{- |

Module : $Header$

Description : CASL static analysis for basic specifications

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

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

Maintainer : Christian.Maeder@dfki.de

Stability : provisional

Portability : portable

CASL static analysis for basic specifications

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

The static analysis takes an abstract syntax tree of a basic specification

and outputs a signature and a set of formulas, while checking that

- all sorts used in operation and predicate declarations have been declared

- all sorts, operation and predicate symbols used in formulas have

been declared

- formulas type-check

The formulas are returned with fully-qualified variables, operation

and predicate symbols.

The static analysis functions are parameterized with functions for

treating CASL extensions, that is, additional basic items, signature

items and formulas.

-}

module CASL.StaticAna where

import CASL.AS_Basic_CASL

import CASL.Sign

import CASL.MixfixParser

import CASL.Overload

import CASL.Quantification

import CASL.Utils

import Common.Lib.State

import Common.Doc

import Common.DocUtils

import Common.ExtSign

import qualified Data.Map as Map

import qualified Data.Set as Set

import qualified Common.Lib.Rel as Rel

import Common.Id

import Common.Keywords

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

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

case Map.lookup (head ts) m of

Nothing -> []

Just _ -> alsoWarning s varS i

else []

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

addOp a ty i =

do checkSorts (opRes ty : opArgs ty)

e <- get

let m = opMap e

l = Map.findWithDefault Set.empty i m

ds = checkWithOtherMap opS predS (predMap e) i

++ checkWithVars opS (varMap e) i

check = addDiags $

(if Set.member ty l then [mkDiag Hint "redeclared op" i]

else checkPlaces (opArgs ty) i ++ checkNamePrefix i)

++ ds

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

case opKind ty of

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

addDiags $ mkDiag Warning "partially redeclared" i : ds

else store >> check

Total -> do store

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

addDiags $ mkDiag Hint "redeclared as total" i : ds

else check

addAnnoSet a $ Symbol i $ OpAsItemType ty

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

addAssocOp ty i = do

e <- get

put e { assocOps = addOpTo i ty $ assocOps e

, globAnnos = updAssocMap (addAssocId i) $ globAnnos 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 :: Annoted a -> PredType -> Id -> State (Sign f e) ()

addPred a ty i =

do checkSorts $ predArgs ty

e <- get

let m = predMap e

l = Map.findWithDefault Set.empty i m

ds = checkWithOtherMap predS opS (opMap e) i

++ checkWithVars predS (varMap e) i

if Set.member ty l then

addDiags $ mkDiag Hint "redeclared pred" i : ds

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

addDiags $ checkPlaces (predArgs ty) i

++ checkNamePrefix i ++ ds

addAnnoSet a $ Symbol i $ PredAsItemType ty

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

allOpIds = Map.keysSet . opMap

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

addAssocs e = updAssocMap (\ m -> foldr addAssocId m $ Map.keys $ assocOps e)

updAssocMap :: (AssocMap -> AssocMap) -> GlobalAnnos -> GlobalAnnos

updAssocMap f ga = ga { assoc_annos = f $ assoc_annos ga }

addAssocId :: Id -> AssocMap -> AssocMap

addAssocId i m = case Map.lookup i m of

Nothing -> Map.insert i ALeft m

_ -> m

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 = Map.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 :: (PosItem f, Pretty f, FreeVars f) => Min f e

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

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

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

mapAnM (ana_BASIC_ITEMS mef ab anas mix) 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 :: (PosItem f, Pretty f, FreeVars f) => Min f e

-> Ana b b s f e

-> Ana s b s f e

-> Mix b s f e -> BASIC_ITEMS b s f

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

ana_BASIC_ITEMS mef ab anas mix bi =

case bi of

Sig_items sis -> fmap Sig_items $

ana_SIG_ITEMS mef anas mix Loose sis

Free_datatype sk al ps ->

do mapM_ (\ i -> case item i of

Datatype_decl s _ _ -> addSort sk i s) al

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 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 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

qf = mkForall il f ps

vs = map ( \ (v, s) -> Var_decl [v] s ps)

$ Set.toList $ freeVars sign qf

in stripQuant sign $ mkForall vs qf ps))

anaFs

sens = map makeNamedSen 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

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 sign f

in stripQuant sign $ mkForall vs f ps)) anaFs

sens = map makeNamedSen fufs

addDiags es

addSentences sens

return $ Axiom_items resFs ps

Ext_BASIC_ITEMS b -> fmap Ext_BASIC_ITEMS $ ab mix 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 (mkUniqueInjName s t)

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

$ Rel.irreflex rel

allSyms = opSyms ++ injSyms

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) allSyms) s

constrs = map collectOps sortList

resList = Set.fromList $ map (\ (Qual_op_name _ t _) -> res_OP_TYPE t)

allSyms

noConsList = Set.difference sorts resList

voidOps = Set.difference resList sorts

f = Sort_gen_ax constrs isFree

if null sortList then

addDiags[Diag Error "missing generated sort" ps]

else return ()

if Set.null noConsList then return () else

addDiags[mkDiag Warning "generated sorts without constructor"

noConsList]

if Set.null voidOps then return () else

addDiags[mkDiag Warning "non-generated sorts as constructor result"

voidOps]

addSentences [makeNamed ("ga_generated_" ++

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

ana_SIG_ITEMS :: (PosItem f, Pretty f) => Min f e -> Ana s b s f e

-> Mix b s f e -> GenKind -> SIG_ITEMS s f

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

ana_SIG_ITEMS mef anas mix gk si =

case si of

Sort_items sk al ps ->

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

closeSubsortRel

return $ Sort_items sk ul ps

Op_items al ps ->

do ul <- mapM (ana_OP_ITEM mef mix) al

return $ Op_items ul ps

Pred_items al ps ->

do ul <- mapM (ana_PRED_ITEM mef mix) al

return $ Pred_items ul ps

Datatype_items sk al _ ->

do mapM_ (\ i -> case item i of

Datatype_decl s _ _ -> addSort sk i s) al

mapAnM (ana_DATATYPE_DECL gk) al

closeSubsortRel

return si

Ext_SIG_ITEMS s -> fmap Ext_SIG_ITEMS $ anas mix s

-- helper

ana_Generated :: (PosItem f, Pretty f) => Min f e -> Ana s b s f e

-> Mix b s f e -> [Annoted (SIG_ITEMS s f)]

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

ana_Generated mef anas mix al = do

ul <- mapAnM (ana_SIG_ITEMS mef anas mix 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

isPartAlt :: ALTERNATIVE -> Bool

isPartAlt a = case a of

Subsorts _ _ -> False

Alt_construct p _ _ _ -> p == Partial

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 :: (PosItem f, Pretty f) => Min f e -> Mix b s f e

-> SortsKind -> Annoted (SORT_ITEM f)

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

ana_SORT_ITEM mef mix sk asi =

case item asi of

Sort_decl il _ ->

do mapM_ (addSort sk asi) il

return asi

Subsort_decl il i _ ->

do mapM_ (addSort sk asi) (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 sign $ item af

lb = getRLabel af

lab = if null lb then getRLabel asi else lb

addDiags ds

addSort sk asi 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[(makeNamed lab $

mkForall [Var_decl [v] super pv]

(Equivalence

(Membership (Qual_var v super pv) sub p)

anaF p) p) {

isAxiom = notImplied af }]

return asi { item = Subsort_defn sub v super

af { item = resF } ps}

Iso_decl il _ ->

do mapM_ (addSort sk asi) il

case il of

[] -> return ()

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

$ zip tl il

return asi

ana_OP_ITEM :: (PosItem f, Pretty f) => Min f e -> Mix b s f e

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

ana_OP_ITEM mef mix aoi =

case item aoi of

Op_decl ops ty il ps ->

do let oty = toOpType ty

ni = notImplied aoi

mapM_ (addOp aoi oty) ops

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

if any ( \ a -> case a of

Assoc_op_attr -> True

_ -> False) il then do

mapM_ (addAssocOp oty) ops

if any ( \ a -> case a of

Comm_op_attr -> True

_ -> False) il then

addSentences $ map (addLeftComm oty ni) ops

else return ()

else return ()

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 aoi (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 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 [(makeNamed lab $ mkForall vs

(Strong_equation

(Application (Qual_op_name i ty p) arg ps)

anaT p) ps) {

isAxiom = notImplied at, isDef = True }]

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)

-- see Isabelle/doc/ref.pdf 10.6 Permutative rewrite rules (p. 137)

addLeftComm :: OpType -> Bool -> Id -> Named (FORMULA f)

addLeftComm ty ni i =

let sty = toOP_TYPE ty

rty = opRes ty

q = posOfId rty

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

p = posOfId i

qi = Qual_op_name i sty p

in (makeNamed ("ga_left_comm_" ++ showId i "") $

mkForall vs

(Strong_equation

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

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

{ isAxiom = ni }

ana_OP_ATTR :: (PosItem f, Pretty f) => Min f e -> Mix b s f e -> OpType

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

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

ana_OP_ATTR mef mix 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

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

(makeNamed ("ga_assoc_" ++ showId i "") $

mkForall vs

(Strong_equation

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

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

{ isAxiom = ni }

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

(makeNamed ("ga_comm_" ++ showId i "") $

mkForall vs

(Strong_equation

(Application qi args p)

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

isAxiom = ni }

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

(makeNamed ("ga_idem_" ++ showId i "") $

mkForall [vd]

(Strong_equation

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

qv p) p) { isAxiom = ni }

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 (makeNamed lab $ mkForall [Var_decl [v] vty q]

(Strong_equation

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

qv p) p) {isAxiom = ni }

ana_PRED_ITEM :: (PosItem f, Pretty f) => Min f e -> Mix b s f e

-> Annoted (PRED_ITEM f)

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

ana_PRED_ITEM mef mix ap =

case item ap of

Pred_decl preds ty _ ->

do mapM (addPred ap $ 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 ap (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 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 [(makeNamed lab $

mkForall vs

(Equivalence (Predication (Qual_pred_name i ty p)

arg p) anaF p) p) {

isDef = True }]

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 Pretty Component where

pretty (Component i ty) =

pretty i <+> colon <> pretty 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) 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 ",")

showDoc (Set.toList totalSels)

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

case gk of

Free -> do

let allts = map item al

pfs = filter isPartAlt allts

(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

addDiags $ map ( \ (Alt_construct _ i _ _) -> mkDiag Error

"illegal free partial constructor" i) pfs

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 makeNamed ("ga_disjoint_sorts_" ++ showId s1 "_" ++ showId s2 "")

$ 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 makeNamed ("ga_disjoint_" ++ showId c "_sort_" ++ showId s "")

$ 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 makeNamed ("ga_injective_" ++ showId c "")

$ 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 makeNamed ("ga_disjoint_" ++ showId c1 "_" ++ showId c2 "")

$ 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 $ makeNamed ("ga_selector_undef_" ++ showId s "_" ++ showId i "")

$ 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

[makeNamed ("ga_selector_" ++ showId j "")

$ 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 -> Annoted ALTERNATIVE

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

ana_ALTERNATIVE s c =

case item c of

Subsorts ss _ -> do

mapM_ (addSubsort s) ss

return Nothing

ic -> do

let cons@(i, ty, il) = getConsType s ic

addOp c 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 (emptyAnno ()) 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 -> a -> State (Sign f e) a

anaForm :: (PosItem f, Pretty f) => Min f e -> Mix b s f e -> Sign f e

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

anaForm mef mix sign f = do

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

(globAnnos sign) (mixRules mix) f

anaF <- minExpFORMULA mef sign

$ assert (noMixfixF (checkMix mix) resF) resF

return (resF, anaF)

anaTerm :: (PosItem f, Pretty f) => Min f e -> Mix b s f e -> Sign f e

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

anaTerm mef mix sign srt pos t = do

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

(globAnnos sign) (mixRules mix) t

anaT <- oneExpTerm mef sign

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

return (resT, anaT)

basicAnalysis :: (PosItem f, Pretty f, FreeVars 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

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

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

-- ^ (BS with analysed mixfix formulas for pretty printing,

-- differences to input Sig,accumulated Sig,analysed Sentences)

basicAnalysis mef anab anas mix (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 }

bs) inSig { globAnnos = addAssocs inSig ga }

ds = reverse $ envDiags accSig

sents = reverse $ sentences accSig

cleanSig = (emptySign $ extendedInfo accSig)

{ sortSet = sortSet accSig

, emptySortSet = emptySortSet accSig

, sortRel = Rel.irreflex $ sortRel accSig

, opMap = opMap accSig

, assocOps = assocOps accSig

, predMap = predMap accSig

, globAnnos = ga }

in Result ds $

Just (newBs, ExtSign cleanSig $ declaredSymbols accSig, sents)

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

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

ExtSign (Sign () ()) Symbol,

[Named (FORMULA ())])

basicCASLAnalysis =

basicAnalysis (const return) (const return) (const return) emptyMix