{-# LANGUAGE DeriveDataTypeable #-}
{- |
Module : ./CASL/Sign.hs
Description : CASL signatures and local environments for basic analysis
Copyright : (c) Christian Maeder and Uni Bremen 2002-2006
License : GPLv2 or higher, see LICENSE.txt
Maintainer : Christian.Maeder@dfki.de
Stability : provisional
Portability : portable
CASL signatures also serve as local environments for the basic static analysis
-}
module CASL.Sign where
import CASL.AS_Basic_CASL
import CASL.Fold
import CASL.ToDoc ()
import qualified Data.Map as Map
import qualified Data.Set as Set
import qualified Common.Lib.MapSet as MapSet
import qualified Common.Lib.Rel as Rel
import qualified Common.Lib.State as State
import Common.Keywords
import Common.Id
import Common.Result
import Common.AS_Annotation
import Common.GlobalAnnotations
import Common.Prec (mkPrecIntMap, PrecMap)
import Common.Doc
import Common.DocUtils
import Data.Data
import Data.Maybe (fromMaybe)
import Data.List (isPrefixOf)
import Control.Monad (when, unless)
-- constants have empty argument lists
data OpType = OpType {opKind :: OpKind, opArgs :: [SORT], opRes :: SORT}
deriving (Show, Eq, Ord, Typeable, Data)
-- | result sort added to argument sorts
opSorts :: OpType -> [SORT]
opSorts o = opRes o : opArgs o
mkTotOpType :: [SORT] -> SORT -> OpType
mkTotOpType = OpType Total
sortToOpType :: SORT -> OpType
sortToOpType = mkTotOpType []
isSingleArgOp :: OpType -> Bool
isSingleArgOp = isSingle . opArgs
data PredType = PredType {predArgs :: [SORT]} deriving (Show, Eq, Ord, Typeable, Data)
sortToPredType :: SORT -> PredType
sortToPredType s = PredType [s]
isBinPredType :: PredType -> Bool
isBinPredType (PredType l) = case l of
[_, _] -> True
_ -> False
type OpMap = MapSet.MapSet OP_NAME OpType
type PredMap = MapSet.MapSet PRED_NAME PredType
type AnnoMap = MapSet.MapSet Symbol Annotation
data SymbType = SortAsItemType
| SubsortAsItemType SORT -- special symbols for xml output
| OpAsItemType OpType
{- since symbols do not speak about totality, the totality
information in OpType has to be ignored -}
| PredAsItemType PredType
deriving (Show, Eq, Ord, Typeable, Data)
symbolKind :: SymbType -> SYMB_KIND
symbolKind t = case t of
OpAsItemType _ -> Ops_kind
PredAsItemType _ -> Preds_kind
_ -> Sorts_kind
data Symbol = Symbol {symName :: Id, symbType :: SymbType}
deriving (Show, Eq, Ord, Typeable, Data)
instance GetRange Symbol where
getRange = getRange . symName
rangeSpan = rangeSpan . symName
idToSortSymbol :: Id -> Symbol
idToSortSymbol idt = Symbol idt SortAsItemType
idToOpSymbol :: Id -> OpType -> Symbol
idToOpSymbol idt = Symbol idt . OpAsItemType
idToPredSymbol :: Id -> PredType -> Symbol
idToPredSymbol idt = Symbol idt . PredAsItemType
type CASLSign = Sign () ()
{- | the data type for the basic static analysis to accumulate variables,
sentences, symbols, diagnostics and annotations, that are removed or ignored
when looking at signatures from outside, i.e. during logic-independent
processing. -}
data Sign f e = Sign
{ sortRel :: Rel.Rel SORT
-- ^ every sort is a subsort of itself
, revSortRel :: Maybe (Rel.Rel SORT)
-- ^ reverse sort relation for more efficient lookup of subsorts
, emptySortSet :: Set.Set SORT
-- ^ a subset of the sort set of possibly empty sorts
, opMap :: OpMap
, assocOps :: OpMap -- ^ the subset of associative operators
, predMap :: PredMap
, varMap :: Map.Map SIMPLE_ID SORT -- ^ temporary variables
, sentences :: [Named (FORMULA f)] -- ^ current sentences
, declaredSymbols :: Set.Set Symbol -- ^ introduced or redeclared symbols
, envDiags :: [Diagnosis] -- ^ diagnostics for basic spec
, annoMap :: AnnoMap -- ^ annotated symbols
, globAnnos :: GlobalAnnos -- ^ global annotations to use
, extendedInfo :: e
} deriving (Show, Typeable, Data)
sortSet :: Sign f e -> Set.Set SORT
sortSet = Rel.keysSet . sortRel
-- better ignore assoc flags for equality
instance Eq e => Eq (Sign f e) where
a == b = compare a {extendedInfo = ()} b {extendedInfo = ()} == EQ
&& extendedInfo a == extendedInfo b
instance Ord e => Ord (Sign f e) where
compare a b = compare
(emptySortSet a, sortRel a, opMap a, predMap a, extendedInfo a)
(emptySortSet b, sortRel b, opMap b, predMap b, extendedInfo b)
emptySign :: e -> Sign f e
emptySign e = Sign
{ sortRel = Rel.empty
, revSortRel = Nothing
, emptySortSet = Set.empty
, opMap = MapSet.empty
, assocOps = MapSet.empty
, predMap = MapSet.empty
, varMap = Map.empty
, sentences = []
, declaredSymbols = Set.empty
, envDiags = []
, annoMap = MapSet.empty
, globAnnos = emptyGlobalAnnos
, extendedInfo = e }
embedSign :: e -> Sign f1 e1 -> Sign f e
embedSign e sign = (emptySign e)
{ sortRel = sortRel sign
, opMap = opMap sign
, assocOps = assocOps sign
, predMap = predMap sign }
mapForm :: f -> FORMULA f1 -> FORMULA f
mapForm c = foldFormula $ mapRecord (const c)
mapFORMULA :: FORMULA f1 -> FORMULA f
mapFORMULA = mapForm $ error "CASL.mapFORMULA"
embedTheory :: (FORMULA f1 -> FORMULA f) -> e
-> (Sign f1 e1, [Named (FORMULA f1)])
-> (Sign f e, [Named (FORMULA f)])
embedTheory f e (sign, sens) =
(embedSign e sign, map (mapNamed f) sens)
embedCASLTheory :: e -> (Sign f1 e1, [Named (FORMULA f1)])
-> (Sign f e, [Named (FORMULA f)])
embedCASLTheory = embedTheory mapFORMULA
getSyntaxTable :: Sign f e -> (PrecMap, AssocMap)
getSyntaxTable sig = let gannos = globAnnos sig
in (mkPrecIntMap $ prec_annos gannos, assoc_annos gannos)
class SignExtension e where
isSubSignExtension :: e -> e -> Bool
instance SignExtension () where
isSubSignExtension _ _ = True
-- | proper subsorts (possibly excluding input sort)
subsortsOf :: SORT -> Sign f e -> Set.Set SORT
subsortsOf s e = case revSortRel e of
Nothing -> Rel.predecessors (sortRel e) s
Just r -> Rel.succs r s
setRevSortRel :: Sign f e -> Sign f e
setRevSortRel s = s { revSortRel = Just . Rel.transpose $ sortRel s }
-- | proper supersorts (possibly excluding input sort)
supersortsOf :: SORT -> Sign f e -> Set.Set SORT
supersortsOf s e = Rel.succs (sortRel e) s
toOP_TYPE :: OpType -> OP_TYPE
toOP_TYPE OpType { opArgs = args, opRes = res, opKind = k } =
Op_type k args res nullRange
toPRED_TYPE :: PredType -> PRED_TYPE
toPRED_TYPE PredType { predArgs = args } = Pred_type args nullRange
toOpType :: OP_TYPE -> OpType
toOpType (Op_type k args r _) = OpType k args r
toPredType :: PRED_TYPE -> PredType
toPredType (Pred_type args _) = PredType args
instance Pretty OpType where
pretty = pretty . toOP_TYPE
instance Pretty PredType where
pretty = pretty . toPRED_TYPE
instance (Show f, Pretty e) => Pretty (Sign f e) where
pretty = printSign pretty
instance Pretty Symbol where
pretty sy = let n = pretty (symName sy) in
case symbType sy of
SortAsItemType -> keyword sortS <+> n
SubsortAsItemType s -> keyword sortS <+> n <+> less <+> pretty s
PredAsItemType pt -> keyword predS <+> n <+> colon <+> pretty pt
OpAsItemType ot -> keyword opS <+> n <+> colon <> pretty ot
eqAndSubsorts :: Bool -> Rel.Rel SORT -> ([[SORT]], [(SORT, [SORT])])
eqAndSubsorts groupSubsorts srel = let
cs = Rel.sccOfClosure srel
in ( filter ((> 1) . length) $ map Set.toList cs
, Map.toList . Map.map Set.toList . Rel.toMap . Rel.rmNullSets
. (if groupSubsorts then Rel.transpose else id)
. Rel.transReduce . Rel.irreflex $ Rel.collaps cs srel)
singleAndRelatedSorts :: Rel.Rel SORT -> ([SORT], [[SORT]])
singleAndRelatedSorts srel = let
ss = Rel.keysSet srel
rs = Rel.sccOfClosure
. Rel.transClosure . Rel.union srel $ Rel.transpose srel
is = Set.difference ss $ Set.unions rs
in (Set.toList is, map Set.toList rs)
printSign :: (e -> Doc) -> Sign f e -> Doc
printSign fE s = let
printRel (supersort, subsorts) =
ppWithCommas subsorts <+> text lessS <+>
idDoc supersort
esorts = emptySortSet s
srel = sortRel s
(es, ss) = eqAndSubsorts True srel
nsorts = Set.difference (sortSet s) esorts in
(if Set.null nsorts then empty else text (sortS ++ sS) <+>
sepByCommas (map idDoc (Set.toList nsorts))) $+$
(if Set.null esorts then empty else text (esortS ++ sS) <+>
sepByCommas (map idDoc (Set.toList esorts))) $+$
(if Rel.noPairs srel then empty
else text (sortS ++ sS) <+>
fsep (punctuate semi $
map (fsep . punctuate (space <> equals) . map pretty) es
++ map printRel ss))
$+$ printSetMap (text opS) empty (MapSet.toMap $ opMap s)
$+$ printSetMap (text predS) space (MapSet.toMap $ predMap s)
$+$ fE (extendedInfo s)
-- working with Sign
closeSortRel :: Sign f e -> Sign f e
closeSortRel s =
s { sortRel = Rel.transClosure $ sortRel s }
nonEmptySortSet :: Sign f e -> Set.Set Id
nonEmptySortSet s = Set.difference (sortSet s) $ emptySortSet s
-- op kinds of op types
setOpKind :: OpKind -> OpType -> OpType
setOpKind k o = o { opKind = k }
mkPartial :: OpType -> OpType
mkPartial = setOpKind Partial
mkTotal :: OpType -> OpType
mkTotal = setOpKind Total
isTotal :: OpType -> Bool
isTotal = (== Total) . opKind
isPartial :: OpType -> Bool
isPartial = not . isTotal
makePartial :: Set.Set OpType -> Set.Set OpType
makePartial = Set.mapMonotonic mkPartial
-- | remove (True) or add (False) partial op if it is included as total
rmOrAddParts :: Bool -> Set.Set OpType -> Set.Set OpType
rmOrAddParts b s =
let t = makePartial $ Set.filter isTotal s
in (if b then Set.difference else Set.union) s t
rmOrAddPartsMap :: Bool -> OpMap -> OpMap
rmOrAddPartsMap b = MapSet.mapSet (rmOrAddParts b)
diffMapSet :: PredMap -> PredMap -> PredMap
diffMapSet = MapSet.difference
diffOpMapSet :: OpMap -> OpMap -> OpMap
diffOpMapSet m = MapSet.difference m . rmOrAddPartsMap False
diffSig :: (e -> e -> e) -> Sign f e -> Sign f e -> Sign f e
diffSig dif a b = let s = sortSet a `Set.difference` sortSet b in
closeSortRel a
{ emptySortSet = Set.difference s
$ nonEmptySortSet a `Set.difference` nonEmptySortSet b
, sortRel = Rel.difference (Rel.transReduce $ sortRel a)
. Rel.transReduce $ sortRel b
, opMap = opMap a `diffOpMapSet` opMap b
, assocOps = assocOps a `diffOpMapSet` assocOps b
, predMap = predMap a `diffMapSet` predMap b
, annoMap = annoMap a `MapSet.difference` annoMap b
, extendedInfo = dif (extendedInfo a) $ extendedInfo b }
{- transClosure needed: {a < b < c} - {a < c; b}
is not transitive! -}
addOpMapSet :: OpMap -> OpMap -> OpMap
addOpMapSet m = rmOrAddPartsMap True . MapSet.union m
addMapSet :: PredMap -> PredMap -> PredMap
addMapSet = MapSet.union
addSig :: (e -> e -> e) -> Sign f e -> Sign f e -> Sign f e
addSig ad a b = let s = sortSet a `Set.union` sortSet b in
closeSortRel a
{ emptySortSet = Set.difference s
$ nonEmptySortSet a `Set.union` nonEmptySortSet b
, sortRel = Rel.union (sortRel a) $ sortRel b
, opMap = addOpMapSet (opMap a) $ opMap b
, assocOps = addOpMapSet (assocOps a) $ assocOps b
, predMap = MapSet.union (predMap a) $ predMap b
, annoMap = MapSet.union (annoMap a) $ annoMap b
, extendedInfo = ad (extendedInfo a) $ extendedInfo b }
uniteCASLSign :: CASLSign -> CASLSign -> CASLSign
uniteCASLSign = addSig (\ _ _ -> ())
interRel :: (Show a, Ord a) => Rel.Rel a -> Rel.Rel a -> Rel.Rel a
interRel a =
Rel.fromSet
. Set.intersection (Rel.toSet a) . Rel.toSet
interOpMapSet :: OpMap -> OpMap -> OpMap
interOpMapSet m = rmOrAddPartsMap True
. MapSet.intersection (rmOrAddPartsMap False m) . rmOrAddPartsMap False
interMapSet :: PredMap -> PredMap -> PredMap
interMapSet = MapSet.intersection
interSig :: (e -> e -> e) -> Sign f e -> Sign f e -> Sign f e
interSig ef a b = let s = sortSet a `Set.intersection` sortSet b in
closeSortRel a
{ emptySortSet = Set.difference s
$ nonEmptySortSet a `Set.intersection` nonEmptySortSet b
, sortRel = interRel (sortRel a) $ sortRel b
, opMap = interOpMapSet (opMap a) $ opMap b
, assocOps = interOpMapSet (assocOps a) $ assocOps b
, predMap = interMapSet (predMap a) $ predMap b
, annoMap = MapSet.intersection (annoMap a) $ annoMap b
, extendedInfo = ef (extendedInfo a) $ extendedInfo b }
isSubOpMap :: OpMap -> OpMap -> Bool
isSubOpMap m = Map.isSubmapOfBy (\ s t -> MapSet.setAll
(\ e -> Set.member e t || isPartial e && Set.member (mkTotal e) t)
s) (MapSet.toMap m) . MapSet.toMap
isSubMap :: PredMap -> PredMap -> Bool
isSubMap = MapSet.isSubmapOf
isSubSig :: (e -> e -> Bool) -> Sign f e -> Sign f e -> Bool
isSubSig isSubExt a b =
Rel.isSubrelOf (sortRel a) (sortRel b)
-- ignore empty sort sorts
&& isSubOpMap (opMap a) (opMap b)
-- ignore associativity properties!
&& isSubMap (predMap a) (predMap b)
&& isSubExt (extendedInfo a) (extendedInfo b)
mapSetToList :: MapSet.MapSet a b -> [(a, b)]
mapSetToList = MapSet.toPairList
addDiags :: [Diagnosis] -> State.State (Sign f e) ()
addDiags ds = do
e <- State.get
State.put e { envDiags = reverse ds ++ envDiags e }
addAnnoSet :: Annoted a -> Symbol -> State.State (Sign f e) ()
addAnnoSet a s = do
addSymbol s
let v = Set.union (Set.fromList $ l_annos a) $ Set.fromList $ r_annos a
unless (Set.null v) $ do
e <- State.get
State.put e { annoMap = MapSet.update (Set.union v) s $ annoMap e }
addSymbol :: Symbol -> State.State (Sign f e) ()
addSymbol s = do
e <- State.get
State.put $ addSymbToDeclSymbs e s
addSymbToDeclSymbs :: Sign e f -> Symbol -> Sign e f
addSymbToDeclSymbs cs sy =
cs { declaredSymbols = Set.insert sy $ declaredSymbols cs }
addSort :: SortsKind -> Annoted a -> SORT -> State.State (Sign f e) ()
addSort sk a s = do
e <- State.get
let r = sortRel e
em = emptySortSet e
known = Rel.memberKey s r
if known then addDiags [mkDiag Hint "redeclared sort" s]
else do
State.put e { sortRel = Rel.insertKey s r }
addDiags $ checkNamePrefix s
case sk of
NonEmptySorts -> when (Set.member s em) $ do
e2 <- State.get
State.put e2 { emptySortSet = Set.delete s em }
addDiags [mkDiag Warning "redeclared sort as non-empty" s]
PossiblyEmptySorts -> if known then
addDiags [mkDiag Warning "non-empty sort remains non-empty" s]
else do
e2 <- State.get
State.put e2 { emptySortSet = Set.insert s em }
addAnnoSet a $ Symbol s SortAsItemType
hasSort :: Sign f e -> SORT -> [Diagnosis]
hasSort e s =
[ mkDiag Error "unknown sort" s
| not $ Set.member s $ sortSet e ]
checkSorts :: [SORT] -> State.State (Sign f e) ()
checkSorts s = do
e <- State.get
addDiags $ concatMap (hasSort e) s
addSubsort :: SORT -> SORT -> State.State (Sign f e) ()
addSubsort = addSubsortOrIso True
addSubsortOrIso :: Bool -> SORT -> SORT -> State.State (Sign f e) ()
addSubsortOrIso b super sub = do
when b $ checkSorts [super, sub]
e <- State.get
let r = sortRel e
State.put e { sortRel = (if b then id else Rel.insertDiffPair super sub)
$ Rel.insertDiffPair sub super r }
let p = posOfId sub
rel = " '" ++
showDoc sub (if b then " < " else " = ") ++ showDoc super "'"
if super == sub then addDiags [mkDiag Warning "void reflexive subsort" sub]
else if b then
if Rel.path super sub r then
addDiags $ if Rel.path sub super r
then [Diag Warning ("sorts are isomorphic" ++ rel) p]
else [Diag Warning ("added subsort cycle by" ++ rel) p]
else when (Rel.path sub super r)
$ addDiags [Diag Hint ("redeclared subsort" ++ rel) p]
else if Rel.path super sub r then
addDiags $ if Rel.path sub super r
then [Diag Hint ("redeclared isomoprhic sorts" ++ rel) p]
else [Diag Warning ("subsort '" ++
showDoc super "' made isomorphic by" ++ rel) $ posOfId super]
else when (Rel.path sub super r)
$ addDiags [Diag Warning ("subsort '" ++
showDoc sub "' made isomorphic by" ++ rel) p]
closeSubsortRel :: State.State (Sign f e) ()
closeSubsortRel =
do e <- State.get
State.put e { sortRel = Rel.transClosure $ sortRel e }
checkNamePrefix :: Id -> [Diagnosis]
checkNamePrefix i =
[ mkDiag Warning "identifier may conflict with generated names" i
| isPrefixOf genNamePrefix $ showId i ""]
alsoWarning :: String -> String -> Id -> [Diagnosis]
alsoWarning new old i = let is = ' ' : showId i "'" in
[Diag Warning ("new '" ++ new ++ is ++ " is also known as '" ++ old ++ is)
$ posOfId i]
checkWithMap :: String -> String -> Map.Map Id a -> Id -> [Diagnosis]
checkWithMap s1 s2 m i = if Map.member i m then alsoWarning s1 s2 i else []
checkWithOtherMap :: String -> String -> MapSet.MapSet Id a -> Id -> [Diagnosis]
checkWithOtherMap s1 s2 = checkWithMap s1 s2 . MapSet.toMap
addVars :: VAR_DECL -> State.State (Sign f e) ()
addVars (Var_decl vs s _) = do
checkSorts [s]
mapM_ (addVar s) vs
addVar :: SORT -> SIMPLE_ID -> State.State (Sign f e) ()
addVar s v =
do e <- State.get
let m = varMap e
i = simpleIdToId v
ds = case Map.lookup v m of
Just _ -> [mkDiag Hint "known variable shadowed" v]
Nothing -> []
State.put e { varMap = Map.insert v s m }
addDiags $ ds ++ checkWithOtherMap varS opS (opMap e) i
++ checkWithOtherMap varS predS (predMap e) i
++ checkNamePrefix i
addOpTo :: Id -> OpType -> OpMap -> OpMap
addOpTo = MapSet.insert
type VarSet = Set.Set (VAR, SORT)
{- | extract the sort and free variables from an analysed term. The input
signature for free variables is (currently only) used for statements in the
VSE logic. The conversion for boolean terms to formulas is only used for FPL.
-}
class TermExtension f where
freeVarsOfExt :: Sign f e -> f -> VarSet
freeVarsOfExt _ = const Set.empty
optTermSort :: f -> Maybe SORT
optTermSort = const Nothing
sortOfTerm :: f -> SORT
sortOfTerm = fromMaybe (genName "unknown") . optTermSort
termToFormula :: TERM f -> Result (FORMULA f)
termToFormula = const $ Result [] Nothing
instance TermExtension ()
instance TermExtension f => TermExtension (TERM f) where
optTermSort = optSortOfTerm optTermSort
optSortOfTerm :: (f -> Maybe SORT) -> TERM f -> Maybe SORT
optSortOfTerm f term = case term of
Qual_var _ ty _ -> Just ty
Application (Qual_op_name _ ot _) _ _ -> Just $ res_OP_TYPE ot
Sorted_term _ ty _ -> Just ty
Cast _ ty _ -> Just ty
Conditional t1 _ _ _ -> optSortOfTerm f t1
ExtTERM t -> f t
_ -> Nothing
mkAxName :: String -> SORT -> SORT -> String
mkAxName str s s' = "ga_" ++ str ++ "_" ++ show s ++ "_to_" ++ show s'
mkAxNameSingle :: String -> SORT -> String
mkAxNameSingle str s = "ga_" ++ str ++ "_" ++ show s
mkSortGenName :: [SORT] -> String
mkSortGenName sl = "ga_generated_" ++ showSepList (showString "_") showId sl ""
{- | The sort generation constraint is given a generated name,
built from the sort list -}
toSortGenNamed :: FORMULA f -> [SORT] -> Named (FORMULA f)
toSortGenNamed f sl = makeNamed (mkSortGenName sl) f
getConstructors :: [Named (FORMULA f)] -> Set.Set (Id, OpType)
getConstructors = foldr (\ f s -> case sentence f of
Sort_gen_ax cs _ -> let
(_, ops, _) = recover_Sort_gen_ax cs
in foldr ( \ o -> case o of
Qual_op_name i t _ ->
Set.insert (i, mkPartial $ toOpType t)
_ -> id)
s ops
_ -> s) Set.empty
-- | adds a symbol to a given signature
addSymbToSign :: Sign e f -> Symbol -> Result (Sign e f)
addSymbToSign sig sy =
let addSort' cs s =
cs { sortRel = Rel.insertKey s $ sortRel cs }
addToMap' m n t = MapSet.insert n t m
addOp' cs n ot = cs { opMap = addToMap' (opMap cs) n ot }
addPred' cs n pt = cs { predMap = addToMap' (predMap cs) n pt }
in do
let sig' = addSymbToDeclSymbs sig sy
n = symName sy
case symbType sy of
SortAsItemType -> return $ addSort' sig' n
SubsortAsItemType _ -> return sig
PredAsItemType pt -> return $ addPred' sig' n pt
OpAsItemType ot -> return $ addOp' sig' n ot
-- The function below belong in a different file. But I put them here for now.
-- dual of a quantifier
dualQuant :: QUANTIFIER -> QUANTIFIER
dualQuant q = case q of
Universal -> Existential
Existential -> Universal
Unique_existential -> error "unique existential quantifier has no dual" -- should not get here