{-# LANGUAGE NoMonomorphismRestriction #-} {-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE DeriveTraversable #-} {-# LANGUAGE DeriveFoldable #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE OverloadedStrings #-} {-# LANGUAGE StandaloneDeriving #-} {-# LANGUAGE GeneralizedNewtypeDeriving #-} -- | This module contains the data types, operations and serialization functions -- for representing Fixpoint's implication (i.e. subtyping) and well-formedness -- constraints in Haskell. The actual constraint solving is done by the -- `fixpoint.native` which is written in Ocaml. module Language.Fixpoint.Types ( -- * Top level serialization Fixpoint (..) , toFixpoint , FInfo (..) -- * Rendering , showFix , traceFix , resultDoc -- * Symbols , Symbol(..) , anfPrefix, tempPrefix, vv, intKvar , symChars, isNonSymbol, nonSymbol , isNontrivialVV , symbolText, symbolString -- * Creating Symbols , dummySymbol , intSymbol , tempSymbol , qualifySymbol , suffixSymbol -- * Embedding to Fixpoint Types , Sort (..), FTycon, TCEmb , intFTyCon , boolFTyCon , realFTyCon , strFTyCon , propFTyCon , appFTyCon , fTyconSymbol , symbolFTycon , fApp , fObj -- * Expressions and Predicates , SymConst (..) , Constant (..) , Bop (..), Brel (..) , Expr (..), Pred (..) , eVar , eProp , pAnd, pOr, pIte , isTautoPred , symConstLits , zero -- * Generalizing Embedding with Typeclasses , Symbolic (..) , Expression (..) , Predicate (..) -- * Constraints and Solutions , SubC --(..) , WfC --(..) , sid , subC, lhsCs, rhsCs, wfC , Tag , FixResult (..) , FixSolution , addIds, sinfo , trueSubCKvar , removeLhsKvars -- * Environments , SEnv, SESearch(..) , emptySEnv, toListSEnv, fromListSEnv , mapSEnv, mapSEnvWithKey , insertSEnv, deleteSEnv, memberSEnv, lookupSEnv , intersectWithSEnv , filterSEnv , lookupSEnvWithDistance , FEnv, insertFEnv , IBindEnv, BindId , emptyIBindEnv, insertsIBindEnv, deleteIBindEnv , BindEnv , rawBindEnv, insertBindEnv, emptyBindEnv, mapBindEnv -- * Refinements , Refa (..), SortedReft (..), Reft(..), Reftable(..) -- * Constructing Refinements , trueSortedReft -- trivial reft , trueRefa -- trivial reft , trueReft -- trivial reft , exprReft -- singleton: v == e , notExprReft -- singleton: v /= e , uexprReft -- singleton: v ~~ e , symbolReft -- singleton: v == x , propReft -- singleton: Prop(v) <=> p , predReft -- any pred : p , isFunctionSortedReft , isNonTrivialSortedReft , isTautoReft , isSingletonReft , isEVar , isFalse , flattenRefas, squishRefas , shiftVV -- * Substitutions , Subst , Subable (..) , mkSubst -- , emptySubst -- , catSubst , substExcept , substfExcept , subst1Except , sortSubst -- * Visitors , reftKVars -- * Functions on @Result@ , colorResult -- * Cut KVars , Kuts (..) , ksEmpty , ksUnion -- * Qualifiers , Qualifier (..) -- * FQ Definitions , Def (..) -- * Located Values , Located (..) , LocSymbol, LocText , dummyLoc, dummyPos, dummyName, isDummy ) where import Debug.Trace (trace) import GHC.Generics (Generic) import Data.Typeable (Typeable) import Data.Generics (Data) import Data.Monoid hiding ((<>)) import Data.Functor import Data.Char (ord, chr, isAlpha, isUpper, toLower) import Data.List (nub, foldl', sort, stripPrefix, intersect) import Data.Hashable import qualified Data.Foldable as F import Data.Traversable import Data.Interned import Data.String import Data.Text (Text) import qualified Data.Text as T import Data.Maybe (fromMaybe) import Text.Printf (printf) import Control.DeepSeq import Control.Arrow ((***)) import Control.Exception (assert) import Language.Fixpoint.Misc import Text.PrettyPrint.HughesPJ import Text.Parsec.Pos import qualified Data.HashMap.Strict as M import qualified Data.HashSet as S import Data.Array hiding (indices) import Language.Fixpoint.Names class Fixpoint a where toFix :: a -> Doc simplify :: a -> a simplify = id ------------------------------------------------------------------------ -- | Entities in Query File -------------------------------------------- ------------------------------------------------------------------------ data Def a = Srt Sort | Axm Pred | Cst (SubC a) | Wfc (WfC a) | Con Symbol Sort | Qul Qualifier | Kut Symbol | IBind Int Symbol SortedReft deriving (Generic) -- Sol of solbind -- Dep of FixConstraint.dep ------------------------------------------------------------------------ showFix :: (Fixpoint a) => a -> String showFix = render . toFix traceFix :: (Fixpoint a) => String -> a -> a traceFix s x = trace ("\nTrace: [" ++ s ++ "] : " ++ showFix x) $ x type TCEmb a = M.HashMap a FTycon -- instance (Eq a, Hashable a) => Monoid (TCEmb a) where -- mappend m1 m2 = M.fromList (M.toList m1 ++ M.toList m2) -- mempty = M.empty exprSymbols :: Expr -> [Symbol] exprSymbols = go where go (EVar x) = [x] -- go (EDat x _) = [x] go (ELit x _) = [val x] go (EApp f es) = val f : concatMap go es go (EBin _ e1 e2) = go e1 ++ go e2 go (EIte p e1 e2) = predSymbols p ++ go e1 ++ go e2 go (ECst e _) = go e go _ = [] predSymbols :: Pred -> [Symbol] predSymbols = go where go (PAnd ps) = concatMap go ps go (POr ps) = concatMap go ps go (PNot p) = go p go (PIff p1 p2) = go p1 ++ go p2 go (PImp p1 p2) = go p1 ++ go p2 go (PBexp e) = exprSymbols e go (PAtom _ e1 e2) = exprSymbols e1 ++ exprSymbols e2 go (PAll xts p) = (fst <$> xts) ++ go p go _ = [] reftKVars :: Reft -> [Symbol] reftKVars (Reft (_,ras)) = [k | (RKvar k _) <- ras] --------------------------------------------------------------- ---------- (Kut) Sets of Kvars -------------------------------- --------------------------------------------------------------- newtype Kuts = KS (S.HashSet Symbol) instance NFData Kuts where rnf (KS _) = () -- rnf s instance Fixpoint Kuts where toFix (KS s) = vcat $ ((text "cut " <>) . toFix) <$> S.toList s ksEmpty = KS S.empty ksUnion kvs (KS s') = KS (S.union (S.fromList kvs) s') --------------------------------------------------------------- ---------- Converting Constraints to Fixpoint Input ----------- --------------------------------------------------------------- instance (Eq a, Hashable a, Fixpoint a) => Fixpoint (S.HashSet a) where toFix xs = brackets $ sep $ punctuate (text ";") (toFix <$> S.toList xs) simplify = S.fromList . map simplify . S.toList instance Fixpoint a => Fixpoint (Maybe a) where toFix = maybe (text "Nothing") ((text "Just" <+>) . toFix) simplify = fmap simplify instance Fixpoint a => Fixpoint [a] where toFix xs = brackets $ sep $ punctuate (text ";") (fmap toFix xs) simplify = map simplify instance (Fixpoint a, Fixpoint b) => Fixpoint (a,b) where toFix (x,y) = (toFix x) <+> text ":" <+> (toFix y) simplify (x,y) = (simplify x, simplify y) toFix_gs (SE e) = vcat $ map (toFix_constant . mapSnd sr_sort) $ hashMapToAscList e toFix_constant (c, so) = text "constant" <+> toFix c <+> text ":" <+> toFix so ---------------------------------------------------------------------- ------------------------ Type Constructors --------------------------- ---------------------------------------------------------------------- newtype FTycon = TC LocSymbol deriving (Eq, Ord, Show, Data, Typeable, Generic) intFTyCon = TC $ dummyLoc "int" boolFTyCon = TC $ dummyLoc "bool" realFTyCon = TC $ dummyLoc "real" strFTyCon = TC $ dummyLoc strConName propFTyCon = TC $ dummyLoc propConName appFTyCon = TC $ dummyLoc "FAppTy" isListTC (TC (Loc _ c)) = c == listConName isTupTC (TC (Loc _ c)) = c == tupConName isFAppTyTC = (== appFTyCon) fTyconSymbol (TC s) = s symbolFTycon :: LocSymbol -> FTycon symbolFTycon c | val c == listConName = TC $ fmap (const listConName) c | otherwise = TC c -- stringSort :: String -> Sort -- stringSort s = FApp (stringFTycon s) [] -- -- ALTERNATIVEL = FObj . stringSymbol fApp :: Either FTycon Sort -> [Sort] -> Sort fApp (Left c) ts | c == intFTyCon = FInt | c == realFTyCon = FReal | otherwise = fAppSorts (fTyconSort c) ts fApp (Right t) ts = fAppSorts t ts fAppSorts t ts = foldl' (\t1 t2 -> FApp appFTyCon [t1, t2]) t ts fTyconSort :: FTycon -> Sort fTyconSort = (`FApp` []) fObj :: LocSymbol -> Sort fObj = fTyconSort . TC ---------------------------------------------------------------------- ------------------------------- Sorts -------------------------------- ---------------------------------------------------------------------- data Sort = FInt | FReal | FNum -- ^ numeric kind for Num tyvars | FObj Symbol -- ^ uninterpreted type | FVar !Int -- ^ fixpoint type variable | FFunc !Int ![Sort] -- ^ type-var arity, in-ts ++ [out-t] | FApp FTycon [Sort] -- ^ constructed type deriving (Eq, Ord, Show, Data, Typeable, Generic) instance Hashable Sort newtype Sub = Sub [(Int, Sort)] instance Fixpoint Sort where toFix = toFix_sort toFix_sort (FVar i) = text "@" <> parens (toFix i) toFix_sort FInt = text "int" toFix_sort FReal = text "real" toFix_sort (FObj x) = toFix x toFix_sort FNum = text "num" toFix_sort (FFunc n ts) = text "func" <> parens ((toFix n) <> (text ", ") <> (toFix ts)) toFix_sort (FApp c [t]) | isListTC c = brackets $ toFix_sort t toFix_sort (FApp c [FApp c' [],t]) | isFAppTyTC c && isListTC c' = brackets $ toFix_sort t toFix_sort (FApp c ts) | otherwise = toFix c <+> intersperse space (fp <$> ts) where fp s@(FApp _ (_:_)) = parens $ toFix_sort s fp s = toFix_sort s instance Fixpoint FTycon where toFix (TC s) = toFix s ------------------------------------------------------------------------ sortSubst :: (M.HashMap Symbol Sort) -> Sort -> Sort ------------------------------------------------------------------------ sortSubst θ t@(FObj x) = fromMaybe t (M.lookup x θ) sortSubst θ (FFunc n ts) = FFunc n (sortSubst θ <$> ts) sortSubst θ (FApp c ts) = FApp c (sortSubst θ <$> ts) sortSubst _ t = t instance Show Subst where show = showFix instance Fixpoint Subst where toFix (Su m) = case {- hashMapToAscList -} m of [] -> empty xys -> hcat $ map (\(x,y) -> brackets $ (toFix x) <> text ":=" <> (toFix y)) xys --------------------------------------------------------------- ------------------------- Expressions ------------------------- --------------------------------------------------------------- -- | Uninterpreted constants that are embedded as "constant symbol : Str" data SymConst = SL !Text deriving (Eq, Ord, Show, Data, Typeable, Generic) data Constant = I !Integer | R !Double | L !Text !Sort deriving (Eq, Ord, Show, Data, Typeable, Generic) data Brel = Eq | Ne | Gt | Ge | Lt | Le | Ueq | Une deriving (Eq, Ord, Show, Data, Typeable, Generic) data Bop = Plus | Minus | Times | Div | Mod deriving (Eq, Ord, Show, Data, Typeable, Generic) -- NOTE: For "Mod" 2nd expr should be a constant or a var *) data Expr = ESym !SymConst | ECon !Constant | EVar !Symbol | ELit !LocSymbol !Sort | EApp !LocSymbol ![Expr] | EBin !Bop !Expr !Expr | EIte !Pred !Expr !Expr | ECst !Expr !Sort | EBot deriving (Eq, Ord, Show, Data, Typeable, Generic) instance Fixpoint Integer where toFix = integer instance Fixpoint Double where toFix = double instance Fixpoint Constant where toFix (I i) = toFix i toFix (R i) = toFix i toFix (L s t) = parens $ text "lit" <+> toFix s <+> toFix t instance Fixpoint SymConst where toFix = toFix . encodeSymConst instance Fixpoint Symbol where toFix = text . encode . T.unpack . symbolText instance Fixpoint Text where toFix = text . T.unpack instance Fixpoint Brel where toFix Eq = text "=" toFix Ne = text "!=" toFix Ueq = text "~~" toFix Une = text "!~" toFix Gt = text ">" toFix Ge = text ">=" toFix Lt = text "<" toFix Le = text "<=" instance Fixpoint Bop where toFix Plus = text "+" toFix Minus = text "-" toFix Times = text "*" toFix Div = text "/" toFix Mod = text "mod" instance Fixpoint Expr where toFix (ESym c) = toFix $ encodeSymConst c toFix (ECon c) = toFix c toFix (EVar s) = toFix s toFix (ELit s _) = toFix s toFix (EApp f es) = (toFix f) <> (parens $ toFix es) toFix (EBin o e1 e2) = parens $ toFix e1 <+> toFix o <+> toFix e2 toFix (EIte p e1 e2) = parens $ toFix p <+> text "?" <+> toFix e1 <+> text ":" <+> toFix e2 toFix (ECst e so) = parens $ toFix e <+> text " : " <+> toFix so toFix (EBot) = text "_|_" ---------------------------------------------------------- --------------------- Predicates ------------------------- ---------------------------------------------------------- data Pred = PTrue | PFalse | PAnd ![Pred] | POr ![Pred] | PNot !Pred | PImp !Pred !Pred | PIff !Pred !Pred | PBexp !Expr | PAtom !Brel !Expr !Expr | PAll ![(Symbol, Sort)] !Pred | PTop deriving (Eq, Ord, Show, Data, Typeable, Generic) instance Fixpoint Pred where toFix PTop = text "???" toFix PTrue = text "true" toFix PFalse = text "false" toFix (PBexp e) = parens $ text "?" <+> toFix e toFix (PNot p) = parens $ text "~" <+> parens (toFix p) toFix (PImp p1 p2) = parens $ (toFix p1) <+> text "=>" <+> (toFix p2) toFix (PIff p1 p2) = parens $ (toFix p1) <+> text "<=>" <+> (toFix p2) toFix (PAnd ps) = text "&&" <+> toFix ps toFix (POr ps) = text "||" <+> toFix ps toFix (PAtom r e1 e2) = parens $ toFix e1 <+> toFix r <+> toFix e2 toFix (PAll xts p) = text "forall" <+> (toFix xts) <+> text "." <+> (toFix p) simplify (PAnd []) = PTrue simplify (POr []) = PFalse simplify (PAnd [p]) = simplify p simplify (POr [p]) = simplify p simplify (PAnd ps) | any isContraPred ps = PFalse | otherwise = PAnd $ filter (not . isTautoPred) $ map simplify ps simplify (POr ps) | any isTautoPred ps = PTrue | otherwise = POr $ filter (not . isContraPred) $ map simplify ps simplify p | isContraPred p = PFalse | isTautoPred p = PTrue | otherwise = p zero = ECon (I 0) one = ECon (I 1) isContraPred z = eqC z || (z `elem` contras) where contras = [PFalse] eqC (PAtom Eq (ECon x) (ECon y)) = x /= y eqC (PAtom Ueq (ECon x) (ECon y)) = x /= y eqC (PAtom Ne x y) = x == y eqC (PAtom Une x y) = x == y eqC _ = False isTautoPred z = eqT z || (z `elem` tautos) where tautos = [PTop, PTrue] eqT (PAtom Le x y) = x == y eqT (PAtom Ge x y) = x == y eqT (PAtom Eq x y) = x == y eqT (PAtom Ueq x y) = x == y eqT (PAtom Ne (ECon x) (ECon y)) = x /= y eqT (PAtom Une (ECon x) (ECon y)) = x /= y eqT _ = False isTautoReft (Reft (_, ras)) = all isTautoRa ras isTautoRa (RConc p) = isTautoPred p isTautoRa _ = False isEVar (EVar _) = True isEVar _ = False isEq r = r == Eq || r == Ueq isSingletonReft (Reft (v, [RConc (PAtom r e1 e2)])) | e1 == EVar v && isEq r = Just e2 | e2 == EVar v && isEq r = Just e1 isSingletonReft _ = Nothing pAnd = simplify . PAnd pOr = simplify . POr pIte p1 p2 p3 = pAnd [p1 `PImp` p2, (PNot p1) `PImp` p3] mkProp = PBexp . EApp (dummyLoc propConName) . (: []) ppr_reft (Reft (v, ras)) d | all isTautoRa ras = d | otherwise = braces (toFix v <+> colon <+> d <+> text "|" <+> ppRas ras) ppr_reft_pred (Reft (_, ras)) | all isTautoRa ras = text "true" | otherwise = ppRas ras ppRas = cat . punctuate comma . map toFix . flattenRefas ------------------------------------------------------------------------ -- | Generalizing Symbol, Expression, Predicate into Classes ----------- ------------------------------------------------------------------------ -- | Values that can be viewed as Constants -- | Values that can be viewed as Expressions class Expression a where expr :: a -> Expr -- | Values that can be viewed as Predicates class Predicate a where prop :: a -> Pred instance Expression Expr where expr = id -- | The symbol may be an encoding of a SymConst. instance Expression Symbol where expr s = maybe (eVar s) ESym (decodeSymConst s) -- expr = eVar instance Expression Text where expr = ESym . SL instance Expression Integer where expr = ECon . I instance Expression Int where expr = expr . toInteger instance Predicate Symbol where prop = eProp instance Predicate Pred where prop = id instance Predicate Bool where prop True = PTrue prop False = PFalse eVar :: Symbolic a => a -> Expr eVar = EVar . symbol eProp :: Symbolic a => a -> Pred eProp = mkProp . eVar relReft :: (Expression a) => Brel -> a -> Reft relReft r e = Reft (vv_, [RConc $ PAtom r (eVar vv_) (expr e)]) exprReft, notExprReft, uexprReft :: (Expression a) => a -> Reft exprReft = relReft Eq notExprReft = relReft Ne uexprReft = relReft Ueq propReft :: (Predicate a) => a -> Reft propReft p = Reft (vv_, [RConc $ PIff (eProp vv_) (prop p)]) predReft :: (Predicate a) => a -> Reft predReft p = Reft (vv_, [RConc $ prop p]) --------------------------------------------------------------- ----------------- Refinements --------------------------------- --------------------------------------------------------------- data Refa = RConc !Pred | RKvar !Symbol !Subst deriving (Eq, Ord, Show, Data, Typeable, Generic) newtype Reft = Reft (Symbol, [Refa]) deriving (Eq, Ord, Data, Typeable, Generic) instance Show Reft where show (Reft x) = render $ toFix x data SortedReft = RR { sr_sort :: !Sort, sr_reft :: !Reft } deriving (Eq, Show, Data, Typeable, Generic) isNonTrivialSortedReft (RR _ (Reft (_, ras))) = not $ null ras isFunctionSortedReft (RR (FFunc _ _) _) = True isFunctionSortedReft _ = False sortedReftValueVariable (RR _ (Reft (v,_))) = v --------------------------------------------------------------- ----------------- Environments ------------------------------- --------------------------------------------------------------- toListSEnv :: SEnv a -> [(Symbol, a)] toListSEnv (SE env) = M.toList env fromListSEnv :: [(Symbol, a)] -> SEnv a fromListSEnv = SE . M.fromList mapSEnv f (SE env) = SE (fmap f env) mapSEnvWithKey f = fromListSEnv . fmap f . toListSEnv deleteSEnv x (SE env) = SE (M.delete x env) insertSEnv x y (SE env) = SE (M.insert x y env) lookupSEnv x (SE env) = M.lookup x env emptySEnv = SE M.empty memberSEnv x (SE env) = M.member x env intersectWithSEnv f (SE m1) (SE m2) = SE (M.intersectionWith f m1 m2) filterSEnv f (SE m) = SE (M.filter f m) lookupSEnvWithDistance x (SE env) = case M.lookup x env of Just x -> Found x Nothing -> Alts $ symbol . T.pack <$> alts where alts = takeMin $ (zip (editDistance x' <$> ss) ss) ss = T.unpack . symbolText <$> fst <$> M.toList env x' = T.unpack $ symbolText x takeMin = \xs -> [x | (d, x) <- xs, d == getMin xs] getMin = minimum . (fst <$>) data SESearch a = Found a | Alts [Symbol] -- | Functions for Indexed Bind Environment emptyIBindEnv :: IBindEnv emptyIBindEnv = FB (S.empty) deleteIBindEnv :: BindId -> IBindEnv -> IBindEnv deleteIBindEnv i (FB s) = FB (S.delete i s) insertsIBindEnv :: [BindId] -> IBindEnv -> IBindEnv insertsIBindEnv is (FB s) = FB (foldr S.insert s is) -- | Functions for Global Binder Environment insertBindEnv :: Symbol -> SortedReft -> BindEnv -> (BindId, BindEnv) insertBindEnv x r (BE n m) = (n, BE (n + 1) (M.insert n (x, r) m)) emptyBindEnv :: BindEnv emptyBindEnv = BE 0 M.empty rawBindEnv :: [(BindId, Symbol, SortedReft)] -> BindEnv rawBindEnv bs = BE (1 + nbs) be' where nbs = length bs be = M.fromList [(n, (x, r)) | (n, x, r) <- bs] be' = assert (M.size be == nbs) be mapBindEnv :: ((Symbol, SortedReft) -> (Symbol, SortedReft)) -> BindEnv -> BindEnv mapBindEnv f (BE n m) = (BE n $ M.map f m) instance Functor SEnv where fmap f (SE m) = SE $ fmap f m instance Fixpoint Refa where toFix (RConc p) = toFix p toFix (RKvar k su) = toFix k <> toFix su -- toFix (RPvar p) = toFix p instance Fixpoint Reft where toFix = ppr_reft_pred instance Fixpoint SortedReft where toFix (RR so (Reft (v, ras))) = braces $ (toFix v) <+> (text ":") <+> (toFix so) <+> (text "|") <+> toFix ras instance Fixpoint FEnv where toFix (SE m) = toFix (hashMapToAscList m) instance Fixpoint BindEnv where toFix (BE _ m) = vcat $ map toFix_bind $ hashMapToAscList m toFix_bind (i, (x, r)) = text "bind" <+> toFix i <+> toFix x <+> text ":" <+> toFix r insertFEnv = insertSEnv . lower where lower s = case unconsSym s of Nothing -> s Just (c,s') -> consSym (toLower c) s' instance (Fixpoint a) => Fixpoint (SEnv a) where toFix (SE e) = vcat $ map pprxt $ hashMapToAscList e where pprxt (x, t) = toFix x <+> colon <> colon <+> toFix t instance Fixpoint (SEnv a) => Show (SEnv a) where show = render . toFix ----------------------------------------------------------------------------- ------------------- Constraints --------------------------------------------- ----------------------------------------------------------------------------- {-@ type Tag = { v : [Int] | len(v) = 1 } @-} type Tag = [Int] type BindId = Int type FEnv = SEnv SortedReft newtype IBindEnv = FB (S.HashSet BindId) deriving (Data, Typeable) newtype SEnv a = SE { se_binds :: M.HashMap Symbol a } deriving (Eq, Data, Typeable, Generic, F.Foldable, Traversable) data BindEnv = BE { be_size :: Int , be_binds :: M.HashMap BindId (Symbol, SortedReft) } data SubC a = SubC { senv :: !IBindEnv , sgrd :: !Pred , slhs :: !SortedReft , srhs :: !SortedReft , sid :: !(Maybe Integer) , stag :: !Tag , sinfo :: !a } deriving (Generic) data WfC a = WfC { wenv :: !IBindEnv , wrft :: !SortedReft , wid :: !(Maybe Integer) , winfo :: !a } deriving (Generic) data FixResult a = Crash [a] String | Safe | Unsafe ![a] | UnknownError !String deriving (Show, Generic) type FixSolution = M.HashMap Symbol Pred instance Eq a => Eq (FixResult a) where Crash xs _ == Crash ys _ = xs == ys Unsafe xs == Unsafe ys = xs == ys Safe == Safe = True _ == _ = False instance Monoid (FixResult a) where mempty = Safe mappend Safe x = x mappend x Safe = x mappend _ c@(Crash _ _) = c mappend c@(Crash _ _) _ = c mappend (Unsafe xs) (Unsafe ys) = Unsafe (xs ++ ys) mappend u@(UnknownError _) _ = u mappend _ u@(UnknownError _) = u instance Functor FixResult where fmap f (Crash xs msg) = Crash (f <$> xs) msg fmap f (Unsafe xs) = Unsafe (f <$> xs) fmap _ Safe = Safe fmap _ (UnknownError d) = UnknownError d instance (Ord a, Fixpoint a) => Fixpoint (FixResult (SubC a)) where toFix Safe = text "Safe" toFix (UnknownError d) = text $ "Unknown Error: " ++ d toFix (Crash xs msg) = vcat $ [ text "Crash!" ] ++ ppr_sinfos "CRASH: " xs ++ [parens (text msg)] toFix (Unsafe xs) = vcat $ text "Unsafe:" : ppr_sinfos "WARNING: " xs ppr_sinfos :: (Ord a, Fixpoint a) => String -> [SubC a] -> [Doc] ppr_sinfos msg = map ((text msg <>) . toFix) . sort . fmap sinfo resultDoc :: (Ord a, Fixpoint a) => FixResult a -> Doc resultDoc Safe = text "Safe" resultDoc (UnknownError d) = text $ "Unknown Error: " ++ d resultDoc (Crash xs msg) = vcat $ (text ("Crash!: " ++ msg)) : (((text "CRASH:" <+>) . toFix) <$> xs) resultDoc (Unsafe xs) = vcat $ (text "Unsafe:") : (((text "WARNING:" <+>) . toFix) <$> xs) colorResult (Safe) = Happy colorResult (Unsafe _) = Angry colorResult (_) = Sad instance Show (SubC a) where show = showFix instance Fixpoint (IBindEnv) where toFix (FB ids) = text "env" <+> toFix ids instance Fixpoint (SubC a) where toFix c = hang (text "\n\nconstraint:") 2 bd where bd = -- text "env" <+> toFix (senv c) toFix (senv c) $+$ text "grd" <+> toFix (sgrd c) $+$ text "lhs" <+> toFix (slhs c) $+$ text "rhs" <+> toFix (srhs c) $+$ (pprId (sid c) <+> pprTag (stag c)) instance Fixpoint (WfC a) where toFix w = hang (text "\n\nwf:") 2 bd where bd = -- text "env" <+> toFix (wenv w) toFix (wenv w) $+$ text "reft" <+> toFix (wrft w) $+$ pprId (wid w) pprId (Just i) = text "id" <+> tshow i pprId _ = text "" pprTag [] = text "" pprTag is = text "tag" <+> toFix is instance Fixpoint Int where toFix = tshow ------------------------------------------------------- ------------------- Substitutions --------------------- ------------------------------------------------------- class Subable a where syms :: a -> [Symbol] substa :: (Symbol -> Symbol) -> a -> a -- substa f = substf (EVar . f) substf :: (Symbol -> Expr) -> a -> a subst :: Subst -> a -> a subst1 :: a -> (Symbol, Expr) -> a -- subst1 y (x, e) = subst (Su $ M.singleton x e) y subst1 y (x, e) = subst (Su [(x,e)]) y subst1Except :: (Subable a) => [Symbol] -> a -> (Symbol, Expr) -> a subst1Except xs z su@(x, _) | x `elem` xs = z | otherwise = subst1 z su substfExcept :: (Symbol -> Expr) -> [Symbol] -> (Symbol -> Expr) substfExcept f xs y = if y `elem` xs then EVar y else f y substExcept :: Subst -> [Symbol] -> Subst -- substExcept (Su m) xs = Su (foldr M.delete m xs) substExcept (Su xes) xs = Su $ filter (not . (`elem` xs) . fst) xes instance Subable Symbol where substa f x = f x substf f x = subSymbol (Just (f x)) x subst su x = subSymbol (Just $ appSubst su x) x -- subSymbol (M.lookup x s) x syms x = [x] subSymbol (Just (EVar y)) _ = y subSymbol Nothing x = x subSymbol a b = errorstar (printf "Cannot substitute symbol %s with expression %s" (showFix b) (showFix a)) instance Subable Expr where syms = exprSymbols substa f = substf (EVar . f) substf f (EApp s es) = EApp (substf f s) $ map (substf f) es substf f (EBin op e1 e2) = EBin op (substf f e1) (substf f e2) substf f (EIte p e1 e2) = EIte (substf f p) (substf f e1) (substf f e2) substf f (ECst e so) = ECst (substf f e) so substf f e@(EVar x) = f x substf _ e = e subst su (EApp f es) = EApp (subst su f) $ map (subst su) es subst su (EBin op e1 e2) = EBin op (subst su e1) (subst su e2) subst su (EIte p e1 e2) = EIte (subst su p) (subst su e1) (subst su e2) subst su (ECst e so) = ECst (subst su e) so subst su (EVar x) = appSubst su x subst _ e = e instance Subable Pred where syms = predSymbols substa f = substf (EVar . f) substf f (PAnd ps) = PAnd $ map (substf f) ps substf f (POr ps) = POr $ map (substf f) ps substf f (PNot p) = PNot $ substf f p substf f (PImp p1 p2) = PImp (substf f p1) (substf f p2) substf f (PIff p1 p2) = PIff (substf f p1) (substf f p2) substf f (PBexp e) = PBexp $ substf f e substf f (PAtom r e1 e2) = PAtom r (substf f e1) (substf f e2) substf _ (PAll _ _) = errorstar $ "substf: FORALL" substf _ p = p subst su (PAnd ps) = PAnd $ map (subst su) ps subst su (POr ps) = POr $ map (subst su) ps subst su (PNot p) = PNot $ subst su p subst su (PImp p1 p2) = PImp (subst su p1) (subst su p2) subst su (PIff p1 p2) = PIff (subst su p1) (subst su p2) subst su (PBexp e) = PBexp $ subst su e subst su (PAtom r e1 e2) = PAtom r (subst su e1) (subst su e2) subst _ (PAll _ _) = errorstar $ "subst: FORALL" subst _ p = p instance Subable Refa where syms (RConc p) = syms p syms (RKvar k (Su su')) = k : concatMap syms ({- M.elems -} su') subst su (RConc p) = RConc $ subst su p subst su (RKvar k su') = RKvar k $ su' `catSubst` su -- subst _ (RPvar p) = RPvar p substa f = substf (EVar . f) substf f (RConc p) = RConc (substf f p) substf _ ra@(RKvar _ _) = ra instance (Subable a, Subable b) => Subable (a,b) where syms (x, y) = syms x ++ syms y subst su (x,y) = (subst su x, subst su y) substf f (x,y) = (substf f x, substf f y) substa f (x,y) = (substa f x, substa f y) instance Subable a => Subable [a] where syms = concatMap syms subst = map . subst substf = map . substf substa = map . substa instance Subable a => Subable (M.HashMap k a) where syms = syms . M.elems subst = M.map . subst substf = M.map . substf substa = M.map . substa instance Subable Reft where syms (Reft (v, ras)) = v : syms ras substa f (Reft (v, ras)) = Reft (f v, substa f ras) subst su (Reft (v, ras)) = Reft (v, subst (substExcept su [v]) ras) substf f (Reft (v, ras)) = Reft (v, substf (substfExcept f [v]) ras) subst1 (Reft (v, ras)) su = Reft (v, subst1Except [v] ras su) instance Subable SortedReft where syms = syms . sr_reft subst su (RR so r) = RR so $ subst su r substf f (RR so r) = RR so $ substf f r substa f (RR so r) = RR so $ substa f r newtype Subst = Su [(Symbol, Expr)] deriving (Eq, Ord, Data, Typeable, Generic) appSubst (Su s) x = fromMaybe (EVar x) (lookup x s) emptySubst = Su [] -- M.empty catSubst = unsafeCatSubst mkSubst = unsafeMkSubst unsafeMkSubst = Su -- . M.fromList unsafeCatSubst (Su s1) θ2@(Su s2) = Su $ s1' ++ s2 where s1' = mapSnd (subst θ2) <$> s1 -- TODO: this is **not used**, because of degenerate substitutions. -- e.g. consider: s1 = [v := v], s2 = [v := x]. -- We want s1 `cat` s2 to be [v := x] and not [v := v] ... unsafeCatSubstIgnoringDead (Su s1) (Su s2) = Su $ s1' ++ s2' where s1' = mapSnd (subst (Su s2')) <$> s1 s2' = filter (\(x,_) -> not (x `elem` (fst <$> s1))) s2 -- TODO: nano-js throws all sorts of issues, will look into this later... -- but also, the check is too conservative, because of degenerate substitutions, -- see above. safeCatSubst θ1@(Su s1) θ2@(Su s2) | null $ intersect xs1 xs2 = unsafeCatSubst θ1 θ2 | otherwise = errorstar msg where s1' = mapSnd (subst (Su s2)) <$> s1 xs1 = fst <$> s1 xs2 = fst <$> s2 msg = printf "Fixpoint.Types catSubst on overlapping substitutions θ1 = %s, θ2 = %s" (showFix θ1) (showFix θ2) safeMkSubst θ | nub θ == θ = Su θ | otherwise = errorstar msg where msg = printf "Fixpoint.Types mkSubst on overlapping substitution θ = %s" (showFix θ) instance Monoid Subst where mempty = emptySubst mappend = catSubst ------------------------------------------------------------ ------------- Generally Useful Refinements ----------------- ------------------------------------------------------------ symbolReft :: (Symbolic a) => a -> Reft symbolReft = exprReft . eVar vv_ = vv Nothing trueSortedReft :: Sort -> SortedReft trueSortedReft = (`RR` trueReft) trueReft = Reft (vv_, []) falseReft = Reft (vv_, [RConc PFalse]) trueRefa = RConc PTrue flattenRefas :: [Refa] -> [Refa] flattenRefas = concatMap flatRa where flatRa (RConc p) = RConc <$> flatP p flatRa ra = [ra] flatP (PAnd ps) = concatMap flatP ps flatP p = [p] squishRefas :: [Refa] -> [Refa] squishRefas ras = (squish [p | RConc p <- ras]) : [] where squish = RConc . pAnd . sortNub . filter (not . isTautoPred) . concatMap conjuncts conjuncts (PAnd ps) = concatMap conjuncts ps conjuncts p | isTautoPred p = [] | otherwise = [p] ---------------------------------------------------------------- ---------------------- Strictness ------------------------------ ---------------------------------------------------------------- instance NFData FTycon where rnf (TC c) = rnf c instance NFData Sort where rnf (FVar x) = rnf x rnf (FFunc n ts) = rnf n `seq` (rnf <$> ts) `seq` () rnf (FApp c ts) = rnf c `seq` (rnf <$> ts) `seq` () rnf (z) = z `seq` () instance NFData Sub where rnf (Sub x) = rnf x instance NFData Subst where rnf (Su x) = rnf x instance NFData FEnv where rnf (SE x) = rnf x instance NFData IBindEnv where rnf (FB x) = rnf x instance NFData BindEnv where rnf (BE x m) = rnf x `seq` rnf m instance NFData Constant where rnf (I x) = rnf x rnf (R x) = rnf x rnf (L s t) = rnf s `seq` rnf t instance NFData SymConst where rnf (SL x) = rnf x instance NFData Brel instance NFData Bop instance NFData Expr where rnf (ESym x) = rnf x rnf (ECon x) = rnf x rnf (EVar x) = rnf x -- rnf (EDat x1 x2) = rnf x1 `seq` rnf x2 rnf (ELit x1 x2) = rnf x1 `seq` rnf x2 rnf (EApp x1 x2) = rnf x1 `seq` rnf x2 rnf (EBin x1 x2 x3) = rnf x1 `seq` rnf x2 `seq` rnf x3 rnf (EIte x1 x2 x3) = rnf x1 `seq` rnf x2 `seq` rnf x3 rnf (ECst x1 x2) = rnf x1 `seq` rnf x2 rnf (_) = () instance NFData Pred where rnf (PAnd x) = rnf x rnf (POr x) = rnf x rnf (PNot x) = rnf x rnf (PBexp x) = rnf x rnf (PImp x1 x2) = rnf x1 `seq` rnf x2 rnf (PIff x1 x2) = rnf x1 `seq` rnf x2 rnf (PAll x1 x2) = rnf x1 `seq` rnf x2 rnf (PAtom x1 x2 x3) = rnf x1 `seq` rnf x2 `seq` rnf x3 rnf (_) = () instance NFData Refa where rnf (RConc x) = rnf x rnf (RKvar x1 x2) = rnf x1 `seq` rnf x2 -- rnf (RPvar _) = () -- rnf x instance NFData Reft where rnf (Reft (v, ras)) = rnf v `seq` rnf ras instance NFData SortedReft where rnf (RR so r) = rnf so `seq` rnf r instance (NFData a) => NFData (SubC a) where rnf (SubC x1 x2 x3 x4 x5 x6 x7) = rnf x1 `seq` rnf x2 `seq` rnf x3 `seq` rnf x4 `seq` rnf x5 `seq` rnf x6 `seq` rnf x7 instance (NFData a) => NFData (WfC a) where rnf (WfC x1 x2 x3 x4) = rnf x1 `seq` rnf x2 `seq` rnf x3 `seq` rnf x4 ---------------------------------------------------------------------------- -------------- Hashable Instances ----------------------------------------- --------------------------------------------------------------------------- instance Hashable FTycon where hashWithSalt i (TC s) = hashWithSalt i s --------------------------------------------------------------------------- -------- Constraint Constructor Wrappers ---------------------------------- --------------------------------------------------------------------------- wfC = WfC subC γ p (RR t1 r1) (RR t2 (Reft (v2, ra2s))) x y z = [subC' r2' | r2' <- [r2K, r2P], not $ isTauto r2'] where subC' r2' = SubC γ p (RR t1 (shiftVV r1 vvCon)) (RR t2 (shiftVV r2' vvCon)) x y z r2K = Reft (v2, [ra | ra@(RKvar _ _) <- ra2s]) r2P = Reft (v2, [ra | ra@(RConc _ ) <- ra2s]) lhsCs = sr_reft . slhs rhsCs = sr_reft . srhs removeLhsKvars cs vs = cs{slhs = goRR (slhs cs)} where goRR rr = rr{sr_reft = goReft (sr_reft rr)} goReft (Reft(v, rs)) = Reft(v, filter f rs) f (RKvar v _) | v `elem` vs = False f r = True trueSubCKvar v = subC emptyIBindEnv PTrue mempty (RR mempty (Reft(vv_, [RKvar v emptySubst]))) Nothing [0] shiftVV :: Reft -> Symbol -> Reft shiftVV r@(Reft (v, ras)) v' | v == v' = r | otherwise = Reft (v', (subst1 ras (v, EVar v'))) addIds = zipWith (\i c -> (i, shiftId i $ c {sid = Just i})) [1..] where -- Adding shiftId to have distinct VV for SMT conversion shiftId i c = c { slhs = shiftSR i $ slhs c } { srhs = shiftSR i $ srhs c } shiftSR i sr = sr { sr_reft = shiftR i $ sr_reft sr } shiftR i r@(Reft (v, _)) = shiftVV r (v `mappend` symbol (show i)) -- subC γ p r1 r2 x y z = (vvsu, SubC γ p r1' r2' x y z) -- where (vvsu, r1', r2') = unifySRefts r1 r2 -- unifySRefts (RR t1 r1) (RR t2 r2) = (z, RR t1 r1', RR t2 r2') -- where (r1', r2') = unifyRefts r1 r2 -- unifyRefts r1@(Reft (v1, _)) r2@(Reft (v2, _)) -- | v1 == v2 = (r1, r2) -- | otherwise = (r1, shiftVV r2 v1) -- unifySRefts (RR t1 r1) (RR t2 r2) = (z, RR t1 r1', RR t2 r2') -- where (z, r1', r2') = unifyRefts r1 r2 -- -- unifyRefts r1@(Reft (v1, _)) r2@(Reft (v2, _)) -- | v1 == v2 = ((v1, emptySubst), r1, r2) -- | v1 /= vv_ = let (su, r2') = shiftVV r2 v1 in ((v1, su), r1 , r2') -- | otherwise = let (su, r1') = shiftVV r1 v2 in ((v2, su), r1', r2 ) -- -- shiftVV (Reft (v, ras)) v' = (su, (Reft (v', subst su ras))) -- where su = mkSubst [(v, EVar v')] ------------------------------------------------------------------------ ----------------- Qualifiers ------------------------------------------- ------------------------------------------------------------------------ data Qualifier = Q { q_name :: Symbol -- ^ Name , q_params :: [(Symbol, Sort)] -- ^ Parameters , q_body :: Pred -- ^ Predicate , q_pos :: !SourcePos -- ^ Source Location } deriving (Eq, Ord, Show, Data, Typeable, Generic) instance Fixpoint Qualifier where toFix = pprQual instance NFData Qualifier where rnf (Q x1 x2 x3 _) = rnf x1 `seq` rnf x2 `seq` rnf x3 pprQual (Q n xts p _) = text "qualif" <+> text (symbolString n) <> parens args <> colon <+> toFix p where args = intersperse comma (toFix <$> xts) data FInfo a = FI { cm :: M.HashMap Integer (SubC a) , ws :: ![WfC a] , bs :: !BindEnv , gs :: !FEnv , lits :: ![(Symbol, Sort)] , kuts :: Kuts , quals :: ![Qualifier] } -- Original Ocaml definition -- -- type 'bind cfg = { -- a : int (* Tag arity *) -- ; ts : Ast.Sort.t list (* New sorts, now = [] *) -- ; ps : Ast.pred list (* New axioms, now = [] *) -- ; cs : FixConstraint.t list (* Implication Constraints *) -- ; ws : FixConstraint.wf list (* Well-formedness Constraints *) -- ; ds : FixConstraint.dep list (* Constraint Dependencies *) -- ; qs : Qualifier.t list (* Qualifiers *) -- ; kuts : Ast.Symbol.t list (* "Cut"-Kvars, which break cycles *) -- ; bm : 'bind Ast.Symbol.SMap.t (* Initial Sol Bindings *) -- ; uops : Ast.Sort.t Ast.Symbol.SMap.t (* Globals: measures + distinct consts) *) -- ; cons : Ast.Symbol.t list (* Distinct Constants, defined in uops *) -- ; assm : FixConstraint.soln (* Seed Solution: must be a fixpoint over constraints *) -- } -- toFixs = brackets . hsep . punctuate comma -- . map toFix toFixpoint x' = kutsDoc x' $+$ gsDoc x' $+$ conDoc x' $+$ bindsDoc x' $+$ csDoc x' $+$ wsDoc x' where conDoc = vcat . map toFix_constant . getLits csDoc = vcat . map toFix . M.elems . cm wsDoc = vcat . map toFix . ws kutsDoc = toFix . kuts bindsDoc = toFix . bs gsDoc = toFix_gs . gs getLits x = lits x -- ++ symConstLits x ------------------------------------------------------------------------- -- | A Class Predicates for Valid Refinements Types --------------------- ------------------------------------------------------------------------- class (Monoid r, Subable r) => Reftable r where isTauto :: r -> Bool ppTy :: r -> Doc -> Doc top :: r -> r top _ = mempty bot :: r -> r meet :: r -> r -> r meet = mappend toReft :: r -> Reft ofReft :: Reft -> r params :: r -> [Symbol] -- ^ parameters for Reft, vv + others instance Monoid Pred where mempty = PTrue mappend p q = pAnd [p, q] instance Monoid Reft where mempty = trueReft mappend = meetReft meetReft r@(Reft (v, ras)) r'@(Reft (v', ras')) | v == v' = Reft (v , ras ++ ras') | v == dummySymbol = Reft (v', ras' ++ (ras `subst1` (v , EVar v'))) | otherwise = Reft (v , ras ++ (ras' `subst1` (v', EVar v ))) instance Subable () where syms _ = [] subst _ () = () substf _ () = () substa _ () = () instance Reftable () where isTauto _ = True ppTy _ d = d top _ = () bot _ = () meet _ _ = () toReft _ = mempty ofReft _ = mempty params _ = [] instance Reftable Reft where isTauto = isTautoReft ppTy = ppr_reft toReft = id ofReft = id params _ = [] bot _ = falseReft top (Reft(v,_)) = Reft(v,[]) instance Monoid Sort where mempty = FObj "any" mappend t1 t2 | t1 == mempty = t2 | t2 == mempty = t1 | t1 == t2 = t1 | otherwise = errorstar $ "mappend-sort: conflicting sorts t1 =" ++ show t1 ++ " t2 = " ++ show t2 instance Monoid SortedReft where mempty = RR mempty mempty mappend t1 t2 = RR (mappend (sr_sort t1) (sr_sort t2)) (mappend (sr_reft t1) (sr_reft t2)) instance Reftable SortedReft where isTauto = isTauto . toReft ppTy = ppTy . toReft toReft = sr_reft ofReft = error "No instance of ofReft for SortedReft" params _ = [] bot s = s { sr_reft = falseReft } class Falseable a where isFalse :: a -> Bool instance Falseable Pred where isFalse (PFalse) = True isFalse _ = False instance Falseable Refa where isFalse (RConc p) = isFalse p isFalse _ = False instance Falseable Reft where isFalse (Reft(_, rs)) = or [isFalse p | RConc p <- rs] --------------------------------------------------------------- -- | String Constants ----------------------------------------- --------------------------------------------------------------- symConstLits :: FInfo a -> [(Symbol, Sort)] symConstLits fi = [(encodeSymConst c, sortSymConst c) | c <- symConsts fi] -- | Replace all symbol-representations-of-string-literals with string-literal -- Used to transform parsed output from fixpoint back into fq. encodeSymConst :: SymConst -> Symbol encodeSymConst (SL s) = symbol $ litPrefix `mappend` s sortSymConst :: SymConst -> Sort sortSymConst (SL _) = strSort decodeSymConst :: Symbol -> Maybe SymConst decodeSymConst = fmap SL . T.stripPrefix litPrefix . symbolText litPrefix :: Text litPrefix = "lit" `T.snoc` symSepName strSort :: Sort strSort = FApp strFTyCon [] class SymConsts a where symConsts :: a -> [SymConst] instance SymConsts (FInfo a) where symConsts fi = sortNub $ csLits ++ bsLits ++ gsLits ++ qsLits where csLits = concatMap symConsts $ M.elems $ cm fi bsLits = concatMap symConsts $ map snd $ M.elems $ be_binds $ bs fi gsLits = concatMap symConsts $ M.elems $ se_binds $ gs fi qsLits = concatMap symConsts $ q_body <$> quals fi instance SymConsts (SubC a) where symConsts c = symConsts (sgrd c) ++ symConsts (slhs c) ++ symConsts (srhs c) instance SymConsts SortedReft where symConsts = symConsts . sr_reft instance SymConsts Reft where symConsts (Reft (_, ras)) = concatMap symConsts ras instance SymConsts Refa where symConsts (RConc p) = symConsts p symConsts (RKvar _ (Su xes)) = concatMap symConsts $ snd <$> xes instance SymConsts Expr where symConsts (ESym c) = [c] symConsts (EApp _ es) = concatMap symConsts es symConsts (EBin _ e e') = concatMap symConsts [e, e'] symConsts (EIte p e e') = symConsts p ++ concatMap symConsts [e, e'] symConsts (ECst e _) = symConsts e symConsts _ = [] instance SymConsts Pred where symConsts (PNot p) = symConsts p symConsts (PAnd ps) = concatMap symConsts ps symConsts (POr ps) = concatMap symConsts ps symConsts (PImp p q) = concatMap symConsts [p, q] symConsts (PIff p q) = concatMap symConsts [p, q] symConsts (PAll _ p) = symConsts p symConsts (PBexp e) = symConsts e symConsts (PAtom _ e e') = concatMap symConsts [e, e'] symConsts _ = [] --------------------------------------------------------------- -- | Edit Distance -------------------------------------------- --------------------------------------------------------------- editDistance :: Eq a => [a] -> [a] -> Int editDistance xs ys = table ! (m,n) where (m,n) = (length xs, length ys) x = array (1,m) (zip [1..] xs) y = array (1,n) (zip [1..] ys) table :: Array (Int,Int) Int table = array bnds [(ij, dist ij) | ij <- range bnds] bnds = ((0,0),(m,n)) dist (0,j) = j dist (i,0) = i dist (i,j) = minimum [table ! (i-1,j) + 1, table ! (i,j-1) + 1, if x ! i == y ! j then table ! (i-1,j-1) else 1 + table ! (i-1,j-1)] ----------------------------------------------------------------------------- -- | Located Values --------------------------------------------------------- ----------------------------------------------------------------------------- data Located a = Loc { loc :: !SourcePos , val :: a } deriving (Data, Typeable, Generic) instance (IsString a) => IsString (Located a) where fromString = dummyLoc . fromString type LocSymbol = Located Symbol type LocText = Located Text dummyLoc :: a -> Located a dummyLoc = Loc (dummyPos "Fixpoint.Types.dummyLoc") dummyPos :: String -> SourcePos dummyPos s = newPos s 0 0 isDummy :: (Symbolic a) => a -> Bool isDummy a = symbol a == symbol dummyName instance Fixpoint SourcePos where toFix = text . show instance Fixpoint a => Fixpoint (Located a) where toFix = toFix . val instance Symbolic a => Symbolic (Located a) where symbol = symbol . val instance Expression a => Expression (Located a) where expr = expr . val instance Functor Located where fmap f (Loc l x) = Loc l (f x) instance F.Foldable Located where foldMap f (Loc _ x) = f x instance Traversable Located where traverse f (Loc l x) = Loc l <$> f x instance Show a => Show (Located a) where show (Loc l x) = show x ++ " defined at " ++ show l instance Eq a => Eq (Located a) where (Loc _ x) == (Loc _ y) = x == y instance Ord a => Ord (Located a) where compare x y = compare (val x) (val y) instance Subable a => Subable (Located a) where syms (Loc _ x) = syms x substa f (Loc l x) = Loc l (substa f x) substf f (Loc l x) = Loc l (substf f x) subst su (Loc l x) = Loc l (subst su x) instance Hashable a => Hashable (Located a) where hashWithSalt i = hashWithSalt i . val instance (NFData a) => NFData (Located a) where -- FIXME: no instance NFData SrcSpan rnf (Loc l x) = rnf x