-# LINE 1 "" #-} +{-# LINE 9 "" #-} +# 1 "/usr/include/stdc-predef.h" 1 3 4 + +# 17 "/usr/include/stdc-predef.h" 3 4 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +{-# LINE 9 "" #-} +{-# 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 21 "templates/GenericTemplate.hs" #-} + + + + + +-- Do not remove this comment. Required to fix CPP parsing when using GCC and a clang-compiled alex. +#if __GLASGOW_HASKELL__ > 706 +#define GTE(n,m) (tagToEnum# (n >=# m)) +#define EQ(n,m) (tagToEnum# (n ==# m)) +#else +#define GTE(n,m) (n >=# m) +#define EQ(n,m) (n ==# m) +#endif +{-# LINE 51 "templates/GenericTemplate.hs" #-} + + +data AlexAddr = AlexA# Addr# +-- Do not remove this comment. Required to fix CPP parsing when using GCC and a clang-compiled alex. +#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 GTE(offset,0#) && EQ(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 198 "templates/GenericTemplate.hs" #-} + +data AlexLastAcc a + = AlexNone + | AlexLastAcc a !AlexInput !Int + | AlexLastSkip !AlexInput !Int + +instance Functor AlexLastAcc where + fmap _ AlexNone = AlexNone + fmap f (AlexLastAcc x y z) = AlexLastAcc (f x) y z + fmap _ (AlexLastSkip x y) = AlexLastSkip x y + +data AlexAcc a user + = AlexAccNone + | AlexAcc a + | AlexAccSkip diff --git a/src/Sit/Lex.x b/src/Sit/Lex.x new file mode 100644 --- /dev/null +++ b/src/Sit/Lex.x @@ -0,0 +1,185 @@ +-- -*- haskell -*- +-- This Alex file was machine-generated by the BNF converter +{ +{-# OPTIONS -fno-warn-incomplete-patterns #-} +{-# OPTIONS_GHC -w #-} +module Sit.Lex where + + + +import qualified Data.Bits +import Data.Word (Word8) +import Data.Char (ord) +} + + +$l = [a-zA-Z\192 - \255] # [\215 \247] -- isolatin1 letter FIXME +$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 # [\- \}]])* ("-")+ "}" ; + +$white+ ; +@rsyms { tok (\p s -> PT p (eitherResIdent (TV . share) s)) } + +$l $i* { tok (\p s -> PT p (eitherResIdent (TV . share) s)) } + + +$d+ { tok (\p s -> PT p (TI $ share s)) } + + +{ + +tok :: (Posn -> String -> Token) -> (Posn -> String -> Token) +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 + + deriving (Eq,Show,Ord) + +data Token = + PT Posn Tok + | Err Posn + deriving (Eq,Show,Ord) + +printPosn :: Posn -> String +printPosn (Pn _ l c) = "line " ++ show l ++ ", column " ++ show c + +tokenPos :: [Token] -> String +tokenPos (t:_) = printPosn (tokenPosn t) +tokenPos [] = "end of file" + +tokenPosn :: Token -> Posn +tokenPosn (PT p _) = p +tokenPosn (Err p) = p + +tokenLineCol :: Token -> (Int, Int) +tokenLineCol = posLineCol . tokenPosn + +posLineCol :: Posn -> (Int, Int) +posLineCol (Pn _ l c) = (l,c) + +mkPosToken :: Token -> ((Int, Int), String) +mkPosToken t@(PT p _) = (posLineCol p, prToken t) + +prToken :: Token -> String +prToken t = case t of + PT _ (TS s _) -> s + PT _ (TL s) -> show s + PT _ (TI s) -> s + PT _ (TV s) -> s + PT _ (TD s) -> s + PT _ (TC s) -> s + Err _ -> "#error" + + +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 :: BTree +resWords = b "\\" 16 (b ":" 8 (b "--;" 4 (b ")" 2 (b "(" 1 N N) (b "+" 3 N N)) (b "." 6 (b "->" 5 N N) (b ".." 7 N N))) (b "Set" 12 (b "=" 10 (b ";" 9 N N) (b "Nat" 11 N N)) (b "Set2" 14 (b "Set1" 13 N N) (b "Size" 15 N N)))) (b "of" 24 (b "forall" 20 (b "case" 18 (b "_" 17 N N) (b "fix" 19 N N)) (b "lsuc" 22 (b "import" 21 N N) (b "lzero" 23 N N))) (b "suc" 28 (b "open" 26 (b "oo" 25 N N) (b "return" 27 N N)) (b "{" 30 (b "zero" 29 N N) (b "}" 31 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/Sit/Par.hs b/src/Sit/Par.hs new file mode 100644 --- /dev/null +++ b/src/Sit/Par.hs @@ -0,0 +1,993 @@ +{-# OPTIONS_GHC -w #-} +{-# OPTIONS -fglasgow-exts -cpp #-} +{-# OPTIONS_GHC -fno-warn-incomplete-patterns -fno-warn-overlapping-patterns #-} +module Sit.Par where +import Sit.Abs +import Sit.Lex +import Sit.ErrM +import qualified Data.Array as Happy_Data_Array +import qualified GHC.Exts as Happy_GHC_Exts +import Control.Applicative(Applicative(..)) +import Control.Monad (ap) + +-- parser produced by Happy Version 1.19.5 + +newtype HappyAbsSyn = HappyAbsSyn HappyAny +#if __GLASGOW_HASKELL__ >= 607 +type HappyAny = Happy_GHC_Exts.Any +#else +type HappyAny = forall a . a +#endif +happyIn15 :: (Ident) -> (HappyAbsSyn ) +happyIn15 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn15 #-} +happyOut15 :: (HappyAbsSyn ) -> (Ident) +happyOut15 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut15 #-} +happyIn16 :: (Integer) -> (HappyAbsSyn ) +happyIn16 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn16 #-} +happyOut16 :: (HappyAbsSyn ) -> (Integer) +happyOut16 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut16 #-} +happyIn17 :: (Prg) -> (HappyAbsSyn ) +happyIn17 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn17 #-} +happyOut17 :: (HappyAbsSyn ) -> (Prg) +happyOut17 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut17 #-} +happyIn18 :: (Decl) -> (HappyAbsSyn ) +happyIn18 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn18 #-} +happyOut18 :: (HappyAbsSyn ) -> (Decl) +happyOut18 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut18 #-} +happyIn19 :: (QualId) -> (HappyAbsSyn ) +happyIn19 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn19 #-} +happyOut19 :: (HappyAbsSyn ) -> (QualId) +happyOut19 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut19 #-} +happyIn20 :: ([Decl]) -> (HappyAbsSyn ) +happyIn20 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn20 #-} +happyOut20 :: (HappyAbsSyn ) -> ([Decl]) +happyOut20 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut20 #-} +happyIn21 :: (IdU) -> (HappyAbsSyn ) +happyIn21 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn21 #-} +happyOut21 :: (HappyAbsSyn ) -> (IdU) +happyOut21 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut21 #-} +happyIn22 :: (Bind) -> (HappyAbsSyn ) +happyIn22 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn22 #-} +happyOut22 :: (HappyAbsSyn ) -> (Bind) +happyOut22 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut22 #-} +happyIn23 :: ([Bind]) -> (HappyAbsSyn ) +happyIn23 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn23 #-} +happyOut23 :: (HappyAbsSyn ) -> ([Bind]) +happyOut23 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut23 #-} +happyIn24 :: ([Ident]) -> (HappyAbsSyn ) +happyIn24 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn24 #-} +happyOut24 :: (HappyAbsSyn ) -> ([Ident]) +happyOut24 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut24 #-} +happyIn25 :: ([IdU]) -> (HappyAbsSyn ) +happyIn25 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn25 #-} +happyOut25 :: (HappyAbsSyn ) -> ([IdU]) +happyOut25 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut25 #-} +happyIn26 :: (Exp) -> (HappyAbsSyn ) +happyIn26 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn26 #-} +happyOut26 :: (HappyAbsSyn ) -> (Exp) +happyOut26 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut26 #-} +happyIn27 :: (Exp) -> (HappyAbsSyn ) +happyIn27 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn27 #-} +happyOut27 :: (HappyAbsSyn ) -> (Exp) +happyOut27 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut27 #-} +happyIn28 :: (Exp) -> (HappyAbsSyn ) +happyIn28 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyIn28 #-} +happyOut28 :: (HappyAbsSyn ) -> (Exp) +happyOut28 x = Happy_GHC_Exts.unsafeCoerce# x +{-# INLINE happyOut28 #-} +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# "\x7f\x00\x7f\x00\xf0\x00\x7f\x00\xf0\xff\x04\x00\x04\x00\xf0\x00\xf0\xff\x52\x00\x1a\x00\x52\x00\xf0\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x01\x00\x1a\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\xeb\x00\x3b\x00\x1a\x00\xf3\xff\x1a\x00\x04\x00\xeb\x00\xf0\xff\xeb\x00\xea\x00\xe6\x00\x04\x00\xe6\x00\xe7\x00\xe7\x00\xe7\x00\xe4\x00\xe4\x00\x43\x00\x01\x01\xe2\x00\xe1\x00\x00\x00\xfd\xff\xd2\x00\xd2\x00\x00\x00\xd1\x00\xd1\x00\x7f\x00\x1a\x00\x1a\x00\x00\x00\x00\x00\xdd\x00\x00\x00\x00\x00\x00\x00\xee\x00\xc5\x00\xe9\x00\xdc\x00\xf9\x00\x00\x00\xc2\x00\x1a\x00\xe0\x00\x00\x00\x00\x00\x00\x00\x1a\x00\xb7\x00\x1a\x00\x1a\x00\x1a\x00\x1a\x00\x00\x00\x00\x00\x00\x00\xc9\x00\x00\x00\xd0\x00\x00\x00\xb4\x00\x00\x00\xc0\x00\xbf\x00\xbe\x00\xae\x00\x1a\x00\x00\x00\x00\x00\xad\x00\x1a\x00\x00\x00\x1a\x00\x98\x00\x9d\x00\x80\x00\x66\x00\xf0\xff\x6b\x00\x54\x00\x1a\x00\xe8\xff\x00\x00\x00\x00"# + +happyGotoOffsets :: HappyAddr +happyGotoOffsets = HappyA# "\x8b\x00\x06\x00\x3f\x00\xbb\x00\x82\x00\x5f\x00\xfb\x00\x38\x00\x50\x00\x61\x00\xec\x00\xef\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x44\x00\xde\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\x44\x00\xdb\x00\x2f\x00\xcd\x00\xf8\x00\x00\x00\x16\x00\x00\x00\x34\x00\x00\x00\xf6\x00\x00\x00\x29\x00\x55\x00\x42\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x24\x00\x15\x00\xaa\x00\xca\x00\xbc\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\x07\x00\xb9\x00\x00\x00\x00\x00\x00\x00\x00\x00\xab\x00\x00\x00\xa8\x00\x9a\x00\x97\x00\x89\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\x86\x00\x00\x00\x00\x00\x00\x00\x78\x00\x00\x00\x74\x00\x00\x00\x00\x00\x00\x00\x00\x00\x64\x00\x00\x00\x00\x00\x70\x00\x00\x00\x00\x00\x00\x00"# + +happyDefActions :: HappyAddr +happyDefActions = HappyA# "\xed\xff\xed\xff\x00\x00\xed\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf3\xff\xe8\xff\xdc\xff\xdd\xff\xc7\xff\x00\x00\x00\x00\xda\xff\xd9\xff\xd8\xff\xd7\xff\xe7\xff\xd4\xff\xd2\xff\xd3\xff\xdb\xff\xd5\xff\xd6\xff\xf2\xff\x00\x00\xc9\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xdf\xff\x00\x00\xe1\xff\x00\x00\xe3\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xea\xff\x00\x00\x00\x00\xec\xff\x00\x00\x00\x00\x00\x00\xf1\xff\x00\x00\x00\x00\xed\xff\x00\x00\x00\x00\xe5\xff\xe6\xff\x00\x00\xe2\xff\xe0\xff\xde\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xc8\xff\x00\x00\x00\x00\x00\x00\xd1\xff\xcd\xff\xcb\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xef\xff\xf0\xff\xe9\xff\xee\xff\xeb\xff\x00\x00\xcf\xff\x00\x00\xd0\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xe4\xff\xcc\xff\x00\x00\x00\x00\xce\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xca\xff"# + +happyCheck :: HappyAddr +happyCheck = HappyA# "\xff\xff\x11\x00\x01\x00\x06\x00\x11\x00\x01\x00\x00\x00\x1f\x00\x01\x00\x03\x00\x06\x00\x07\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x20\x00\x1e\x00\x11\x00\x20\x00\x13\x00\x00\x00\x00\x00\x16\x00\x17\x00\x04\x00\x19\x00\x01\x00\x06\x00\x1c\x00\x1d\x00\x22\x00\x0a\x00\x20\x00\x21\x00\x22\x00\x00\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x00\x00\x10\x00\x11\x00\x12\x00\x13\x00\x14\x00\x00\x00\x16\x00\x17\x00\x09\x00\x19\x00\x00\x00\x06\x00\x1c\x00\x1d\x00\x00\x00\x0a\x00\x20\x00\x21\x00\x01\x00\x09\x00\x03\x00\x00\x00\x05\x00\x09\x00\x00\x00\x04\x00\x00\x00\x01\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x06\x00\x08\x00\x11\x00\x0a\x00\x13\x00\x0b\x00\x00\x00\x16\x00\x17\x00\x01\x00\x19\x00\x00\x00\x06\x00\x1c\x00\x1d\x00\x05\x00\x0a\x00\x20\x00\x21\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x00\x00\x01\x00\x11\x00\x00\x00\x13\x00\x07\x00\x06\x00\x16\x00\x17\x00\x06\x00\x19\x00\x0b\x00\x02\x00\x1c\x00\x1d\x00\x00\x00\x01\x00\x20\x00\x21\x00\x00\x00\x01\x00\x06\x00\x11\x00\x00\x00\x01\x00\x06\x00\x0b\x00\x0c\x00\x0d\x00\x06\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x06\x00\x00\x00\x01\x00\x00\x00\x06\x00\x02\x00\x03\x00\x06\x00\x05\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x1a\x00\x00\x00\x01\x00\x1c\x00\x06\x00\x01\x00\x20\x00\x06\x00\x09\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x00\x00\x00\x00\x01\x00\x03\x00\x06\x00\x05\x00\x02\x00\x06\x00\x05\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x00\x00\x00\x00\x01\x00\x03\x00\x06\x00\x05\x00\x02\x00\x06\x00\x05\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x18\x00\x00\x00\x01\x00\x06\x00\x06\x00\x11\x00\x02\x00\x06\x00\x1d\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x01\x00\x00\x00\x01\x00\x1b\x00\x06\x00\x02\x00\x21\x00\x06\x00\x08\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x0c\x00\x0d\x00\x00\x00\x01\x00\x05\x00\x00\x00\x01\x00\x20\x00\x06\x00\x05\x00\x22\x00\x06\x00\x15\x00\x0b\x00\x0c\x00\x0d\x00\x0b\x00\x02\x00\x0d\x00\x07\x00\x08\x00\x07\x00\x08\x00\x08\x00\x07\x00\x08\x00\x22\x00\x04\x00\x22\x00\x20\x00\x22\x00\xff\xff\x20\x00\xff\xff\xff\xff\x22\x00\xff\xff\xff\xff\x20\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"# + +happyTable :: HappyAddr +happyTable = HappyA# "\x00\x00\x19\x00\x14\x00\x3c\x00\x19\x00\x2e\x00\x32\x00\x76\x00\x51\x00\x38\x00\x2f\x00\x30\x00\x15\x00\x16\x00\x17\x00\x18\x00\x0e\x00\x4a\x00\x19\x00\x0e\x00\x1a\x00\x36\x00\x0e\x00\x1b\x00\x1c\x00\x5b\x00\x1d\x00\x23\x00\x27\x00\x1e\x00\x1f\x00\xff\xff\x45\x00\x0e\x00\x20\x00\xff\xff\x5c\x00\x15\x00\x16\x00\x17\x00\x18\x00\x29\x00\x24\x00\x19\x00\x25\x00\x1a\x00\x26\x00\x0e\x00\x1b\x00\x1c\x00\x42\x00\x1d\x00\x29\x00\x27\x00\x1e\x00\x1f\x00\x29\x00\x48\x00\x0e\x00\x20\x00\x14\x00\x44\x00\x4d\x00\x36\x00\x4e\x00\x2a\x00\x40\x00\x37\x00\x0e\x00\x0f\x00\x15\x00\x16\x00\x17\x00\x18\x00\x10\x00\x3f\x00\x19\x00\x40\x00\x1a\x00\x4b\x00\x0e\x00\x1b\x00\x1c\x00\x14\x00\x1d\x00\x41\x00\x27\x00\x1e\x00\x1f\x00\x74\x00\x28\x00\x0e\x00\x20\x00\x15\x00\x16\x00\x17\x00\x18\x00\x0e\x00\x0f\x00\x19\x00\x0e\x00\x1a\x00\x30\x00\x10\x00\x1b\x00\x1c\x00\x71\x00\x1d\x00\x26\x00\x73\x00\x1e\x00\x1f\x00\x0e\x00\x0f\x00\x0e\x00\x20\x00\x0e\x00\x0f\x00\x10\x00\x71\x00\x0e\x00\x0f\x00\x10\x00\x11\x00\x74\x00\x21\x00\x10\x00\x11\x00\x6c\x00\x21\x00\x0e\x00\x11\x00\x6a\x00\x21\x00\x0e\x00\x0f\x00\x31\x00\x0e\x00\x0f\x00\x32\x00\x10\x00\x39\x00\x33\x00\x10\x00\x3a\x00\x11\x00\x67\x00\x21\x00\x11\x00\x5d\x00\x21\x00\x0e\x00\x0f\x00\x36\x00\x0e\x00\x0f\x00\x70\x00\x10\x00\x6f\x00\x0e\x00\x10\x00\x6e\x00\x11\x00\x5e\x00\x21\x00\x11\x00\x5f\x00\x21\x00\x0e\x00\x0f\x00\x32\x00\x0e\x00\x0f\x00\x33\x00\x10\x00\x5a\x00\x69\x00\x10\x00\x6c\x00\x11\x00\x60\x00\x21\x00\x11\x00\x62\x00\x21\x00\x0e\x00\x0f\x00\x32\x00\x0e\x00\x0f\x00\x33\x00\x10\x00\x34\x00\x64\x00\x10\x00\x6a\x00\x11\x00\x50\x00\x21\x00\x11\x00\x58\x00\x21\x00\x0e\x00\x0f\x00\x66\x00\x0e\x00\x0f\x00\x3c\x00\x10\x00\x65\x00\x67\x00\x10\x00\x62\x00\x11\x00\x59\x00\x21\x00\x11\x00\x47\x00\x21\x00\x0e\x00\x0f\x00\x54\x00\x0e\x00\x0f\x00\x56\x00\x10\x00\x50\x00\x20\x00\x10\x00\x58\x00\x11\x00\x4a\x00\x21\x00\x11\x00\x4e\x00\x21\x00\x0e\x00\x0f\x00\x55\x00\x0e\x00\x0f\x00\x0e\x00\x10\x00\x57\x00\xff\xff\x10\x00\x3d\x00\x11\x00\x20\x00\x21\x00\x11\x00\x50\x00\x12\x00\x2b\x00\x43\x00\x2b\x00\x46\x00\x53\x00\x2b\x00\x2c\x00\xff\xff\x3e\x00\xff\xff\x0e\x00\xff\xff\x00\x00\x0e\x00\x00\x00\x00\x00\xff\xff\x00\x00\x00\x00\x0e\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 (12, 56) [ + (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) + ] + +happy_n_terms = 35 :: Int +happy_n_nonterms = 14 :: Int + +happyReduce_12 = happySpecReduce_1 0# happyReduction_12 +happyReduction_12 happy_x_1 + = case happyOutTok happy_x_1 of { (PT _ (TV happy_var_1)) -> + happyIn15 + (Ident happy_var_1 + )} + +happyReduce_13 = happySpecReduce_1 1# happyReduction_13 +happyReduction_13 happy_x_1 + = case happyOutTok happy_x_1 of { (PT _ (TI happy_var_1)) -> + happyIn16 + ((read ( happy_var_1)) :: Integer + )} + +happyReduce_14 = happySpecReduce_1 2# happyReduction_14 +happyReduction_14 happy_x_1 + = case happyOut20 happy_x_1 of { happy_var_1 -> + happyIn17 + (Sit.Abs.Prg happy_var_1 + )} + +happyReduce_15 = happySpecReduce_3 3# happyReduction_15 +happyReduction_15 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut15 happy_x_1 of { happy_var_1 -> + case happyOut27 happy_x_3 of { happy_var_3 -> + happyIn18 + (Sit.Abs.Sig happy_var_1 happy_var_3 + )}} + +happyReduce_16 = happySpecReduce_3 3# happyReduction_16 +happyReduction_16 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut15 happy_x_1 of { happy_var_1 -> + case happyOut27 happy_x_3 of { happy_var_3 -> + happyIn18 + (Sit.Abs.Def happy_var_1 happy_var_3 + )}} + +happyReduce_17 = happySpecReduce_3 3# happyReduction_17 +happyReduction_17 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut19 happy_x_3 of { happy_var_3 -> + happyIn18 + (Sit.Abs.Open happy_var_3 + )} + +happyReduce_18 = happySpecReduce_0 3# happyReduction_18 +happyReduction_18 = happyIn18 + (Sit.Abs.Blank + ) + +happyReduce_19 = happySpecReduce_1 4# happyReduction_19 +happyReduction_19 happy_x_1 + = case happyOut15 happy_x_1 of { happy_var_1 -> + happyIn19 + (Sit.Abs.Sg happy_var_1 + )} + +happyReduce_20 = happySpecReduce_3 4# happyReduction_20 +happyReduction_20 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut19 happy_x_1 of { happy_var_1 -> + case happyOut15 happy_x_3 of { happy_var_3 -> + happyIn19 + (Sit.Abs.Cons happy_var_1 happy_var_3 + )}} + +happyReduce_21 = happySpecReduce_1 5# happyReduction_21 +happyReduction_21 happy_x_1 + = case happyOut18 happy_x_1 of { happy_var_1 -> + happyIn20 + ((:[]) happy_var_1 + )} + +happyReduce_22 = happySpecReduce_3 5# happyReduction_22 +happyReduction_22 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut18 happy_x_1 of { happy_var_1 -> + case happyOut20 happy_x_3 of { happy_var_3 -> + happyIn20 + ((:) happy_var_1 happy_var_3 + )}} + +happyReduce_23 = happySpecReduce_1 6# happyReduction_23 +happyReduction_23 happy_x_1 + = case happyOut15 happy_x_1 of { happy_var_1 -> + happyIn21 + (Sit.Abs.Id happy_var_1 + )} + +happyReduce_24 = happySpecReduce_1 6# happyReduction_24 +happyReduction_24 happy_x_1 + = happyIn21 + (Sit.Abs.Under + ) + +happyReduce_25 = happySpecReduce_2 7# happyReduction_25 +happyReduction_25 happy_x_2 + happy_x_1 + = case happyOut15 happy_x_2 of { happy_var_2 -> + happyIn22 + (Sit.Abs.BIrrel happy_var_2 + )} + +happyReduce_26 = happySpecReduce_2 7# happyReduction_26 +happyReduction_26 happy_x_2 + happy_x_1 + = case happyOut15 happy_x_2 of { happy_var_2 -> + happyIn22 + (Sit.Abs.BRel happy_var_2 + )} + +happyReduce_27 = happyReduce 5# 7# happyReduction_27 +happyReduction_27 (happy_x_5 `HappyStk` + happy_x_4 `HappyStk` + happy_x_3 `HappyStk` + happy_x_2 `HappyStk` + happy_x_1 `HappyStk` + happyRest) + = case happyOut24 happy_x_2 of { happy_var_2 -> + case happyOut27 happy_x_4 of { happy_var_4 -> + happyIn22 + (Sit.Abs.BAnn happy_var_2 happy_var_4 + ) `HappyStk` happyRest}} + +happyReduce_28 = happySpecReduce_1 8# happyReduction_28 +happyReduction_28 happy_x_1 + = case happyOut22 happy_x_1 of { happy_var_1 -> + happyIn23 + ((:[]) happy_var_1 + )} + +happyReduce_29 = happySpecReduce_2 8# happyReduction_29 +happyReduction_29 happy_x_2 + happy_x_1 + = case happyOut22 happy_x_1 of { happy_var_1 -> + case happyOut23 happy_x_2 of { happy_var_2 -> + happyIn23 + ((:) happy_var_1 happy_var_2 + )}} + +happyReduce_30 = happySpecReduce_1 9# happyReduction_30 +happyReduction_30 happy_x_1 + = case happyOut15 happy_x_1 of { happy_var_1 -> + happyIn24 + ((:[]) happy_var_1 + )} + +happyReduce_31 = happySpecReduce_2 9# happyReduction_31 +happyReduction_31 happy_x_2 + happy_x_1 + = case happyOut15 happy_x_1 of { happy_var_1 -> + case happyOut24 happy_x_2 of { happy_var_2 -> + happyIn24 + ((:) happy_var_1 happy_var_2 + )}} + +happyReduce_32 = happySpecReduce_1 10# happyReduction_32 +happyReduction_32 happy_x_1 + = case happyOut21 happy_x_1 of { happy_var_1 -> + happyIn25 + ((:[]) happy_var_1 + )} + +happyReduce_33 = happySpecReduce_2 10# happyReduction_33 +happyReduction_33 happy_x_2 + happy_x_1 + = case happyOut21 happy_x_1 of { happy_var_1 -> + case happyOut25 happy_x_2 of { happy_var_2 -> + happyIn25 + ((:) happy_var_1 happy_var_2 + )}} + +happyReduce_34 = happySpecReduce_1 11# happyReduction_34 +happyReduction_34 happy_x_1 + = case happyOut21 happy_x_1 of { happy_var_1 -> + happyIn26 + (Sit.Abs.Var happy_var_1 + )} + +happyReduce_35 = happySpecReduce_1 11# happyReduction_35 +happyReduction_35 happy_x_1 + = case happyOut16 happy_x_1 of { happy_var_1 -> + happyIn26 + (Sit.Abs.Int happy_var_1 + )} + +happyReduce_36 = happySpecReduce_1 11# happyReduction_36 +happyReduction_36 happy_x_1 + = happyIn26 + (Sit.Abs.Infty + ) + +happyReduce_37 = happySpecReduce_1 11# happyReduction_37 +happyReduction_37 happy_x_1 + = happyIn26 + (Sit.Abs.Nat + ) + +happyReduce_38 = happySpecReduce_1 11# happyReduction_38 +happyReduction_38 happy_x_1 + = happyIn26 + (Sit.Abs.Set + ) + +happyReduce_39 = happySpecReduce_1 11# happyReduction_39 +happyReduction_39 happy_x_1 + = happyIn26 + (Sit.Abs.Set1 + ) + +happyReduce_40 = happySpecReduce_1 11# happyReduction_40 +happyReduction_40 happy_x_1 + = happyIn26 + (Sit.Abs.Set2 + ) + +happyReduce_41 = happySpecReduce_1 11# happyReduction_41 +happyReduction_41 happy_x_1 + = happyIn26 + (Sit.Abs.Zero + ) + +happyReduce_42 = happySpecReduce_1 11# happyReduction_42 +happyReduction_42 happy_x_1 + = happyIn26 + (Sit.Abs.Suc + ) + +happyReduce_43 = happySpecReduce_1 11# happyReduction_43 +happyReduction_43 happy_x_1 + = happyIn26 + (Sit.Abs.Fix + ) + +happyReduce_44 = happySpecReduce_1 11# happyReduction_44 +happyReduction_44 happy_x_1 + = happyIn26 + (Sit.Abs.LZero + ) + +happyReduce_45 = happySpecReduce_1 11# happyReduction_45 +happyReduction_45 happy_x_1 + = happyIn26 + (Sit.Abs.LSuc + ) + +happyReduce_46 = happySpecReduce_3 11# happyReduction_46 +happyReduction_46 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut27 happy_x_2 of { happy_var_2 -> + happyIn26 + (happy_var_2 + )} + +happyReduce_47 = happyReduce 4# 12# happyReduction_47 +happyReduction_47 (happy_x_4 `HappyStk` + happy_x_3 `HappyStk` + happy_x_2 `HappyStk` + happy_x_1 `HappyStk` + happyRest) + = case happyOut25 happy_x_2 of { happy_var_2 -> + case happyOut27 happy_x_4 of { happy_var_4 -> + happyIn27 + (Sit.Abs.Lam happy_var_2 happy_var_4 + ) `HappyStk` happyRest}} + +happyReduce_48 = happyReduce 4# 12# happyReduction_48 +happyReduction_48 (happy_x_4 `HappyStk` + happy_x_3 `HappyStk` + happy_x_2 `HappyStk` + happy_x_1 `HappyStk` + happyRest) + = case happyOut23 happy_x_2 of { happy_var_2 -> + case happyOut27 happy_x_4 of { happy_var_4 -> + happyIn27 + (Sit.Abs.Forall happy_var_2 happy_var_4 + ) `HappyStk` happyRest}} + +happyReduce_49 = happyReduce 7# 12# happyReduction_49 +happyReduction_49 (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 happyOut27 happy_x_2 of { happy_var_2 -> + case happyOut27 happy_x_4 of { happy_var_4 -> + case happyOut27 happy_x_7 of { happy_var_7 -> + happyIn27 + (Sit.Abs.Pi happy_var_2 happy_var_4 happy_var_7 + ) `HappyStk` happyRest}}} + +happyReduce_50 = happySpecReduce_3 12# happyReduction_50 +happyReduction_50 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut28 happy_x_1 of { happy_var_1 -> + case happyOut27 happy_x_3 of { happy_var_3 -> + happyIn27 + (Sit.Abs.Arrow happy_var_1 happy_var_3 + )}} + +happyReduce_51 = happyReduce 6# 12# happyReduction_51 +happyReduction_51 (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 happyOut27 happy_x_2 of { happy_var_2 -> + case happyOut27 happy_x_4 of { happy_var_4 -> + case happyOut27 happy_x_6 of { happy_var_6 -> + happyIn27 + (Sit.Abs.Case happy_var_2 happy_var_4 happy_var_6 + ) `HappyStk` happyRest}}} + +happyReduce_52 = happySpecReduce_3 12# happyReduction_52 +happyReduction_52 happy_x_3 + happy_x_2 + happy_x_1 + = case happyOut28 happy_x_1 of { happy_var_1 -> + case happyOut16 happy_x_3 of { happy_var_3 -> + happyIn27 + (Sit.Abs.Plus happy_var_1 happy_var_3 + )}} + +happyReduce_53 = happyReduce 17# 12# happyReduction_53 +happyReduction_53 (happy_x_17 `HappyStk` + happy_x_16 `HappyStk` + happy_x_15 `HappyStk` + happy_x_14 `HappyStk` + happy_x_13 `HappyStk` + happy_x_12 `HappyStk` + happy_x_11 `HappyStk` + happy_x_10 `HappyStk` + 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 happyOut27 happy_x_8 of { happy_var_8 -> + case happyOut21 happy_x_13 of { happy_var_13 -> + case happyOut27 happy_x_16 of { happy_var_16 -> + happyIn27 + (Sit.Abs.ELam happy_var_8 happy_var_13 happy_var_16 + ) `HappyStk` happyRest}}} + +happyReduce_54 = happySpecReduce_1 12# happyReduction_54 +happyReduction_54 happy_x_1 + = case happyOut28 happy_x_1 of { happy_var_1 -> + happyIn27 + (happy_var_1 + )} + +happyReduce_55 = happySpecReduce_2 13# happyReduction_55 +happyReduction_55 happy_x_2 + happy_x_1 + = case happyOut28 happy_x_1 of { happy_var_1 -> + case happyOut26 happy_x_2 of { happy_var_2 -> + happyIn28 + (Sit.Abs.App happy_var_1 happy_var_2 + )}} + +happyReduce_56 = happySpecReduce_1 13# happyReduction_56 +happyReduction_56 happy_x_1 + = case happyOut26 happy_x_1 of { happy_var_1 -> + happyIn28 + (happy_var_1 + )} + +happyNewToken action sts stk [] = + happyDoAction 34# 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 _ (TS _ 12) -> cont 12#; + PT _ (TS _ 13) -> cont 13#; + PT _ (TS _ 14) -> cont 14#; + PT _ (TS _ 15) -> cont 15#; + PT _ (TS _ 16) -> cont 16#; + PT _ (TS _ 17) -> cont 17#; + PT _ (TS _ 18) -> cont 18#; + PT _ (TS _ 19) -> cont 19#; + PT _ (TS _ 20) -> cont 20#; + PT _ (TS _ 21) -> cont 21#; + PT _ (TS _ 22) -> cont 22#; + PT _ (TS _ 23) -> cont 23#; + PT _ (TS _ 24) -> cont 24#; + PT _ (TS _ 25) -> cont 25#; + PT _ (TS _ 26) -> cont 26#; + PT _ (TS _ 27) -> cont 27#; + PT _ (TS _ 28) -> cont 28#; + PT _ (TS _ 29) -> cont 29#; + PT _ (TS _ 30) -> cont 30#; + PT _ (TS _ 31) -> cont 31#; + PT _ (TV happy_dollar_dollar) -> cont 32#; + PT _ (TI happy_dollar_dollar) -> cont 33#; + _ -> happyError' (tk:tks) + } + +happyError_ 34# 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 + +pPrg tks = happySomeParser where + happySomeParser = happyThen (happyParse 0# tks) (\x -> happyReturn (happyOut17 x)) + +pDecl tks = happySomeParser where + happySomeParser = happyThen (happyParse 1# tks) (\x -> happyReturn (happyOut18 x)) + +pQualId tks = happySomeParser where + happySomeParser = happyThen (happyParse 2# tks) (\x -> happyReturn (happyOut19 x)) + +pListDecl tks = happySomeParser where + happySomeParser = happyThen (happyParse 3# tks) (\x -> happyReturn (happyOut20 x)) + +pIdU tks = happySomeParser where + happySomeParser = happyThen (happyParse 4# tks) (\x -> happyReturn (happyOut21 x)) + +pBind tks = happySomeParser where + happySomeParser = happyThen (happyParse 5# tks) (\x -> happyReturn (happyOut22 x)) + +pListBind tks = happySomeParser where + happySomeParser = happyThen (happyParse 6# tks) (\x -> happyReturn (happyOut23 x)) + +pListIdent tks = happySomeParser where + happySomeParser = happyThen (happyParse 7# tks) (\x -> happyReturn (happyOut24 x)) + +pListIdU tks = happySomeParser where + happySomeParser = happyThen (happyParse 8# tks) (\x -> happyReturn (happyOut25 x)) + +pExp2 tks = happySomeParser where + happySomeParser = happyThen (happyParse 9# tks) (\x -> happyReturn (happyOut26 x)) + +pExp tks = happySomeParser where + happySomeParser = happyThen (happyParse 10# tks) (\x -> happyReturn (happyOut27 x)) + +pExp1 tks = happySomeParser where + happySomeParser = happyThen (happyParse 11# tks) (\x -> happyReturn (happyOut28 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" + t:_ -> " before `" ++ id(prToken t) ++ "'" + +myLexer = tokens +{-# LINE 1 "templates/GenericTemplate.hs" #-} +{-# LINE 1 "templates/GenericTemplate.hs" #-} +{-# LINE 1 "" #-} +{-# LINE 10 "" #-} +# 1 "/usr/include/stdc-predef.h" 1 3 4 + +# 17 "/usr/include/stdc-predef.h" 3 4 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +{-# LINE 10 "" #-} +{-# LINE 1 "templates/GenericTemplate.hs" #-} +-- Id: GenericTemplate.hs,v 1.26 2005/01/14 14:47:22 simonmar Exp + +{-# LINE 13 "templates/GenericTemplate.hs" #-} + + + + + +-- Do not remove this comment. Required to fix CPP parsing when using GCC and a clang-compiled alex. +#if __GLASGOW_HASKELL__ > 706 +#define LT(n,m) ((Happy_GHC_Exts.tagToEnum# (n Happy_GHC_Exts.<# m)) :: Bool) +#define GTE(n,m) ((Happy_GHC_Exts.tagToEnum# (n Happy_GHC_Exts.>=# m)) :: Bool) +#define EQ(n,m) ((Happy_GHC_Exts.tagToEnum# (n Happy_GHC_Exts.==# m)) :: Bool) +#else +#define LT(n,m) (n Happy_GHC_Exts.<# m) +#define GTE(n,m) (n Happy_GHC_Exts.>=# m) +#define EQ(n,m) (n Happy_GHC_Exts.==# m) +#endif +{-# LINE 46 "templates/GenericTemplate.hs" #-} + + +data Happy_IntList = HappyCons Happy_GHC_Exts.Int# Happy_IntList + + + + + +{-# LINE 67 "templates/GenericTemplate.hs" #-} + +{-# LINE 77 "templates/GenericTemplate.hs" #-} + +{-# LINE 86 "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 | LT(n,(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 GTE(off_i,(0# :: Happy_GHC_Exts.Int#)) + then EQ(indexShortOffAddr happyCheck off_i, i) + else False + action + | check = indexShortOffAddr happyTable off_i + | otherwise = indexShortOffAddr happyDefActions st + + +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 170 "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 = + case happyDrop k (HappyCons (st) (sts)) of + sts1@((HappyCons (st1@(action)) (_))) -> + let drop_stk = happyDropStk k stk in + happyThen1 (fn stk tk) (\r -> happyGoto nt j tk st1 sts1 (r `HappyStk` drop_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 = + case happyDrop k (HappyCons (st) (sts)) of + sts1@((HappyCons (st1@(action)) (_))) -> + let drop_stk = happyDropStk k stk + + off = indexShortOffAddr happyGotoOffsets st1 + off_i = (off Happy_GHC_Exts.+# nt) + new_state = indexShortOffAddr happyTable off_i + + + + in + happyThen1 (fn stk tk) (\r -> happyNewToken new_state sts1 (r `HappyStk` drop_stk)) + +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/src/Sit/Par.y b/src/Sit/Par.y new file mode 100644 --- /dev/null +++ b/src/Sit/Par.y @@ -0,0 +1,135 @@ +-- This Happy file was machine-generated by the BNF converter +{ +{-# OPTIONS_GHC -fno-warn-incomplete-patterns -fno-warn-overlapping-patterns #-} +module Sit.Par where +import Sit.Abs +import Sit.Lex +import Sit.ErrM + +} + +%name pPrg Prg +%name pDecl Decl +%name pQualId QualId +%name pListDecl ListDecl +%name pIdU IdU +%name pBind Bind +%name pListBind ListBind +%name pListIdent ListIdent +%name pListIdU ListIdU +%name pExp2 Exp2 +%name pExp Exp +%name pExp1 Exp1 +-- 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) } + '..' { PT _ (TS _ 7) } + ':' { PT _ (TS _ 8) } + ';' { PT _ (TS _ 9) } + '=' { PT _ (TS _ 10) } + 'Nat' { PT _ (TS _ 11) } + 'Set' { PT _ (TS _ 12) } + 'Set1' { PT _ (TS _ 13) } + 'Set2' { PT _ (TS _ 14) } + 'Size' { PT _ (TS _ 15) } + '\\' { PT _ (TS _ 16) } + '_' { PT _ (TS _ 17) } + 'case' { PT _ (TS _ 18) } + 'fix' { PT _ (TS _ 19) } + 'forall' { PT _ (TS _ 20) } + 'import' { PT _ (TS _ 21) } + 'lsuc' { PT _ (TS _ 22) } + 'lzero' { PT _ (TS _ 23) } + 'of' { PT _ (TS _ 24) } + 'oo' { PT _ (TS _ 25) } + 'open' { PT _ (TS _ 26) } + 'return' { PT _ (TS _ 27) } + 'suc' { PT _ (TS _ 28) } + 'zero' { PT _ (TS _ 29) } + '{' { PT _ (TS _ 30) } + '}' { PT _ (TS _ 31) } + +L_ident { PT _ (TV $$) } +L_integ { PT _ (TI $$) } + + +%% + +Ident :: { Ident } : L_ident { Ident $1 } +Integer :: { Integer } : L_integ { (read ( $1)) :: Integer } + +Prg :: { Prg } +Prg : ListDecl { Sit.Abs.Prg $1 } +Decl :: { Decl } +Decl : Ident ':' Exp { Sit.Abs.Sig $1 $3 } + | Ident '=' Exp { Sit.Abs.Def $1 $3 } + | 'open' 'import' QualId { Sit.Abs.Open $3 } + | {- empty -} { Sit.Abs.Blank } +QualId :: { QualId } +QualId : Ident { Sit.Abs.Sg $1 } + | QualId '.' Ident { Sit.Abs.Cons $1 $3 } +ListDecl :: { [Decl] } +ListDecl : Decl { (:[]) $1 } | Decl '--;' ListDecl { (:) $1 $3 } +IdU :: { IdU } +IdU : Ident { Sit.Abs.Id $1 } | '_' { Sit.Abs.Under } +Bind :: { Bind } +Bind : '.' Ident { Sit.Abs.BIrrel $2 } + | '..' Ident { Sit.Abs.BRel $2 } + | '(' ListIdent ':' Exp ')' { Sit.Abs.BAnn $2 $4 } +ListBind :: { [Bind] } +ListBind : Bind { (:[]) $1 } | Bind ListBind { (:) $1 $2 } +ListIdent :: { [Ident] } +ListIdent : Ident { (:[]) $1 } | Ident ListIdent { (:) $1 $2 } +ListIdU :: { [IdU] } +ListIdU : IdU { (:[]) $1 } | IdU ListIdU { (:) $1 $2 } +Exp2 :: { Exp } +Exp2 : IdU { Sit.Abs.Var $1 } + | Integer { Sit.Abs.Int $1 } + | 'oo' { Sit.Abs.Infty } + | 'Nat' { Sit.Abs.Nat } + | 'Set' { Sit.Abs.Set } + | 'Set1' { Sit.Abs.Set1 } + | 'Set2' { Sit.Abs.Set2 } + | 'zero' { Sit.Abs.Zero } + | 'suc' { Sit.Abs.Suc } + | 'fix' { Sit.Abs.Fix } + | 'lzero' { Sit.Abs.LZero } + | 'lsuc' { Sit.Abs.LSuc } + | '(' Exp ')' { $2 } +Exp :: { Exp } +Exp : '\\' ListIdU '->' Exp { Sit.Abs.Lam $2 $4 } + | 'forall' ListBind '->' Exp { Sit.Abs.Forall $2 $4 } + | '(' Exp ':' Exp ')' '->' Exp { Sit.Abs.Pi $2 $4 $7 } + | Exp1 '->' Exp { Sit.Abs.Arrow $1 $3 } + | 'case' Exp 'return' Exp 'of' Exp { Sit.Abs.Case $2 $4 $6 } + | Exp1 '+' Integer { Sit.Abs.Plus $1 $3 } + | '\\' '{' '(' 'zero' '_' ')' '->' Exp ';' '(' 'suc' '_' IdU ')' '->' Exp '}' { Sit.Abs.ELam $8 $13 $16 } + | Exp1 { $1 } +Exp1 :: { Exp } +Exp1 : Exp1 Exp2 { Sit.Abs.App $1 $2 } | Exp2 { $1 } +{ + +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" + t:_ -> " before `" ++ id(prToken t) ++ "'" + +myLexer = tokens +} + diff --git a/src/Sit/Print.hs b/src/Sit/Print.hs new file mode 100644 --- /dev/null +++ b/src/Sit/Print.hs @@ -0,0 +1,141 @@ +{-# OPTIONS_GHC -fno-warn-incomplete-patterns #-} +module Sit.Print where + +-- pretty-printer generated by the BNF converter + +import Sit.Abs +import Data.Char + + +-- the top-level printing method +printTree :: Print a => a -> String +printTree = render . prt 0 + +type Doc = [ShowS] -> [ShowS] + +doc :: ShowS -> Doc +doc = (:) + +render :: Doc -> String +render d = rend 0 (map ($ "") $ d []) "" where + rend i ss = case ss of + "[" :ts -> showChar '[' . rend i ts + "(" :ts -> showChar '(' . rend i ts + "{" :ts -> showChar '{' . new (i+1) . rend (i+1) ts + "}" : ";":ts -> new (i-1) . space "}" . showChar ';' . new (i-1) . rend (i-1) ts + "}" :ts -> new (i-1) . showChar '}' . new (i-1) . rend (i-1) ts + ";" :ts -> showChar ';' . new i . rend i ts + t : ts@(p:_) | closingOrPunctuation p -> showString t . rend i ts + t :ts -> space t . rend i ts + _ -> id + new i = showChar '\n' . replicateS (2*i) (showChar ' ') . dropWhile isSpace + space t = showString t . (\s -> if null s then "" else ' ':s) + closingOrPunctuation [c] = c `elem` ")],;." + closingOrPunctuation _ = False + +parenth :: Doc -> Doc +parenth ss = doc (showChar '(') . ss . doc (showChar ')') + +concatS :: [ShowS] -> ShowS +concatS = foldr (.) id + +concatD :: [Doc] -> Doc +concatD = foldr (.) id + +replicateS :: Int -> ShowS -> ShowS +replicateS n f = concatS (replicate n f) + +-- the printer class does the job +class Print a where + prt :: Int -> a -> Doc + prtList :: Int -> [a] -> Doc + prtList i = concatD . map (prt i) + +instance Print a => Print [a] where + prt = prtList + +instance Print Char where + prt _ s = doc (showChar '\'' . mkEsc '\'' s . showChar '\'') + prtList _ s = doc (showChar '"' . concatS (map (mkEsc '"') s) . showChar '"') + +mkEsc :: Char -> Char -> ShowS +mkEsc q s = case s of + _ | s == q -> showChar '\\' . showChar s + '\\'-> showString "\\\\" + '\n' -> showString "\\n" + '\t' -> showString "\\t" + _ -> showChar s + +prPrec :: Int -> Int -> Doc -> Doc +prPrec i j = if j prPrec i 0 (concatD [prt 0 decls]) + +instance Print Decl where + prt i e = case e of + Sig id exp -> prPrec i 0 (concatD [prt 0 id, doc (showString ":"), prt 0 exp]) + Def id exp -> prPrec i 0 (concatD [prt 0 id, doc (showString "="), prt 0 exp]) + Open qualid -> prPrec i 0 (concatD [doc (showString "open"), doc (showString "import"), prt 0 qualid]) + Blank -> prPrec i 0 (concatD []) + prtList _ [x] = (concatD [prt 0 x]) + prtList _ (x:xs) = (concatD [prt 0 x, doc (showString "--;"), prt 0 xs]) +instance Print QualId where + prt i e = case e of + Sg id -> prPrec i 0 (concatD [prt 0 id]) + Cons qualid id -> prPrec i 0 (concatD [prt 0 qualid, doc (showString "."), prt 0 id]) + +instance Print IdU where + prt i e = case e of + Id id -> prPrec i 0 (concatD [prt 0 id]) + Under -> prPrec i 0 (concatD [doc (showString "_")]) + prtList _ [x] = (concatD [prt 0 x]) + prtList _ (x:xs) = (concatD [prt 0 x, prt 0 xs]) +instance Print Bind where + prt i e = case e of + BIrrel id -> prPrec i 0 (concatD [doc (showString "."), prt 0 id]) + BRel id -> prPrec i 0 (concatD [doc (showString ".."), prt 0 id]) + BAnn ids exp -> prPrec i 0 (concatD [doc (showString "("), prt 0 ids, doc (showString ":"), prt 0 exp, doc (showString ")")]) + prtList _ [x] = (concatD [prt 0 x]) + prtList _ (x:xs) = (concatD [prt 0 x, prt 0 xs]) +instance Print Exp where + prt i e = case e of + Var idu -> prPrec i 2 (concatD [prt 0 idu]) + Int n -> prPrec i 2 (concatD [prt 0 n]) + Infty -> prPrec i 2 (concatD [doc (showString "oo")]) + Nat -> prPrec i 2 (concatD [doc (showString "Nat")]) + Set -> prPrec i 2 (concatD [doc (showString "Set")]) + Set1 -> prPrec i 2 (concatD [doc (showString "Set1")]) + Set2 -> prPrec i 2 (concatD [doc (showString "Set2")]) + Zero -> prPrec i 2 (concatD [doc (showString "zero")]) + Suc -> prPrec i 2 (concatD [doc (showString "suc")]) + Fix -> prPrec i 2 (concatD [doc (showString "fix")]) + LZero -> prPrec i 2 (concatD [doc (showString "lzero")]) + LSuc -> prPrec i 2 (concatD [doc (showString "lsuc")]) + Size -> prPrec i 0 (concatD [doc (showString "Size")]) + App exp1 exp2 -> prPrec i 1 (concatD [prt 1 exp1, prt 2 exp2]) + Lam idus exp -> prPrec i 0 (concatD [doc (showString "\\"), prt 0 idus, doc (showString "->"), prt 0 exp]) + Forall binds exp -> prPrec i 0 (concatD [doc (showString "forall"), prt 0 binds, doc (showString "->"), prt 0 exp]) + Pi exp1 exp2 exp3 -> prPrec i 0 (concatD [doc (showString "("), prt 0 exp1, doc (showString ":"), prt 0 exp2, doc (showString ")"), doc (showString "->"), prt 0 exp3]) + Arrow exp1 exp2 -> prPrec i 0 (concatD [prt 1 exp1, doc (showString "->"), prt 0 exp2]) + Case exp1 exp2 exp3 -> prPrec i 0 (concatD [doc (showString "case"), prt 0 exp1, doc (showString "return"), prt 0 exp2, doc (showString "of"), prt 0 exp3]) + Plus exp n -> prPrec i 0 (concatD [prt 1 exp, doc (showString "+"), prt 0 n]) + ELam exp1 idu exp2 -> prPrec i 0 (concatD [doc (showString "\\"), doc (showString "{"), doc (showString "("), doc (showString "zero"), doc (showString "_"), doc (showString ")"), doc (showString "->"), prt 0 exp1, doc (showString ";"), doc (showString "("), doc (showString "suc"), doc (showString "_"), prt 0 idu, doc (showString ")"), doc (showString "->"), prt 0 exp2, doc (showString "}")]) + + diff --git a/src/Substitute.hs b/src/Substitute.hs new file mode 100644 --- /dev/null +++ b/src/Substitute.hs @@ -0,0 +1,201 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE LambdaCase #-} +{-# LANGUAGE TypeSynonymInstances, FlexibleInstances #-} + +{-# OPTIONS_GHC -fwarn-incomplete-patterns #-} + +-- | Substitution and weak head evaluation + +module Substitute where + +import Internal + +import Impossible +#include "undefined.h" + +-- | Substitutions are lists of terms. + +type Subst = [Term] + +-- | Weakening substitution @Γ.Δ ⊢ wkS |Δ| : Γ@ + +wkS :: Int -> Subst +wkS n = map (Var . Index) [n,n+1..] + +-- | Identity substitution @Γ ⊢ idS : Γ@. + +idS :: Subst +idS = wkS 0 + +-- | Composing substitution +-- @ +-- Γ₁ ⊢ τ : Γ₂ Γ₂ ⊢ σ : Γ₃ +-- ------------------------- +-- Γ₁ ⊢ compS τ σ : Γ₃ +-- @ + +compS :: Subst -> Subst -> Subst +compS = subst + +-- | Extending a substitution +-- @ +-- Γ ⊢ σ : Δ Δ ⊢ T Γ ⊢ t : Tσ +-- -------------------------------- +-- Γ ⊢ consS t σ : Δ.T +-- @ + +consS :: Term -> Subst -> Subst +consS = (:) + +-- | Lifting a substitution under a binder. +-- @ +-- Γ ⊢ σ : Δ Δ ⊢ T +-- -------------------- +-- Γ.Tσ ⊢ liftS σ : Δ.T +-- @ + +liftS :: Subst -> Subst +liftS s = consS (Var 0) $ weakS s + +-- | Weakening a substitution. +-- +-- @ +-- Γ ⊢ σ : Δ Γ ⊢ T +-- ------------------ +-- Γ.T ⊢ weakS σ : Δ +-- @ + +weakS :: Subst -> Subst +weakS = compS (wkS 1) + +-- | Looking up an entry in a substitution. + +lookupS :: Subst -> Index -> Term +lookupS s i = s !! dbIndex i + +-- | Substitution for various syntactic categories. + +class Substitute a where + subst :: Subst -> a -> a + +instance Substitute a => Substitute [a] where + subst s = map (subst s) + +instance Substitute a => Substitute (Dom a) where + subst s = fmap (subst s) + +instance Substitute a => Substitute (Arg a) where + subst s = fmap (subst s) + +instance Substitute a => Substitute (Elim' a) where + subst s = fmap (subst s) + +instance Substitute Term where + subst s = \case + Type l -> Type $ subst s l + Size -> Size + Nat a -> Nat $ subst s a + Zero a -> Zero $ subst s a + Suc a t -> Suc (subst s a) $ subst s t + Infty -> Infty + Pi u t -> Pi (subst s u) $ subst s t + Lam r t -> Lam r $ subst s t + Var i -> lookupS s i + Def f -> Def f + App t u -> App (subst s t) (subst s u) + +instance Substitute (Abs Term) where + subst s (Abs x t) = Abs x $ subst (liftS s) t + subst s (NoAbs x t) = NoAbs x $ subst s t + +raise :: Substitute a => Int -> a -> a +raise n = subst (wkS n) + +{- TODO!? + +-- | Application + +class Substitute a => Apply a where + applyE :: a -> Elims -> a + applyE t [] = t + applyE t es = substApply t idS es + + substApply :: a -> Subst -> Elims -> a + substApply t s es = subst s t `applyE` es + +instance Apply a => Apply [a] where + applyE ts es = map (`applyE` es) ts + substApply ts s es = map (\ t -> substApply t s es) ts + +instance Apply a => Apply (Dom a) where + applyE ts es = fmap (`applyE` es) ts + substApply ts s es = fmap (\ t -> substApply t s es) ts + +instance Apply a => Apply (Arg a) where + applyE ts es = fmap (`applyE` es) ts + substApply ts s es = fmap (\ t -> substApply t s es) ts + +instance Apply a => Apply (Elim' a) where + applyE ts es = fmap (`applyE` es) ts + substApply ts s es = fmap (\ t -> substApply t s es) ts + +instance Apply Term where + substApply t s es = case t of + -- Eliminations + Var i -> lookupS s i `applyE` es + Def f -> foldl App (Def f) es + App t u -> substApply t s $ Apply (subst s u) : es + -- Eliminateables + + -- Types & non-eliminateables + Type l + | null es -> Type $ subst s l + | otherwise -> __IMPOSSIBLE__ + Size + | null es -> Size + | otherwise -> __IMPOSSIBLE__ + Nat a + | null es -> Nat $ subst s a + | otherwise -> __IMPOSSIBLE__ + Zero + | null es -> Zero + | otherwise -> __IMPOSSIBLE__ + Suc t + | null es -> Suc $ subst s t + | otherwise -> __IMPOSSIBLE__ + Infty + | null es -> Infty + | otherwise -> __IMPOSSIBLE__ + Pi u t + | null es -> Pi (subst s u) $ subst s t + | otherwise -> __IMPOSSIBLE__ + +instance Apply (Abs Term) where + + substApply (Abs x t) s = \case + (Apply (Arg _ u) : es) -> substApply t (consS u s) es + _ -> __IMPOSSIBLE__ + + substApply (NoAbs x t) s = \case + (Apply _ : es) -> substApply t s es + _ -> __IMPOSSIBLE__ + + +-} + + + +-- | Construct the type of the functional for fix. +-- +-- @fixType t = .(i : Size) -> ((x : Nat i) -> T i x) -> (x : Nat (i + 1)) -> T (i + 1) x + +fixType :: Term -> Term +fixType t = + Pi (Dom Irrelevant Size) $ Abs "i" $ + Pi (Dom Relevant $ f $ Var 0) $ NoAbs "_" $ + f $ sSuc $ Var 0 + where + f a = Pi (Dom Relevant (Nat a)) $ Abs "x" $ + raise 2 t + `App` Apply (Arg ShapeIrr $ raise 1 a) + `App` Apply (Arg Relevant $ Var 0) diff --git a/src/TypeChecker.hs b/src/TypeChecker.hs new file mode 100644 --- /dev/null +++ b/src/TypeChecker.hs @@ -0,0 +1,662 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE LambdaCase #-} +{-# LANGUAGE TupleSections #-} +{-# LANGUAGE TemplateHaskell #-} +{-# LANGUAGE TypeSynonymInstances, FlexibleInstances, MultiParamTypeClasses #-} + +module TypeChecker where + +import Control.Applicative +import Control.Monad +import Control.Monad.Except +import Control.Monad.Identity +import Control.Monad.Reader +import Control.Monad.State + +import Data.Functor +import Data.Maybe +import Data.Map (Map) +import qualified Data.Map as Map +import qualified Data.Set as Set + +import Debug.Trace + +import qualified Sit.Abs as A +import Sit.Print +import Sit.ErrM + +import Abstract as A +import Internal +import Substitute +import Evaluation + +import Lens +import Impossible +#include "undefined.h" + +-- | Type errors are just strings. +type TypeError = String + +-- | Local context + +type Cxt = [ (Id, Dom VType) ] + +data TCEnv = TCEnv + { _envCxt :: Cxt -- ^ Typing context. + , _envEnv :: Env -- ^ Default environment. + } + +makeLens ''TCEnv + +-- | Global state + +data TCSt = TCSt + { _stTySigs :: Map Id VType + , _stDefs :: Map Id Val + } + +makeLens ''TCSt + +-- | The type checking monad +type Check = ReaderT TCEnv (StateT TCSt (Except TypeError)) + +-- * Type checker + +typeCheck :: [A.Decl] -> Either String () +typeCheck decls = runExcept (evalStateT (runReaderT (checkDecls decls) initEnv) initSt) + where + initEnv = TCEnv { _envCxt = [] , _envEnv = [] } + initSt = TCSt { _stTySigs = Map.empty , _stDefs = Map.empty } + +checkDecls :: [A.Decl] -> Check () +checkDecls = mapM_ checkDecl + +checkDecl :: A.Decl -> Check () +checkDecl = \case + A.Blank{} -> return () + A.Open{} -> return () + A.Sig x a -> checkSig x a + A.Def x e -> checkDef x e + +-- | Check a type signature. + +checkSig :: A.Ident -> A.Exp -> Check () +checkSig x0@(A.Ident x) a = traceCheck (A.Sig x0 a) $ do + + -- Check that x is not already defined + mt <- lookupTySig x + unless (isNothing mt) $ + throwError $ "Duplicate type signature for " ++ x + + -- Check type and add to signature + t <- checkType a + -- traceM $ "Adding " ++ show x ++ " of type " ++ show t + addTySig x =<< evaluate t + +-- | Check a definition. + +checkDef :: A.Ident -> A.Exp -> Check () +checkDef x0@(A.Ident x) e = traceCheck (A.Def x0 e) $ do + + -- Check that x has a signature + let noSig = throwError $ "Missing type signature for " ++ x + t <- maybe noSig return =<< lookupTySig x + + -- Check that x has not yet a definition + mv <- lookupDef x + unless (isNothing mv) $ + throwError $ "Duplicate definition of " ++ x + + -- Check definition and add to signature + v <- checkExp e t + -- traceM $ "Adding " ++ show x ++ " of value " ++ show v + addDef x =<< evaluate v + +-- | Check well-formedness of a type. + +checkType :: A.Exp -> Check Type +checkType e = fst <$> inferType e + +-- | Check that something is a type and infer its universe level. + +inferType :: A.Exp -> Check (Type, VLevel) +inferType e = do + let invalidType = throwError $ "Not a valid type expression: " ++ printTree e + case e of + + -- Size type (internal use only). + + -- Each universe is closed under size quantification. + -- Thus, we place Size in Set0. + + A.Size -> return (Size, vsConst 0) + + -- Universes (shape irrelevant) + + A.Set -> return (Type sZero, vsConst 1) + A.Set1 -> return (Type $ sSuc sZero, vsConst 2) + A.Set2 -> return (Type $ sSuc $ sSuc sZero, vsConst 3) + A.App A.Set l -> do + a <- resurrect ShapeIrr $ checkLevel l + v <- evaluate a + return (Type a, vsSuc v) + + -- Natural number type (shape irrelevant) + + A.App A.Nat s -> do + a <- resurrect ShapeIrr $ checkSize s + v <- evaluate a + return (Nat a, vsZero) + + -- Function types + + A.Arrow a b -> do + (u, l1) <- inferType a + (t, l2) <- inferType b + return (Pi (defaultDom u) (NoAbs "_" t) , maxSize l1 l2) + + A.Pi e a b -> do + let failure = throwError $ "Expected list of identifiers, found " ++ printTree e + xs <- maybe failure return $ parseIdUs e + inferPisType (map (, defaultDom a) xs) $ inferType b + + A.Forall bs c -> inferPisType (fromBind =<< bs) $ inferType c + where + fromBind :: A.Bind -> [(A.IdU, Dom A.Exp)] + fromBind = \case + A.BIrrel x -> return (A.Id x, Dom Irrelevant A.Size) + A.BRel x -> return (A.Id x, Dom ShapeIrr A.Size) + A.BAnn xs a -> map (\ x -> (A.Id x, defaultDom a)) xs + + -- Neutral types + + e | A.introduction e -> invalidType + + e -> do + (t,v) <- inferExp e + case v of + VType l -> return (t,l) + _ -> invalidType + +inferPisType :: [(A.IdU, Dom A.Exp)] -> Check (Type, VLevel) -> Check (Type, VLevel) +inferPisType = foldr (.) id . map (uncurry inferPiType) + +inferPiType :: A.IdU -> Dom A.Exp -> Check (Type, VLevel) -> Check (Type, VLevel) +inferPiType x dom cont = do + + -- Check the domain + (u, l1) <- inferType $ unDom dom + + -- Check the codomain in the extended context. + v <- evaluate u + addContext (x, v) $ do + (t, l2) <- cont + + -- Compute the universe level of the Pi-type. + let l0 = maxSize l1 l2 + + -- Check that the level does not mention the bound variable + -- If yes, return oo instead. + l <- case fromMaybe __IMPOSSIBLE__ $ sizeView l0 of + SVVar k' _ -> do + k <- length <$> asks _envCxt + return $ if k' >= k then VInfty else l0 + _ -> return l0 + + -- Construct the function type + return ( Pi (dom $> u) $ Abs (fromIdU x) t , l ) + +checkSize :: A.Exp -> Check Size +checkSize e = checkExp e VSize +-- checkSize = \case +-- A.Infty -> return Infty +-- A.LZero -> return $ sZero +-- A.App A.LSuc e -> sSuc <$> checkSize e +-- e@(A.Var x) -> checkExp e VSize +-- e -> throwError $ "Not a valid size expression: " ++ printTree e + +checkLevel :: A.Exp -> Check Level +checkLevel = \case + A.LZero -> return $ sZero + A.App A.LSuc e -> sSuc <$> checkLevel e + e@(A.Var x) -> checkExp e VSize + e -> throwError $ "Not a valid level expression: " ++ printTree e + +-- maxLevel :: A.Exp -> VLevel -> VLevel -> Check VLevel +-- maxLevel e l1 l2 = maybe failure return $ maxSize l1 l2 +-- where failure = throwError $ "Cannot assign a universe level to type " ++ printTree e + +checkExp :: A.Exp -> VType -> Check Term +checkExp e0 t = do + case e0 of + + -- Functions + + A.Lam [] e -> checkExp e t + A.Lam (x:xs) e -> do + case t of + VPi dom cl -> addContext (x, dom) $ do + t' <- applyClosure cl =<< lastVal + u <- checkExp (A.Lam xs e) t' + return $ Lam (_domInfo dom) $ Abs (fromIdU x) u + _ -> throwError $ "Lambda abstraction expects function type, but got " ++ show t + + e@(A.ELam ez x0 es) -> do + case t of + VPi (Dom r (VNat b)) cl -> do + let x = A.fromIdU x0 + unless (r == Relevant) $ throwError $ + "Extended lambda constructs relevant function: " ++ printTree e + -- Infer the type of the case expression + tt <- reifyType t + -- Make sure that b is a successor size + -- let failNotSuc = throwError $ "Splitting Nat is only possible at successor size, when checking " ++ printTree e + -- a <- maybe failNotSuc return $ sizePred b + let a = fromMaybe __IMPOSSIBLE__ $ sizePred b + ta <- reifySize a + tz <- checkExp ez =<< applyClosure cl (VZero a) + (ts0, tS0) <- + addContext (x, Dom Relevant $ VNat a) $ do + vts <- applyClosure cl =<< do VSuc a <$> lastVal + tS0 <- reifyType vts + (,tS0) <$> checkExp es vts + let ts = Lam Relevant $ Abs x ts0 + let tS = Pi (Dom Relevant $ Nat ta) $ Abs x tS0 + return $ Lam Relevant $ Abs "x" $ App (Var 0) $ raise 1 $ + Case tt tz tS ts + + _ -> throwError $ "Extended lambda is function from Nat _, but here it got type " ++ show t + + e -> do + (u, ti) <- inferExp e + coerce u ti t + -- e -> nyi $ "checking " ++ printTree e + +-- | Infers neutrals, natural numbers, types. + +inferExp :: A.Exp -> Check (Term, VType) +inferExp e0 = case (e0, appView e0) of + + (e,_) | mustBeType e -> do + (t, l) <- inferType e + return (t, VType l) + + (e, (A.Zero, es)) -> do + case es of + [ ea ] -> do + a <- resurrect Irrelevant $ checkSize ea + (zero a ,) . VNat . vsSuc <$> evaluate a + _ -> throwError $ "zero expects exactly 1 argument: " ++ printTree e + + (e, (A.Suc, es)) -> do + case es of + [ ea, en ] -> do + a <- resurrect Irrelevant $ checkSize ea + va <- evaluate a + n <- checkExp en $ VNat va + return (suc a n, VNat $ vsSuc va) + _ -> throwError $ "suc expects exactly 2 arguments: " ++ printTree e + + (e, (A.Fix, es)) -> do + case es of + (et : ef : en : []) -> do + -- Check the motive of elimination + tT <- checkExp et fixKindV + -- Check the functional + let tF = fixType tT + tf <- checkExp ef =<< evaluate tF + -- Check the argument + (tn, a) <- inferNat en + -- Compute the type of the elimination + vT <- evaluate tT + admissible vT + vn <- evaluate tn + ve <- applyArgs vT [ Arg ShapeIrr a , Arg Relevant vn ] + -- Return as postfix application + return (App tn $ Fix tT tF tf, ve) + + _ -> throwError $ "fix expects exactly 3 arguments: " ++ printTree e + + (A.Infty, _) -> return (Infty, VSize) + + (A.Plus e k, _) -> do + u <- checkSize e + return (sPlus u k, VSize) + + -- (A.Plus x k, _) -> do + -- (u, t) <- inferId x + -- subType t VSize + -- return (sPlus u k, t) + + (A.Var A.Under, _) -> throwError "Illegal expression: _" + (A.Var (A.Id x), _) -> inferId x + + (e0@(A.App f e), _) -> do + (tf, t) <- inferExp f + case t of + VPi (Dom r tdom) cl -> do + te <- resurrect r $ checkExp e tdom + v <- evaluate te + (App tf $ Apply $ Arg r te,) <$> applyClosure cl v + _ -> throwError $ "Function type expected in application " ++ printTree e0 + ++ " ; but found type" ++ show t + + + (A.Case{}, _) -> nyi "case" + + (e, _) -> nyi $ "inferring type of " ++ printTree e + +-- | Infer type of a variable + +inferId :: A.Ident -> Check (Term, VType) +inferId (A.Ident x) = do + (lookupCxt x <$> asks _envCxt) >>= \case + Just (i, Dom r t) + | r == Relevant -> return (Var $ Index i, t) + | otherwise -> throwError $ "Illegal reference to " ++ show r ++ " variable: " ++ printTree x + + Nothing -> do + (Map.lookup x <$> use stTySigs) >>= \case + Nothing -> throwError $ "Identifier not in scope: " ++ x + Just t -> return (Def x, t) + +inferNat :: A.Exp -> Check (Term, VSize) +inferNat e = do + (u,t) <- inferExp e + case t of + VNat a -> return (u, a) + _ -> throwError $ "Expected natural number, but found " ++ printTree e + +-- | Coercion / subtype checking. + +coerce :: Term -> VType -> VType -> Check Term +coerce u ti tc = do + subType ti tc + return u + +-- | Type checker auxiliary functions. + +traceCheck :: Print a => a -> b -> b +traceCheck a = trace $ "Checking " ++ printTree a + +nyi :: String -> Check a +nyi = throwError . ("Not yet implemented: " ++) + +-- | Signature auxiliary functions + +lookupTySig :: Id -> Check (Maybe VType) +lookupTySig x = Map.lookup x <$> use stTySigs + +lookupDef :: Id -> Check (Maybe Val) +lookupDef x = Map.lookup x <$> use stDefs + +addTySig :: Id -> VType -> Check () +addTySig x t = stTySigs %= Map.insert x t + +addDef :: Id -> Val -> Check () +addDef x v = stDefs %= Map.insert x v + +-- * Invoking evaluation + +instance MonadEval (Reader (Map Id Val)) where + getDef x = fromMaybe __IMPOSSIBLE__ . Map.lookup x <$> ask + +evaluate :: Term -> Check Val +evaluate t = do + sig <- use stDefs + delta <- asks _envEnv + return $ runReader (evalIn t delta) sig + +applyClosure :: VClos -> Val -> Check Val +applyClosure cl v = + runReader (applyClos cl v) <$> use stDefs + +applyElims :: Val -> VElims -> Check Val +applyElims v es = + runReader (applyEs v es) <$> use stDefs + +applyArgs :: Val -> [Arg Val] -> Check Val +applyArgs v = applyElims v . map Apply + +reifyType :: VType -> Check Type +reifyType t = do + n <- length <$> asks _envCxt + sig <- use stDefs + return $ runReader (runReaderT (readbackType t) n) sig + +reifySize :: VSize -> Check Size +reifySize t = do + n <- length <$> asks _envCxt + sig <- use stDefs + return $ runReader (runReaderT (readbackSize t) n) sig + +-- * Context manipulation + +-- | Looking up in the typing context + +lookupCxt :: Id -> Cxt -> Maybe (Int, Dom VType) +lookupCxt x cxt = loop 0 cxt + where + loop i = \case + [] -> Nothing + ((y,t) : cxt) + | x == y -> Just (i,t) + | otherwise -> loop (succ i) cxt + + +-- | Value of last variable added to context. + +lastVal :: Check Val +lastVal = head <$> asks _envEnv + +-- | Extending the typing context + +class AddContext a where + addContext :: a -> Check b -> Check b + +instance AddContext a => AddContext [a] where + addContext as = foldr (.) id $ map addContext as + +-- A.IdU instances + +instance AddContext (A.IdU, Type) where + addContext (x,t) = addContext (fromIdU x, t) + +instance AddContext (A.IdU, VType) where + addContext (x,t) = addContext (fromIdU x, t) + +instance AddContext (A.IdU, Dom VType) where + addContext (x,t) = addContext (fromIdU x, t) + +-- Id instances + +instance AddContext (Id, Type) where + addContext (x,t) cont = do + t <- evaluate t + addContext (x,t) cont + +instance AddContext (Id, VType) where + addContext (x,t) = addContext (x, defaultDom t) + +instance AddContext (Id, Dom VType) where + addContext (x,t) = local + $ over envCxt ((x,t):) + . over envEnv nextVar + where nextVar delta = vVar (unDom t) (length delta) : delta + +-- | Context: resurrecting irrelevant variables +resurrect :: Relevance -> Check a -> Check a +resurrect = \case + -- Relevant application: resurrect nothing. + Relevant -> id + -- Irrelevant application: resurrect everything. + Irrelevant -> local $ over envCxt $ map $ over _2 $ set domInfo Relevant + -- Shape irrelevant application: resurrect shape-irrelevant variables. + ShapeIrr -> local $ over envCxt $ map $ over _2 $ over domInfo $ resSI + where + resSI = \case + ShapeIrr -> Relevant + r -> r + +-- * Subtyping and type equality + +subType :: Val -> Val -> Check () +subType ti tc = do + let failure = throwError $ "Subtyping failed: type " ++ show ti + ++ " is not a subtype of " ++ show tc + case (ti, tc) of + (VNat a, VNat b) -> unless (leqSize a b) failure + (VType a, VType b) -> unless (leqSize a b) failure + (VPi dom1 cl1, VPi dom2 cl2) -> do + unless (_domInfo dom2 <= _domInfo dom1) failure + subType (unDom dom2) (unDom dom1) + addContext (absName $ closBody cl2, dom2) $ do + v <- lastVal + b1 <- applyClosure cl1 v + b2 <- applyClosure cl2 v + subType b1 b2 + _ -> equalType ti tc + +equalType :: Val -> Val -> Check () +equalType v v' = do + t <- reifyType v + t' <- reifyType v' + unless (t == t') $ + throwError $ "Inferred type " ++ show t ++ " is not equal to expected type " ++ show t' + +-- * Admissibility check for the type of @fix@. + +-- | A simple positivity check. +-- +-- For the type constructor T of fix we check that +-- @ +-- i : ..Size, x : Nat i |- T i x <= T oo x +-- @ +-- This does not introduce a new concept an is sound, but excludes +-- @ +-- min : forall .i -> Nat i -> Nat i -> Nat i +-- @ + +admissible :: Val -> Check () +admissible v = do + k <- length <$> asks _envCxt + addContext ("i", VSize) $ do + va <- lastVal + addContext ("x", VNat $ va) $ do + u <- lastVal + t1 <- applyArgs v [ Arg ShapeIrr va, Arg Relevant u] + t2 <- applyArgs v [ Arg ShapeIrr VInfty, Arg Relevant u] + subType t1 t2 + +-- | Semi-continuity check (to be completed) + +admissibleSemi :: Val -> Check () +admissibleSemi v = do + k <- length <$> asks _envCxt + addContext ("i", VSize) $ do + va <- lastVal + addContext ("x", VNat $ va) $ do + u <- lastVal + tv <- applyArgs v [ Arg ShapeIrr va, Arg Relevant u] + debug "testing upperSemi" k tv + ok <- upperSemi k tv + unless ok $ do + t <- reifyType tv + a <- reifySize va + throwError $ + "Type " ++ show t ++ " of fix needs to be upper semi-continuous in size " ++ show a + +debug :: String -> VGen -> VType -> Check () +debug txt k tv = do + a <- reifySize $ vsVar k + t <- reifyType tv + traceM $ txt ++ " " ++ show a ++ " " ++ show t + +-- | For a function type to be upper semi-continuous, +-- its codomain needs to be so, and +-- the domain needs to be lower semi-continous. + +upperSemi :: VGen -> VType -> Check Bool +upperSemi k t = do + debug "upperSemi" k t + case t of + VPi dom cl -> do + lowerSemi k $ unDom dom + addContext (absName $ closBody cl, dom) $ do + v <- lastVal + upperSemi k =<< applyClosure cl v + VType{} -> return True + VSize -> return True + VNat{} -> return True + t@(VUp (VType _) _) -> monotone k True t + t -> do + traceM $ "upperSemi " ++ show k ++ " " ++ show t + __IMPOSSIBLE__ + +-- | Base types and antitone types are lower semi-continuous. + +lowerSemi :: VGen -> VType -> Check Bool +lowerSemi k t = do + debug "lowerSemi" k t + case t of + t@(VPi dom cl) -> monotone k False t + VType{} -> return True + VSize -> return True + VNat{} -> return True + t@(VUp (VType _) _) -> monotone k False t + t -> do + traceM $ "lowerSemi " ++ show k ++ " " ++ show t + __IMPOSSIBLE__ + +-- antitone :: VGen -> VType -> Check Bool +-- antitone k t = do +-- traceM $ "\nantitone " ++ show k ++ " " ++ show t +-- return True + +monotone :: VGen -> Bool -> VType -> Check Bool +monotone k b t = do + debug (if b then "monotone" else "antitone") k t + case t of + VPi dom cl -> do + monotone k (not b) $ unDom dom + addContext (absName $ closBody cl, dom) $ do + u <- lastVal + monotone k b =<< applyClosure cl u + VType a -> monotoneSize k b a + VNat a -> monotoneSize k b a + VSize -> return True + -- VInfty -> return True + -- VZero _ -> return True + -- VSuc _ v -> monotone k b v + -- VLam cl -> addContext ("#", VSize) $ do + -- u <- lastVal + -- monotone k b =<< applyClosure cl u + -- VUp _ (VNe k' es) + -- | k == k' -> return b + -- | otherwise -> return True + VUp (VType _) _ -> return True + _ -> __IMPOSSIBLE__ + + -- traceM $ "\nmonotone " ++ show k ++ " " ++ show t + -- return True + +monotoneSize :: VGen -> Bool -> VSize -> Check Bool +monotoneSize k b t = do + debugSize (if b then "monotone" else "antitone") k t + case t of + VInfty -> return True + VZero _ -> return True + VSuc _ v -> monotoneSize k b v + VUp _ (VNe k' es) + | k == k' -> do + traceM $ "same var" + unless b $ throwError "admissibility check failed" + return b + | otherwise -> return True + _ -> __IMPOSSIBLE__ + +debugSize :: String -> VGen -> VType -> Check () +debugSize txt k v = do + a <- reifySize $ vsVar k + b <- reifySize v + traceM $ txt ++ " " ++ show a ++ " " ++ show b diff --git a/src/undefined.h b/src/undefined.h new file mode 100644 --- /dev/null +++ b/src/undefined.h @@ -0,0 +1,1 @@ +#define __IMPOSSIBLE__ (throwImpossible (Impossible __FILE__ __LINE__)) diff --git a/test/Base.agda b/test/Base.agda new file mode 100644 --- /dev/null +++ b/test/Base.agda @@ -0,0 +1,32 @@ +{-# OPTIONS --experimental-irrelevance #-} + +open import Agda.Primitive + public using (lzero; lsuc) + +open import Agda.Builtin.Size + public using (Size; ↑_) renaming (ω to oo) + +open import Agda.Builtin.Nat + public using (suc) renaming (Nat to ℕ) + +_+_ : Size → ℕ → Size +s + 0 = s +s + suc n = ↑ (s + n) + +data Nat : ..(i : Size) → Set where + zero : ∀ .i → Nat (↑ i) + suc : ∀ .i → Nat i → Nat (↑ i) + +caseof : ∀{a b} {A : Set a} (B : A → Set b) → (x : A) → ((x : A) → B x) → B x +caseof B x f = f x + +syntax caseof B x f = case x return B of f + +fix : ∀{ℓ} + (T : ..(i : Size) → Nat i → Set ℓ) + (f : ∀ .j → ((x : Nat j) → T j x) → (x : Nat (↑ j)) → T (↑ j) x) + .{i} + (x : Nat i) + → T i x +fix T f (zero j) = f j (fix T f) (zero j) +fix T f (suc j n) = f j (fix T f) (suc j n) diff --git a/test/Makefile b/test/Makefile new file mode 100644 --- /dev/null +++ b/test/Makefile @@ -0,0 +1,2 @@ +default : + make -C ../src diff --git a/test/Test.agda b/test/Test.agda new file mode 100644 --- /dev/null +++ b/test/Test.agda @@ -0,0 +1,175 @@ +--- Sample Sit file + +{-# OPTIONS --experimental-irrelevance #-} + +open import Base + +--; --- Leibniz-equality + +Eq : forall (A : Set) (a b : A) -> Set1 --; +Eq = \ A a b -> (P : A -> Set) -> (P a) -> P b + +--; --- Reflexivity + +refl : forall (A : Set) (a : A) -> Eq A a a --; +refl = \ A a P pa -> pa + +--; --- Symmetry + +sym : forall (A : Set) (a b : A) -> Eq A a b -> Eq A b a --; +sym = \ A a b eq P pb -> eq (\ x -> P x -> P a) (\ pa -> pa) pb + +--; --- Transitivity + +trans : forall (A : Set) (a b c : A) -> Eq A a b -> Eq A b c -> Eq A a c --; +trans = \ A a b c p q P pa -> q P (p P pa) + +--; --- Congruence + +cong : forall (A B : Set) (f : A -> B) (a a' : A) -> Eq A a a' -> Eq B (f a) (f a') --; +cong = \ A B f a a' eq P pfa -> eq (\ x -> P (f x)) pfa + +--; --- Addition + +plus : forall .i -> Nat i -> Nat oo -> Nat oo --; +plus = \ i x y -> + fix (\ i x -> Nat oo) + (\ _ f -> \ + { (zero _) -> y + ; (suc _ x) -> suc oo (f x) + }) + x + +--; --- Unit tests for plus + +inc : Nat oo -> Nat oo --; +inc = \ x -> suc oo x --; + +one : Nat oo --; +one = inc (zero oo) --; + +two : Nat oo --; +two = inc one --; + +three : Nat oo --; +three = inc two --; + +four : Nat oo --; +four = inc three --; + +five : Nat oo --; +five = inc four --; + +six : Nat oo --; +six = inc five --; + +plus_one_zero : Eq (Nat oo) (plus oo one (zero oo)) one --; +plus_one_zero = refl (Nat oo) one --; + +plus_one_one : Eq (Nat oo) (plus oo one one) two --; +plus_one_one = refl (Nat oo) two --; + +--; --- Reduction rules for plus + +plus_red_zero : forall .i (y : Nat oo) -> Eq (Nat oo) (plus (i + 1) (zero i) y) y --; +plus_red_zero = \ i y -> refl (Nat oo) y --; + +plus_red_suc : forall .i (x : Nat i) (y : Nat oo) -> Eq (Nat oo) (plus (i + 1) (suc i x) y) (suc oo (plus i x y)) --; +plus_red_suc = \ i x y -> refl (Nat oo) (suc oo (plus i x y)) --; + +--; --- Law: x + 0 = x + +plus_zero : forall .i (x : Nat i) -> Eq (Nat oo) (plus i x (zero oo)) x --; +plus_zero = \ i x -> + fix (\ i x -> Eq (Nat oo) (plus i x (zero oo)) x) + (\ j f -> \ + { (zero _) -> refl (Nat oo) (zero oo) + ; (suc _ y) -> cong (Nat oo) (Nat oo) inc (plus j y (zero oo)) y (f y) + }) + x + +--; --- Law: x + suc y = suc x + y + +plus_suc : forall .i (x : Nat i) (y : Nat oo) -> Eq (Nat oo) (plus i x (inc y)) (inc (plus i x y)) --; +plus_suc = \ i x y -> + fix (\ i x -> Eq (Nat oo) (plus i x (inc y)) (inc (plus i x y))) + (\ j f -> \ + { (zero _) -> refl (Nat oo) (inc y) + ; (suc _ x') -> cong (Nat oo) (Nat oo) inc (plus j x' (inc y)) (inc (plus j x' y)) (f x') + }) + x + +--; --- Another definition of addition + +plus' : forall .i -> Nat i -> Nat oo -> Nat oo --; +plus' = \ i x -> + fix (\ i x -> Nat oo -> Nat oo) + (\ _ f -> \ + { (zero _) -> \ y -> y + ; (suc _ x) -> \ y -> suc oo (f x y) + }) + x + +--; --- Predecessor + +pred : forall .i -> Nat i -> Nat i --; +pred = \ i n -> + fix (\ i _ -> Nat i) + (\ i _ -> \{ (zero _) -> zero i ; (suc _ y) -> y }) + n + +--; --- Subtraction + +sub : forall .j -> Nat j -> forall .i -> Nat i -> Nat i --; +sub = \ j y -> + fix (\ _ _ -> forall .i -> Nat i -> Nat i) + (\ _ f -> \ + { (zero _) -> \ i x -> x + ; (suc _ y) -> \ i x -> f y i (pred i x) + }) --- pred i (f y i x) }) + y + +--; --- Lemma: x - x == 0 + +sub_diag : forall .i (x : Nat i) -> Eq (Nat oo) (sub i x i x) (zero oo) --; +sub_diag = \ i x -> + fix (\ i x -> Eq (Nat oo) (sub i x i x) (zero oo)) + (\ _ f -> \ + { (zero _) -> refl (Nat oo) (zero oo) + ; (suc _ y) -> f y + }) + x + +--- Large eliminations + +--; --- Varying arity + +Fun : forall .i (n : Nat i) (A : Set) (B : Set) -> Set --; +Fun = \ i n A B -> + fix (\ _ _ -> Set) + (\ _ f -> \ + { (zero _) -> B + ; (suc _ x) -> A -> f x + }) + n + +--; --- Type of n-ary Sum function + +Sum : forall .i (n : Nat i) -> Set --; +Sum = \ i n -> Nat oo -> Fun i n (Nat oo) (Nat oo) + +--; --- n-ary summation function + +sum : forall .i (n : Nat i) -> Sum i n --; +sum = \ _ n -> + fix (\ i n -> Sum i n) + (\ _ f -> \ + { (zero _) -> \ acc -> acc + ; (suc _ x) -> \ acc -> \ k -> f x (plus oo k acc) + }) + n + +--; --- Testing sum + +sum123 : Eq (Nat oo) (sum oo three (zero oo) one two three) six --; +sum123 = refl (Nat oo) six