{- |

Module : $Header$

Copyright : (c) Christian Maeder and Uni Bremen 2002-2005

License : similar to LGPL, see HetCATS/LICENSE.txt or LIZENZ.txt

Maintainer : maeder@tzi.de

Stability : provisional

Portability : portable

CASL static analysis for basic specifications

Follows Chaps. III:2 and III:3 of the CASL Reference Manual.

-}

module CASL.StaticAna where

import CASL.AS_Basic_CASL

import CASL.Sign

import CASL.MixfixParser

import CASL.Overload

import CASL.Inject

import CASL.Quantification

import CASL.Utils

import Common.Lib.State

import Common.PrettyPrint

import Common.Lib.Pretty

import qualified Common.Lib.Map as Map

import qualified Common.Lib.Set as Set

import qualified Common.Lib.Rel as Rel

import Common.Id

import Common.AS_Annotation

import Common.GlobalAnnotations

import Common.Result

import Data.Maybe

import Data.List

import Control.Exception (assert)

checkPlaces :: [SORT] -> Id -> [Diagnosis]

checkPlaces args i =

if let n = placeCount i in n == 0 || n == length args then []

else [mkDiag Error "wrong number of places" i]

checkWithVars :: Map.Map SIMPLE_ID a -> Id -> [Diagnosis]

checkWithVars m i@(Id ts _ _) = if isSimpleId i then

case Map.lookup (head ts) m of

Nothing -> []

Just _ -> alsoWarning "variable" i

else []

addOp :: OpType -> Id -> State (Sign f e) ()

addOp ty i =

do checkSorts (opRes ty : opArgs ty)

e <- get

let m = opMap e

l = Map.findWithDefault Set.empty i m

check = addDiags $ checkPlaces (opArgs ty) i

++ checkWithOtherMap "predicate" (predMap e) i

++ checkWithVars (varMap e) i

store = do put e { opMap = addOpTo i ty m }

if Set.member ty l then

addDiags [mkDiag Hint "redeclared op" i]

else case opKind ty of

Partial -> if Set.member ty {opKind = Total} l then

addDiags [mkDiag Warning "partially redeclared" i]

else store >> check

Total -> do store

if Set.member ty {opKind = Partial} l then

addDiags [mkDiag Hint "redeclared as total" i]

else check

addAssocOp :: OpType -> Id -> State (Sign f e) ()

addAssocOp ty i = do

e <- get

put e { assocOps = addOpTo i ty $ assocOps e }

updateExtInfo :: (e -> Result e) -> State (Sign f e) ()

updateExtInfo upd = do

s <- get

let re = upd $ extendedInfo s

case maybeResult re of

Nothing -> return ()

Just e -> put s { extendedInfo = e }

addDiags $ diags re

addPred :: PredType -> Id -> State (Sign f e) ()

addPred ty i =

do checkSorts $ predArgs ty

e <- get

let m = predMap e

l = Map.findWithDefault Set.empty i m

if Set.member ty l then

addDiags [mkDiag Hint "redeclared pred" i]

else do put e { predMap = Map.insert i (Set.insert ty l) m }

addDiags $ checkPlaces (predArgs ty) i

++ checkWithOtherMap "operation" (opMap e) i

++ checkWithVars (varMap e) i

allOpIds :: Sign f e -> Set.Set Id

allOpIds = Rel.keysSet . opMap

addAssocs :: GlobalAnnos -> Sign f e -> GlobalAnnos

addAssocs ga e =

ga { assoc_annos =

foldr ( \ i m -> case Map.lookup i m of

Nothing -> Map.insert i ALeft m

_ -> m ) (assoc_annos ga) (Map.keys $ assocOps e) }

formulaIds :: Sign f e -> Set.Set Id

formulaIds e = let ops = allOpIds e in

Set.fromDistinctAscList (map simpleIdToId $ Map.keys $ varMap e)

`Set.union` ops

allPredIds :: Sign f e -> Set.Set Id

allPredIds = Rel.keysSet . predMap

addSentences :: [Named (FORMULA f)] -> State (Sign f e) ()

addSentences ds =

do e <- get

put e { sentences = reverse ds ++ sentences e }

-- * traversing all data types of the abstract syntax

ana_BASIC_SPEC :: PrettyPrint f => Min f e

-> Ana b b s f e -> Ana s b s f e -> Mix b s f e -> GlobalAnnos

-> BASIC_SPEC b s f -> State (Sign f e) (BASIC_SPEC b s f)

ana_BASIC_SPEC mef ab anas mix ga (Basic_spec al) = fmap Basic_spec $

mapAnM (ana_BASIC_ITEMS mef ab anas mix ga) al

-- looseness of a datatype

data GenKind = Free | Generated | Loose deriving (Show, Eq, Ord)

mkForall :: [VAR_DECL] -> FORMULA f -> Range -> FORMULA f

mkForall vl f ps = if null vl then f else

Quantification Universal vl f ps

unionGenAx :: [GenAx] -> GenAx

unionGenAx = foldr ( \ (s1, r1, f1) (s2, r2, f2) ->

(Set.union s1 s2,

Rel.union r1 r2,

Set.union f1 f2)) emptyGenAx

ana_BASIC_ITEMS :: PrettyPrint f => Min f e -> Ana b b s f e -> Ana s b s f e

-> Mix b s f e -> GlobalAnnos

-> BASIC_ITEMS b s f -> State (Sign f e) (BASIC_ITEMS b s f)

ana_BASIC_ITEMS mef ab anas mix ga bi =

case bi of

Sig_items sis -> fmap Sig_items $

ana_SIG_ITEMS mef anas mix ga Loose sis

Free_datatype al ps ->

do let sorts = map (( \ (Datatype_decl s _ _) -> s) . item) al

mapM_ addSort sorts

mapAnM (ana_DATATYPE_DECL Free) al

toSortGenAx ps True $ getDataGenSig al

closeSubsortRel

return bi

Sort_gen al ps ->

do (gs,ul) <- ana_Generated mef anas mix ga al

toSortGenAx ps False $ unionGenAx gs

return $ Sort_gen ul ps

Var_items il _ ->

do mapM_ addVars il

return bi

Local_var_axioms il afs ps ->

do e <- get -- save

mapM_ addVars il

vds <- gets envDiags

sign <- get

put e { envDiags = vds } -- restore with shadowing warnings

let (es, resFs, anaFs) = foldr ( \ f (dss, ress, ranas) ->

let Result ds m = anaForm mef mix ga sign $ item f

in case m of

Nothing -> (ds ++ dss, ress, ranas)

Just (resF, anaF) ->

(ds ++ dss, f {item = resF} : ress,

f {item = anaF} : ranas))

([], [], []) afs

fufs = map (mapAn (\ f -> let

vs = map ( \ (v, s) ->

Var_decl [v] s ps)

$ Set.toList $ freeVars f

in stripQuant $ mkForall (vs ++ il) f ps))

anaFs

sens = map ( \ a -> NamedSen (getRLabel a)

(notImplied a) False $ item a) fufs

addDiags es

addSentences sens

return $ Local_var_axioms il resFs ps

Axiom_items afs ps ->

do sign <- get

let (es, resFs, anaFs) = foldr ( \ f (dss, ress, ranas) ->

let Result ds m = anaForm mef mix ga

sign $ item f

in case m of

Nothing -> (ds ++ dss, ress, ranas)

Just (resF, anaF) ->

(ds ++ dss, f {item = resF} : ress,

f {item = anaF} : ranas))

([], [], []) afs

fufs = map (mapAn (\ f -> let

vs = map ( \ (v, s) ->

Var_decl [v] s ps)

$ Set.toList $ freeVars f

in stripQuant $ mkForall vs f ps)) anaFs

sens = map ( \ a -> NamedSen (getRLabel a)

(notImplied a) False $ item a) fufs

addDiags es

addSentences sens

return $ Axiom_items resFs ps

Ext_BASIC_ITEMS b -> fmap Ext_BASIC_ITEMS $ ab mix ga b

mapAn :: (a -> b) -> Annoted a -> Annoted b

mapAn f an = replaceAnnoted (f $ item an) an

type GenAx = (Set.Set SORT, Rel.Rel SORT, Set.Set Component)

emptyGenAx :: GenAx

emptyGenAx = (Set.empty, Rel.empty, Set.empty)

toSortGenAx :: Range -> Bool -> GenAx -> State (Sign f e) ()

toSortGenAx ps isFree (sorts, rel, ops) = do

let sortList = Set.toList sorts

opSyms = map ( \ c -> let ide = compId c in Qual_op_name ide

(toOP_TYPE $ compType c) $ posOfId ide) $ Set.toList ops

injSyms = map ( \ (s, t) -> let p = posOfId s in

Qual_op_name injName

(Op_type Total [s] t p) p) $ Rel.toList

$ Rel.irreflex rel

resType _ (Op_name _) = False

resType s (Qual_op_name _ t _) = res_OP_TYPE t ==s

getIndex s = maybe (-1) id $ findIndex (==s) sortList

addIndices (Op_name _) =

error "CASL/StaticAna: Internal error in function addIndices"

addIndices os@(Qual_op_name _ t _) =

(os,map getIndex $ args_OP_TYPE t)

collectOps s =

Constraint s (map addIndices $ filter (resType s)

(opSyms ++ injSyms)) s

constrs = map collectOps sortList

f = Sort_gen_ax constrs isFree

if null sortList then

addDiags[Diag Error "missing generated sort" ps]

else return ()

addSentences [NamedSen

("ga_generated_" ++

showSepList (showString "_") showId sortList "")

True False f]

ana_SIG_ITEMS :: PrettyPrint f => Min f e

-> Ana s b s f e -> Mix b s f e -> GlobalAnnos -> GenKind

-> SIG_ITEMS s f -> State (Sign f e) (SIG_ITEMS s f)

ana_SIG_ITEMS mef anas mix ga gk si =

case si of

Sort_items al ps ->

do ul <- mapM (ana_SORT_ITEM mef mix ga) al

closeSubsortRel

return $ Sort_items ul ps

Op_items al ps ->

do ul <- mapM (ana_OP_ITEM mef mix ga) al

return $ Op_items ul ps

Pred_items al ps ->

do ul <- mapM (ana_PRED_ITEM mef mix ga) al

return $ Pred_items ul ps

Datatype_items al _ ->

do let sorts = map (( \ (Datatype_decl s _ _) -> s) . item) al

mapM_ addSort sorts

mapAnM (ana_DATATYPE_DECL gk) al

closeSubsortRel

return si

Ext_SIG_ITEMS s -> fmap Ext_SIG_ITEMS $ anas mix ga s

-- helper

ana_Generated :: PrettyPrint f => Min f e -> Ana s b s f e -> Mix b s f e

-> GlobalAnnos -> [Annoted (SIG_ITEMS s f)]

-> State (Sign f e) ([GenAx], [Annoted (SIG_ITEMS s f)])

ana_Generated mef anas mix ga al = do

ul <- mapAnM (ana_SIG_ITEMS mef anas mix ga Generated) al

return (map (getGenSig . item) ul, ul)

getGenSig :: SIG_ITEMS s f -> GenAx

getGenSig si = case si of

Sort_items al _ -> unionGenAx $ map (getGenSorts . item) al

Op_items al _ -> (Set.empty, Rel.empty,

Set.unions (map (getOps . item) al))

Datatype_items dl _ -> getDataGenSig dl

_ -> emptyGenAx

isConsAlt :: ALTERNATIVE -> Bool

isConsAlt a = case a of

Subsorts _ _ -> False

_ -> True

getDataGenSig :: [Annoted DATATYPE_DECL] -> GenAx

getDataGenSig dl =

let alts = concatMap (( \ (Datatype_decl s al _) ->

map ( \ a -> (s, item a)) al) . item) dl

sorts = map fst alts

(realAlts, subs) = partition (isConsAlt . snd) alts

cs = map ( \ (s, a) ->

let (i, ty, _) = getConsType s a

in Component i ty) realAlts

rel = foldr ( \ (t, a) r ->

foldr ( \ s ->

Rel.insert s t)

r $ getAltSubsorts a)

Rel.empty subs

in (Set.fromList sorts, rel, Set.fromList cs)

getGenSorts :: SORT_ITEM f -> GenAx

getGenSorts si =

let (sorts, rel) = case si of

Sort_decl il _ -> (Set.fromList il, Rel.empty)

Subsort_decl il i _ -> (Set.fromList (i:il)

, foldr (flip Rel.insert i) Rel.empty il)

Subsort_defn sub _ super _ _ -> (Set.singleton sub

, Rel.insert sub super Rel.empty)

Iso_decl il _ -> (Set.fromList il

, foldr ( \ s r -> foldr ( \ t ->

Rel.insert s t) r il) Rel.empty il)

in (sorts, rel, Set.empty)

getOps :: OP_ITEM f -> Set.Set Component

getOps oi = case oi of

Op_decl is ty _ _ ->

Set.fromList $ map ( \ i -> Component i $ toOpType ty) is

Op_defn i par _ _ ->

Set.singleton $ Component i $ toOpType $ headToType par

ana_SORT_ITEM :: PrettyPrint f => Min f e -> Mix b s f e

-> GlobalAnnos -> Annoted (SORT_ITEM f)

-> State (Sign f e) (Annoted (SORT_ITEM f))

ana_SORT_ITEM mef mix ga asi =

case item asi of

Sort_decl il _ ->

do mapM_ addSort il

return asi

Subsort_decl il i _ ->

do mapM_ addSort (i:il)

mapM_ (addSubsort i) il

return asi

Subsort_defn sub v super af ps ->

do e <- get -- save

put e { varMap = Map.empty }

addVars (Var_decl [v] super ps)

sign <- get

put e -- restore

let Result ds mf = anaForm mef mix ga sign $ item af

lb = getRLabel af

lab = if null lb then getRLabel asi else lb

addDiags ds

addSort sub

addSubsort super sub

case mf of

Nothing -> return asi { item = Subsort_decl [sub] super ps}

Just (resF, anaF) -> do

let p = posOfId sub

pv = tokPos v

addSentences[NamedSen lab (notImplied af) True $

mkForall [Var_decl [v] super pv]

(Equivalence

(Membership (Qual_var v super pv) sub p)

anaF p) p]

return asi { item = Subsort_defn sub v super

af { item = resF } ps}

Iso_decl il _ ->

do mapM_ addSort il

case il of

[] -> return ()

_ : tl -> mapM_ (uncurry $ addSubsortOrIso False)

$ zip tl il

return asi

ana_OP_ITEM :: PrettyPrint f => Min f e -> Mix b s f e -> GlobalAnnos

-> Annoted (OP_ITEM f) -> State (Sign f e) (Annoted (OP_ITEM f))

ana_OP_ITEM mef mix ga aoi =

case item aoi of

Op_decl ops ty il ps ->

do let oty = toOpType ty

ni = notImplied aoi

mapM_ (addOp oty) ops

ul <- mapM (ana_OP_ATTR mef mix ga oty ni ops) il

if null $ filter ( \ i -> case i of

Assoc_op_attr -> True

_ -> False) il

then return ()

else mapM_ (addAssocOp oty) ops

return aoi {item = Op_decl ops ty (catMaybes ul) ps}

Op_defn i ohd at ps ->

do let ty = headToType ohd

lb = getRLabel at

lab = if null lb then getRLabel aoi else lb

args = case ohd of

Op_head _ as _ _ -> as

vs = map (\ (Arg_decl v s qs) -> (Var_decl v s qs)) args

arg = concatMap ( \ (Var_decl v s qs) ->

map ( \ j -> Qual_var j s qs) v) vs

addOp (toOpType ty) i

e <- get -- save

put e { varMap = Map.empty }

mapM_ addVars vs

sign <- get

put e -- restore

let Result ds mt = anaTerm mef mix ga sign

(res_OP_TYPE ty) ps $ item at

addDiags ds

case mt of

Nothing -> return aoi { item = Op_decl [i] ty [] ps }

Just (resT, anaT) -> do

let p = posOfId i

addSentences [NamedSen lab (notImplied at) True $ mkForall vs

(Strong_equation

(Application (Qual_op_name i ty p) arg ps)

anaT p) ps]

return aoi {item = Op_defn i ohd at { item = resT } ps }

headToType :: OP_HEAD -> OP_TYPE

headToType (Op_head k args r ps) = Op_type k (sortsOfArgs args) r ps

sortsOfArgs :: [ARG_DECL] -> [SORT]

sortsOfArgs = concatMap ( \ (Arg_decl l s _) -> map (const s) l)

ana_OP_ATTR :: PrettyPrint f => Min f e -> Mix b s f e -> GlobalAnnos

-> OpType -> Bool -> [Id] -> (OP_ATTR f)

-> State (Sign f e) (Maybe (OP_ATTR f))

ana_OP_ATTR mef mix ga ty ni ois oa = do

let sty = toOP_TYPE ty

rty = opRes ty

atys = opArgs ty

q = posOfId rty

case atys of

[t1,t2] | t1 == t2 -> case oa of

Comm_op_attr -> return ()

_ -> if t1 == rty then return ()

else addDiags [Diag Error

"result sort must be equal to argument sorts" q]

_ -> addDiags [Diag Error

"expecting two arguments of equal sort" q]

case oa of

Unit_op_attr t ->

do sign <- get

let Result ds mt = anaTerm mef mix ga

sign { varMap = Map.empty } rty q t

addDiags ds

case mt of

Nothing -> return Nothing

Just (resT, anaT) -> do

addSentences $ map (makeUnit True anaT ty ni) ois

addSentences $ map (makeUnit False anaT ty ni) ois

return $ Just $ Unit_op_attr resT

Assoc_op_attr -> do

let ns = map mkSimpleId ["x", "y", "z"]

vs = map ( \ v -> Var_decl [v] rty q) ns

[v1, v2, v3] = map ( \ v -> Qual_var v rty q) ns

makeAssoc i = let p = posOfId i

qi = Qual_op_name i sty p in

NamedSen ("ga_assoc_" ++ showId i "") ni False $

mkForall vs

(Strong_equation

(Application qi [v1, Application qi [v2, v3] p] p)

(Application qi [Application qi [v1, v2] p, v3] p) p) p

addSentences $ map makeAssoc ois

return $ Just oa

Comm_op_attr -> do

let ns = map mkSimpleId ["x", "y"]

vs = zipWith ( \ v t -> Var_decl [v] t

$ concatMapRange posOfId atys) ns atys

args = map toQualVar vs

makeComm i = let p = posOfId i

qi = Qual_op_name i sty p in

NamedSen ("ga_comm_" ++ showId i "") ni False $

mkForall vs

(Strong_equation

(Application qi args p)

(Application qi (reverse args) p) p) p

addSentences $ map makeComm ois

return $ Just oa

Idem_op_attr -> do

let v = mkSimpleId "x"

vd = Var_decl [v] rty q

qv = toQualVar vd

makeIdem i = let p = posOfId i in

NamedSen ("ga_idem_" ++ showId i "") ni False $

mkForall [vd]

(Strong_equation

(Application (Qual_op_name i sty p) [qv, qv] p)

qv p) p

addSentences $ map makeIdem ois

return $ Just oa

-- first bool for left and right, second one for no implied annotation

makeUnit :: Bool -> TERM f -> OpType -> Bool -> Id -> Named (FORMULA f)

makeUnit b t ty ni i =

let lab = "ga_" ++ (if b then "right" else "left") ++ "_unit_"

++ showId i ""

v = mkSimpleId "x"

vty = opRes ty

q = posOfId vty

p = posOfId i

qv = Qual_var v vty q

args = [qv, t]

rargs = if b then args else reverse args

in NamedSen lab ni False $ mkForall [Var_decl [v] vty q]

(Strong_equation

(Application (Qual_op_name i (toOP_TYPE ty) p) rargs p)

qv p) p

ana_PRED_ITEM :: PrettyPrint f => Min f e -> Mix b s f e

-> GlobalAnnos -> Annoted (PRED_ITEM f)

-> State (Sign f e) (Annoted (PRED_ITEM f))

ana_PRED_ITEM mef mix ga ap =

case item ap of

Pred_decl preds ty _ ->

do mapM (addPred $ toPredType ty) preds

return ap

Pred_defn i phd@(Pred_head args rs) at ps ->

do let lb = getRLabel at

lab = if null lb then getRLabel ap else lb

ty = Pred_type (sortsOfArgs args) rs

vs = map (\ (Arg_decl v s qs) -> (Var_decl v s qs)) args

arg = concatMap ( \ (Var_decl v s qs) ->

map ( \ j -> Qual_var j s qs) v) vs

addPred (toPredType ty) i

e <- get -- save

put e { varMap = Map.empty }

mapM_ addVars vs

sign <- get

put e -- restore

let Result ds mt = anaForm mef mix ga sign $ item at

addDiags ds

case mt of

Nothing -> return ap {item = Pred_decl [i] ty ps}

Just (resF, anaF) -> do

let p = posOfId i

addSentences [NamedSen lab True True $

mkForall vs

(Equivalence (Predication (Qual_pred_name i ty p)

arg p) anaF p) p]

return ap {item = Pred_defn i phd at { item = resF } ps}

-- full function type of a selector (result sort is component sort)

data Component = Component { compId :: Id, compType :: OpType }

deriving (Show)

instance Eq Component where

Component i1 t1 == Component i2 t2 =

(i1, opArgs t1, opRes t1) == (i2, opArgs t2, opRes t2)

instance Ord Component where

Component i1 t1 <= Component i2 t2 =

(i1, opArgs t1, opRes t1) <= (i2, opArgs t2, opRes t2)

instance PrettyPrint Component where

printText0 ga (Component i ty) =

printText0 ga i <+> colon <> printText0 ga ty

instance PosItem Component where

getRange = getRange . compId

-- | return list of constructors

ana_DATATYPE_DECL :: GenKind -> DATATYPE_DECL -> State (Sign f e) [Component]

ana_DATATYPE_DECL gk (Datatype_decl s al _) =

do ul <- mapM (ana_ALTERNATIVE s . item) al

let constr = catMaybes ul

cs = map fst constr

if null constr then return ()

else do addDiags $ checkUniqueness cs

let totalSels = Set.unions $ map snd constr

wrongConstr = filter ((totalSels /=) . snd) constr

addDiags $ map ( \ (c, _) -> mkDiag Error

("total selectors '" ++ showSepList (showString ",")

showPretty (Set.toList totalSels)

"'\n must appear in alternative") c) wrongConstr

case gk of

Free -> do

let allts = map item al

(alts, subs) = partition isConsAlt allts

sbs = concatMap getAltSubsorts subs

comps = map (getConsType s) alts

ttrips = map (( \ (a, vs, t, ses) -> (a, vs, t, catSels ses))

. selForms1 "X" ) comps

sels = concatMap ( \ (_, _, _, ses) -> ses) ttrips

addSentences $ map makeInjective

$ filter ( \ (_, _, ces) -> not $ null ces)

comps

addSentences $ makeDisjSubsorts s sbs

addSentences $ concatMap ( \ c -> map (makeDisjToSort c) sbs)

comps

addSentences $ makeDisjoint comps

addSentences $ catMaybes $ concatMap

( \ ses ->

map (makeUndefForm ses) ttrips) sels

_ -> return ()

return cs

makeDisjSubsorts :: SORT -> [SORT] -> [Named (FORMULA f)]

makeDisjSubsorts d subs = case subs of

[] -> []

s : rs -> map (makeDisjSubsort s) rs ++ makeDisjSubsorts d rs

where

makeDisjSubsort :: SORT -> SORT -> Named (FORMULA f)

makeDisjSubsort s1 s2 = let

n = mkSimpleId "x"

pd = posOfId d

p1 = posOfId s1

p2 = posOfId s2

p = pd `appRange` p1 `appRange` p2

v = Var_decl [n] d pd

qv = toQualVar v

in NamedSen ("ga_disjoint_sorts_" ++ showId s1 "_"

++ showId s2 "") True False $

mkForall [v] (Negation (Conjunction [

Membership qv s1 p1, Membership qv s2 p2] p) p) p

makeDisjToSort :: (Id, OpType, [COMPONENTS]) -> SORT -> Named (FORMULA f)

makeDisjToSort a s =

let (c, v, t, _) = selForms1 "X" a

p = posOfId s in

NamedSen ("ga_disjoint_" ++ showId c "_sort_"

++ showId s "") True False $

mkForall v (Negation (Membership t s p) p) p

makeInjective :: (Id, OpType, [COMPONENTS]) -> Named (FORMULA f)

makeInjective a =

let (c, v1, t1, _) = selForms1 "X" a

(_, v2, t2, _) = selForms1 "Y" a

p = posOfId c

in NamedSen ("ga_injective_" ++ showId c "") True False $

mkForall (v1 ++ v2)

(Equivalence (Strong_equation t1 t2 p)

(let ces = zipWith ( \ w1 w2 -> Strong_equation

(toQualVar w1) (toQualVar w2) p) v1 v2

in if isSingle ces then head ces else Conjunction ces p)

p) p

makeDisjoint :: [(Id, OpType, [COMPONENTS])] -> [Named (FORMULA f)]

makeDisjoint l = case l of

[] -> []

c : cs -> map (makeDisj c) cs ++ makeDisjoint cs

where

makeDisj :: (Id, OpType, [COMPONENTS]) -> (Id, OpType, [COMPONENTS])

-> Named (FORMULA f)

makeDisj a1 a2 =

let (c1, v1, t1, _) = selForms1 "X" a1

(c2, v2, t2, _) = selForms1 "Y" a2

p = posOfId c1 `appRange` posOfId c2

in NamedSen ("ga_disjoint_" ++ showId c1 "_" ++ showId c2 "") True False

$ mkForall (v1 ++ v2)

(Negation (Strong_equation t1 t2 p) p) p

catSels :: [(Maybe Id, OpType)] -> [(Id, OpType)]

catSels = map ( \ (m, t) -> (fromJust m, t)) .

filter ( \ (m, _) -> isJust m)

makeUndefForm :: (Id, OpType) -> (Id, [VAR_DECL], TERM f, [(Id, OpType)])

-> Maybe (Named (FORMULA f))

makeUndefForm (s, ty) (i, vs, t, sels) =

let p = posOfId s in

if any ( \ (se, ts) -> s == se && opRes ts == opRes ty ) sels

then Nothing else

Just $ NamedSen ("ga_selector_undef_" ++ showId s "_"

++ showId i "") True False $

mkForall vs

(Negation

(Definedness

(Application (Qual_op_name s (toOP_TYPE ty) p) [t] p)

p) p) p

getAltSubsorts :: ALTERNATIVE -> [SORT]

getAltSubsorts c = case c of

Subsorts cs _ -> cs

_ -> []

getConsType :: SORT -> ALTERNATIVE -> (Id, OpType, [COMPONENTS])

getConsType s c =

let getConsTypeAux (part, i, il) =

(i, OpType part (concatMap

(map (opRes . snd) . getCompType s) il) s, il)

in case c of

Subsorts _ _ -> error "getConsType"

Alt_construct k a l _ -> getConsTypeAux (k, a, l)

getCompType :: SORT -> COMPONENTS -> [(Maybe Id, OpType)]

getCompType s (Cons_select k l cs _) =

map (\ i -> (Just i, OpType k [s] cs)) l

getCompType s (Sort cs) = [(Nothing, OpType Partial [s] cs)]

genSelVars :: String -> Int -> [OpType] -> [VAR_DECL]

genSelVars _ _ [] = []

genSelVars str n (ty:rs) =

Var_decl [mkSelVar str n] (opRes ty) nullRange : genSelVars str (n+1) rs

mkSelVar :: String -> Int -> Token

mkSelVar str n = mkSimpleId (str ++ show n)

makeSelForms :: Int -> (Id, [VAR_DECL], TERM f, [(Maybe Id, OpType)])

-> [Named (FORMULA f)]

makeSelForms _ (_, _, _, []) = []

makeSelForms n (i, vs, t, (mi, ty):rs) =

(case mi of

Nothing -> []

Just j -> let p = posOfId j

rty = opRes ty

q = posOfId rty in

[NamedSen ("ga_selector_" ++ showId j "") True False

$ mkForall vs

(Strong_equation

(Application (Qual_op_name j (toOP_TYPE ty) p) [t] p)

(Qual_var (mkSelVar "X" n) rty q) p) p]

) ++ makeSelForms (n+1) (i, vs, t, rs)

selForms1 :: String -> (Id, OpType, [COMPONENTS])

-> (Id, [VAR_DECL], TERM f, [(Maybe Id, OpType)])

selForms1 str (i, ty, il) =

let cs = concatMap (getCompType (opRes ty)) il

vs = genSelVars str 1 $ map snd cs

in (i, vs, Application (Qual_op_name i (toOP_TYPE ty) nullRange)

(map toQualVar vs) nullRange, cs)

toQualVar :: VAR_DECL -> TERM f

toQualVar (Var_decl v s ps) =

if isSingle v then Qual_var (head v) s ps else error "toQualVar"

selForms :: (Id, OpType, [COMPONENTS]) -> [Named (FORMULA f)]

selForms = makeSelForms 1 . selForms1 "X"

-- | return the constructor and the set of total selectors

ana_ALTERNATIVE :: SORT -> ALTERNATIVE

-> State (Sign f e) (Maybe (Component, Set.Set Component))

ana_ALTERNATIVE s c =

case c of

Subsorts ss _ ->

do mapM_ (addSubsort s) ss

return Nothing

_ -> do let cons@(i, ty, il) = getConsType s c

addOp ty i

ul <- mapM (ana_COMPONENTS s) il

let ts = concatMap fst ul

addDiags $ checkUniqueness (ts ++ concatMap snd ul)

addSentences $ selForms cons

return $ Just (Component i ty, Set.fromList ts)

-- | return total and partial selectors

ana_COMPONENTS :: SORT -> COMPONENTS

-> State (Sign f e) ([Component], [Component])

ana_COMPONENTS s c = do

let cs = getCompType s c

sels <- mapM ( \ (mi, ty) ->

case mi of

Nothing -> return Nothing

Just i -> do addOp ty i

return $ Just $ Component i ty) cs

return $ partition ((==Total) . opKind . compType) $ catMaybes sels

-- | utility

resultToState :: (a -> Result a) -> a -> State (Sign f e) a

resultToState f a = do

let r = f a

addDiags $ diags r

case maybeResult r of

Nothing -> return a

Just b -> return b

-- wrap it all up for a logic

type Ana a b s f e = Mix b s f e -> GlobalAnnos -> a -> State (Sign f e) a

anaForm :: PrettyPrint f => Min f e -> Mix b s f e -> GlobalAnnos

-> Sign f e -> (FORMULA f) -> Result (FORMULA f, FORMULA f)

anaForm mef mix ga sign f = do

resF <- resolveFormula (putParen mix) (mixResolve mix)

(addAssocs ga sign) (mixRules mix) f

anaF <- minExpFORMULA mef ga sign

$ assert (noMixfixF (checkMix mix) resF) resF

return (resF, anaF)

anaTerm :: PrettyPrint f => Min f e -> Mix b s f e -> GlobalAnnos

-> Sign f e -> SORT -> Range -> (TERM f) -> Result (TERM f, TERM f)

anaTerm mef mix ga sign srt pos t = do

resT <- resolveMixfix (putParen mix) (mixResolve mix)

(addAssocs ga sign) (mixRules mix) t

anaT <- oneExpTerm mef ga sign

$ assert (noMixfixT (checkMix mix) resT) $ Sorted_term resT srt pos

return (resT, anaT)

basicAnalysis :: PrettyPrint f

=> Min f e -- ^ type analysis of f

-> Ana b b s f e -- ^ static analysis of basic item b

-> Ana s b s f e -- ^ static analysis of signature item s

-> Mix b s f e -- ^ for mixfix analysis

-> (e -> e -> e) -- ^ difference of signature extension e

-> (BASIC_SPEC b s f, Sign f e, GlobalAnnos)

-> Result (BASIC_SPEC b s f, Sign f e, Sign f e, [Named (FORMULA f)])

basicAnalysis mef anab anas mix dif (bs, inSig, ga) =

let allIds = unite $ ids_BASIC_SPEC (getBaseIds mix) (getSigIds mix) bs

: getExtIds mix (extendedInfo inSig) :

[mkIdSets (allOpIds inSig) $ allPredIds inSig]

(newBs, accSig) = runState (ana_BASIC_SPEC mef anab anas

mix { mixRules = makeRules ga allIds }

ga bs) inSig

ds = reverse $ envDiags accSig

sents = reverse $ sentences accSig

cleanSig = accSig { envDiags = [], sentences = [], varMap = Map.empty }

diff = diffSig cleanSig inSig

{ extendedInfo = dif (extendedInfo accSig) $ extendedInfo inSig }

in Result ds $ Just (newBs, diff, cleanSig, sents)

basicCASLAnalysis :: (BASIC_SPEC () () (), Sign () (), GlobalAnnos)

-> Result (BASIC_SPEC () () (), Sign () (),

Sign () (), [Named (FORMULA ())])

basicCASLAnalysis = basicAnalysis (const $ const return)

(const $ const return) (const $ const return) emptyMix const