{-# OPTIONS_GHC -Wall #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE OverloadedStrings #-} module DatabaseDesign.Ampersand.Fspec.ToFspec.Calc ( deriveProofs , lambda , checkMono , showProof, showPrf, assembleECAs, conjuncts, genPAclause -- , testInterface ) where import DatabaseDesign.Ampersand.Basics (fatalMsg,Collection (isc),Identified(..),eqCl,Flippable(..)) import Data.List hiding (head) import GHC.Exts (sortWith) -- import Data.ByteString.Char8 -- import Data.ByteString.Lazy.Char8 import DatabaseDesign.Ampersand.Core.AbstractSyntaxTree hiding (sortWith) import DatabaseDesign.Ampersand.ADL1 import DatabaseDesign.Ampersand.ADL1.Expression import DatabaseDesign.Ampersand.Classes import DatabaseDesign.Ampersand.Fspec.Fspec import DatabaseDesign.Ampersand.Fspec.ShowADL (ShowADL(..), showREL) import DatabaseDesign.Ampersand.Fspec.ShowECA (showECA) import DatabaseDesign.Ampersand.Fspec.ToFspec.NormalForms (delta,conjNF,disjNF,cfProof,dfProof,nfProof,simplify,normPA,proofPA) import DatabaseDesign.Ampersand.Misc (Lang(..),Options(..),PandocFormat(ReST),string2Blocks) import Text.Pandoc.Builder import Prelude hiding (head) -- import Debug.Trace fatal :: Int -> String -> a fatal = fatalMsg "Fspec.ToFspec.Calc" head :: [a] -> a head [] = fatal 30 "head must not be used on an empty list!" head (a:_) = a conjuncts :: Rule -> [DnfClause] conjuncts = map disjuncts.exprIsc2list.conjNF.rrexp disjuncts :: Expression -> DnfClause disjuncts conj = (split (Dnf [] []).exprUni2list) conj where split :: DnfClause -> [Expression] -> DnfClause split (Dnf antc cons) (ECpl e: rest) = split (Dnf (e:antc) cons) rest split (Dnf antc cons) ( e: rest) = split (Dnf antc (e:cons)) rest split dc [] = dc -- testInterface :: Fspc -> Interface -> String -- Deze functie is bedoeld om te bedenken hoe interfaces moeten worden afgeleid uit een vers vertaalde ObjectDef. -- Nadat deze goed werkt kunnen de bewijsgenerator en de codegenerator worden gemaakt. -- testInterface :: Options -> Fspc -> Interface -> String -- testInterface flags fSpec ifc -- = "\nInterface "++ name ifc++"("++intercalate ", " [showADL r++":"++name (target r) | r<-rels]++")\n"++ -- " - The parameters correspond to editable fields in a user interface.\n "++ -- showADL ifc++"\n"++ -- " - Invariants:\n "++intercalate "\n " [showADL rule | rule<-invs]++"\n"++ -- " - Derivation of clauses for ECA-rules:" ++ -- concat [showClause fSpec (allClauses flags rule) | rule<-invs]++"\n"++ --{- -- " - ECA rules:"++concat [ "\n\n "++showECA "\n " (eca{ecaAction=normPA (ecaAction eca)}) -- ++"\n------ Derivation ----->"++showProof (codeBlock . ("\n "++) . showECA "\n ") (proofPA (ecaAction eca))++"\n<------End Derivation --" -- | eca<-ecaRs]++"\n\n"++ ---} -- " - Visible relations:\n "++intercalate "\n " (spread 80 ", " [showADL r | r<-vis])++"\n" -- where ---- showQ i (rel, shs,conj,r) ---- = "\nQuad "++show i++":\nrelation: "++showADL rel++":\nshifts: "++concat ["\n"++showADLe s |s<-shs]++"\nconjunct: "++showADL conj++"\nrule: "++showADL r++"" ----TODO: Deze code komt ook voor in ADL2Fspec.hs. Dat lijkt dubbelop, en derhalve niet goed. -- rels = nub (recur (ifcObj ifc)) -- where recur obj = [editMph (objctx o) | o<-attributes obj, editable (objctx o)]++[r | o<-attributes obj, r<-recur o] -- vis = nub (rels++map (I . target) rels) -- -- visible r = r `elem` vis -- invs = [rule | rule<-invariants fSpec, (not.null) (map makeDeclaration (relsUsedIn rule) `isc` vis)] -- -- qs = vquads fSpec -- -- ecaRs = assembleECAs fSpec ---- editable (ERel Rel{} _) = True --WHY?? Stef, welke functie is de juiste?? TODO deze functie staat ook in ADL2Fspec.hs, maar is daar ANDERS(!)... ---- editable _ = False ---- editMph (ERel r@Rel{} _) = r --WHY?? Stef, welke functie is de juiste?? TODO deze functie staat ook in ADL2Fspec.hs, maar is daar ANDERS(!)... ---- editMph e = fatal 64 $ "cannot determine an editable declaration in a composite expression: "++show e -- -- De functie spread verspreidt strings over kolommen met een breedte van n. -- -- Deze functie garandeert dat alle strings worden afgedrukt in de aangegeven volgorde. -- -- Hij probeert daarbij zo weinig mogelijk regels te gebruiken, -- -- en alleen de grens van n te overschrijden als een string zelf langer is dan n. -- spread :: Int -> String -> [String] -> [String] -- spread n str = f "" -- where f stored [] = [stored | not (null stored)] -- f [] (cs:css) = f cs css -- f stored (cs:css) | length stored > n = stored: f cs css -- | length new <= n = f new css -- | otherwise = stored: f cs css -- where new = stored++str++cs deriveProofs :: Options -> Fspc -> Blocks deriveProofs flags fSpec = para ("Rules and their conjuncts for "<>(str.name) fSpec)<> bulletList [ para ("rule r: "<>str (showADL r)<>linebreak<> "rrexp r: "<>str (showADL (rrexp r))<>linebreak<> "conjNF: "<>str (showADL (conjNF (rrexp r)))<>linebreak<> interText linebreak [ " conj: "<>str (showADL conj) | conj<-conjuncts r ] ) | r<-grules fSpec++vrules fSpec]<> para ("Transformation of user specified rules into ECA rules for "<>(str.name) fSpec)<> para (linebreak<>"--------------"<>linebreak<>"First step: determine the "<>(str.show.length) qs<>" quads:")<> bulletList [ para ( "-- quad ------------"<>linebreak<>"When relation "<>str (showADL rel)<>" is changed," <>linebreak<>str (showADL r) <>(if length (cl_conjNF ccrs)<=1 then space else " ("<>(str.show.length.cl_conjNF) ccrs<>" conjuncts)") <>" must be restored."<>linebreak<>"This quad has conjunct: "<>(str.showADL.rc_conjunct) x <>" and "<>(str.show.length.rc_dnfClauses) x<>" dnf clauses." ) <> bulletList [ para (linebreak<>"Dnf clause "<>str (showADL dc)) | dc<-rc_dnfClauses x] | Quad rel ccrs<-qs, let r=cl_rule ccrs , x<-cl_conjNF ccrs ] <> para (linebreak<>linebreak<>"Second step: assemble dnf clauses.") <> bulletList [ para ( "Dnf clause "<>str (showADL dc) <>linebreak<>"is derived from rule "<>str (showADL r) <>linebreak <>case ms of [] -> "No relations affect this clause." [rel] -> "It can be called when relation " <>str (showADL rel)<>" is affected." _ -> "It can be called when relations "<>str (commaEng "or" [showADL rel | rel<-ms])<>" are affected." ) | (ms,dc,r)<- [ (nub [ dcl |(dcl,_,_)<-cl],dc,r) | cl<-eqCl (\(_,_,dc)->dc) [(dcl,dc,r) |Quad dcl ccrs<-qs, let r=cl_rule ccrs, x<-cl_conjNF ccrs, dc<-rc_dnfClauses x] , let (_,dc,r) = head cl ] ]<> para (linebreak<>"Third step: determine "<>(str.show.length.udefrules) fSpec<>" ECA rules"<> if verboseP flags then " (Turn --verbose off if you want to see ECA rules only)" else " (Turn on --verbose if you want to see more detail)" )<> ( if verboseP flags then para ( "--------------"<>linebreak)<>bulletList derivations else fromList [] )<> bulletList [ para ( "-- ECA Rule "<>(str.show.ecaNum) ecarule<>" ---------")<> codeBlock ("\n "++showECA "\n " ecarule{ecaAction=normPA (ecaAction ecarule)})<> bulletList [ para (linebreak<>"delta expression"<>linebreak<>space<>str (showADL d) <>linebreak<>"derivation:" )<> (showProof (para.str.showADL).nfProof showADL) d<> -- nfProof produces its result in disjunctive normal form para ("disjunctly normalized delta expression"<>linebreak<>(str.showADL.disjNF) d) | verboseP flags, e@Do{}<-[ecaAction ecarule], let d = paDelta e ] | ecarule <- ecaRs] {- ++ [ linebreak<>"--------------", linebreak, linebreak<>"Fourth step: cascade blocking rules" , linebreak ]++ interText [] [ [linebreak<>"-- Raw ECA rule "<>(str.show.ecaNum) er<>"------------"<>linebreak<>str (showECA "\n " er)] | er<- ecaRs] ++ [ linebreak<>"--------------", linebreak, linebreak<>"Fifth step: preEmpt the rules (= optimize)" , linebreak ]++ {- TODO: readdress preEmpt. It is wrong interText [] [ [linebreak<>"-- Preempted ECA rule "<>(str.show.ecaNum) er<>"------------"<>linebreak<>str (showECA "\n " er)] | er<- preEmpt ecaRs] ++ -} {- [ linebreak<>"--------------", linebreak] ++ -- TODO: make an ontological analysis, which explains the delete behaviour. [ Str "Ontological analysis: ", linebreak<>" "] ++ interText [linebreak, linebreak<>" "] [ [Str (name ifc)<>"("] ++ interText ", " [str (name a)<>"["<>(str.name.target.ctx) a<>"]" |a<-attributes (ifcObj ifc)] ++ [Str "):", linebreak<>" "] | ifc<-interfaceS fSpec] ++ [ linebreak<>"--------------", linebreak <>"Analyzing interfaces:", linebreak<>" "] ++ interText [linebreak<>" "] [[Str (testInterface flags fSpec ifc)] | ifc<-take 1 (interfaceG fSpec)] ++ [ linebreak<>"--------------", linebreak] -} -} where -- visible _ = True -- We take all quads into account. qs = vquads fSpec -- the quads that are derived for this fSpec specify dnf clauses, meant to maintain rule r, to be called when relation rel is affected (rel is in r). -- assembleECAs :: Fspc -> [ECArule] commaEng :: String -> [String] -> String commaEng _ [] = "" commaEng _ [x] = x commaEng chs [x,y] = x++" "++chs++" "++y commaEng chs (x:y:ys) = x++", "++commaEng chs (y:ys) -- interText :: (Data.String.IsString a, Data.Monoid.Monoid a) => a -> [a] -> a interText _ [] = "" interText inbetween (xs:xss) = xs<>inbetween<>interText inbetween xss derivations :: [Blocks] ecaRs :: [ECArule] (ecaRs, derivations) = unzip (assembleECAs fSpec) {- [ str ("Available code fragments on rule "<>name rule<>":", linebreak ]<> interText [linebreak] [showADL rule<> " yields\n"<>interText "\n\n" [ ["event = ", str (show ev), space, str (showADL rel), linebreak ] <> [str (showADL r<>"["<>showADL rel<>":="<>showADL (actSem ev (EDcD rel) (delta (sign rel)))<>"] = r'"), linebreak ] <> ["r' = "] <> conjProof r' <> [linebreak ] <> ["viols = r'-"] <> disjProof (ECpl r') <> [ linebreak ] <> "violations, considering that the valuation of "<>showADL rel<>" has just been changed to "<>showADL (actSem ev (EDcD rel) (delta (sign rel)))<> " "<>conjProof (ECpl r) <>"\n"<> "reaction? evaluate r |- r' ("<>(str.showADL.conjNF) (notCpl r .\/. r')<>")"<> conjProof (notCpl r .\/. r')<>"\n"<> "delta: r-/\\r' = "<>conjProof (EIsc[notCpl r,r'])<> "\nNow compute a reaction\n(isTrue.conjNF) (notCpl r .\/. r') = "<>show ((isTrue.conjNF) (notCpl r .\/. r'))<>"\n"<> (if null (lambda ev (ERel rel ) r) then "lambda "<>showADL rel<>" ("<>showADL r<>") = empty\n" else -- for debug purposes: -- "lambda "<>show ev<>" "<>showADL rel<>" ("<>showADL r<>") = \n"<>(interText "\n\n".map showPr.lambda ev (ERel rel)) r<>"\n"<> -- "derivMono ("<>showADL r<>") "<>show ev<>" "<>showADL rel<>"\n = "<>({-interText "\n". map -}showPr.derivMono r ev) rel<>"\n"<> -- "\nNow compute checkMono r ev rel = \n"<>show (checkMono r ev rel)<>"\n"<> if (isTrue.conjNF) (notCpl r .\/. r') then "A reaction is not required, because r |- r'. Proof:"<>conjProof (notCpl r .\/. r')<>"\n" else if checkMono r ev rel then "A reaction is not required, because r |- r'. Proof:"{-<>(str.showPr.derivMono r ev) rel-}<>"NIET TYPECORRECT: (showPr.derivMono r ev) rel"<>"\n" --WHY? Stef, gaarne herstellen...Deze fout vond ik nadat ik het type van showProof had opgegeven. else let ERel _ _ = delta (sign rel) in "An appropriate reaction on this event is required." -- showECA "\n " (ECA (On ev rel) delt (genPAclause visible Ins r viols conj [rule]) 0) ) | rel<-relsUsedIn r -- nub [x |x<-relsUsedIn r, not (isIdent x)] -- TODO: include proofs that allow: isIdent rel' , ev<-[Ins,Del] , r'<-[subst (rel, actSem ev (EDcD rel) (delta (sign rel))) r] -- , viols<-[conjNF (ECpl r')] , True ] -- (isTrue.conjNF) (notCpl r .\/. r') | r<-[dc | cs<-[allClauses flags rule], (_,dnfClauses)<-cl_conjNF cs, dc<-dnfClauses] ] where e = rrexp rule prf = cfProof showADL e (exx',_,_) = last prf -- conjProof = showProof (para.str.showADL) . cfProof showADL disjProof = showProof (para.str.showADL) . dfProof showADL -- showPr = showProof (para.str.showADL) -- hoort bij de uitgecommentaarde code hierboven... --TODO: See ticket #105 -} -- Stel we voeren een actie a uit, die een(1) van de volgende twee is: -- {r} INS rel INTO expr {r'} ofwel -- {r} DEL rel FROM expr {r'} -- Dan toetst checkMono of r|-r' waar is op grond van de afleiding uit derivMono. -- Als dat waar is, betekent dat dat invariant r waar blijft wanneer actie a wordt uitgevoerd. checkMono :: Expression -> InsDel -> Declaration -> Bool checkMono expr ev dcl = case ruleType conclusion of Truth -> fatal 247 "derivMono came up with a Truth!" _ -> simplify expr == simplify (antecedent conclusion) && simplify (subst (dcl, actSem ev (EDcD dcl) (delta (sign dcl))) expr) == simplify (consequent conclusion) where (conclusion,_,_) = last (derivMono expr ev dcl) type Proof expr = [(expr,[String],String)] reversePrf :: Proof e -> Proof e reversePrf [] = [] reversePrf [s] = [s] reversePrf ((r,cs,e'):prf@((r',_ ,_):_)) = init rp++[(r',cs,rev e'),(r,[],"")] where rp = reversePrf prf rev "==>" = "<==" rev "<==" = "==>" rev "-->" = "<--" rev "<--" = "-->" rev x = x showProof :: (expr->Blocks) -> Proof expr -> Blocks showProof shw [(expr,_,_)] = shw expr showProof shw ((expr,ss,equ):prf) = shw expr<> para (if null ss then str equ else if null equ then str (unwords ss) else str equ<>str (" { "++intercalate " and " ss++" }"))<> showProof shw prf --where e'= if null prf then "" else let (expr,_,_):_ = prf in showHS options "" expr showProof _ [] = fromList [] showPrf :: (expr->String) -> Proof expr -> [String] showPrf shw [(expr,_,_)] = [ " "++shw expr] showPrf shw ((expr,ss,equ):prf) = [ " "++shw expr] ++ (if null ss then [ equ ] else if null equ then [ unwords ss ] else [ equ++" { "++intercalate " and " ss++" }" ])++ showPrf shw prf showPrf _ [] = [] -- derivMono provides a derivation to prove that (precondition) r is a subset of (postcondition) r'. -- This is useful in proving that an action {expr} a {expr'} maintains its invariant, i.e. that expr|-expr' holds (proven by monotony properties) -- Derivmono gives a derivation only. derivMono :: Expression -> InsDel -> Declaration -> [(Rule, [String], String)] derivMono expr -- preconditie van actie a tOp -- de actie (Ins of Del) dcl' -- re relatie, zodat de actie bestaat uit INSERT rel' INTO expr of DELETE rel' FROM expr = f (head (lambda tOp (EDcD dcl') expr++[[]])) (start tOp) where f :: [(Expression, [String], whatever)] -> (Expression, Expression) -> [(Rule, [String], String)] f [] (_,_) = [] f [(e',_,_)] (neg',pos') = [(rule (subst (dcl',neg') e') (subst (dcl',pos') e'),[],"")] f ((e',["invert"],_): prf@((_,_,_):_)) (neg',pos') = (rule (subst (dcl',neg') e') (subst (dcl',pos') e'),["r |- s <=> s- |- r-"],"<=>"): f prf (pos',neg') f ((e1,_,_): prf@((e2,_,_):_)) (neg',pos') = (rule (subst (dcl',neg') e1) (subst (dcl',pos') e1),["Monotony of "++showOp e2],"==>"): f prf (neg',pos') start Ins = (EDcD dcl',EDcD dcl' .\/. delta (sign dcl')) start Del = (EDcD dcl' ./\. notCpl (delta (sign dcl')),EDcD dcl') rule :: Expression -> Expression -> Rule rule neg' pos' | isTrue neg' = Ru { rrnm = "" , rrfps = Origin "rule generated for isTrue neg' by Calc" , rrexp = pos' , rrmean = AMeaning [A_Markup Dutch ReST (string2Blocks ReST "Waarom wordt deze regel hier aangemaakt? (In Calc.hs, regel 402)") ,A_Markup English ReST (string2Blocks ReST "Why is this rule created? (In Calc.hs, line 403)")] --TODO Stef, gaarne de explanations aanvullen/verwijderen. Dank! Han. , rrmsg = [] , rrviol = Nothing , rrtyp = sign neg' {- (neg `meet` pos) -} , rrdcl = Nothing , r_env = "" , r_usr = Multiplicity , isSignal = fatal 336 $ "erroneous reference to isSignal in rule ("++showADL neg'++") |- ("++showADL pos'++")" , srrel = fatal 337 $ "erroneous reference to srrel in rule ("++showADL neg'++") |- ("++showADL pos'++")" } | otherwise = Ru { rrnm = "" , rrfps = Origin "rule generated for not(isTrue neg') by Calc" , rrexp = neg' .|-. pos' , rrmean = AMeaning [A_Markup Dutch ReST (string2Blocks ReST "Waarom wordt deze regel hier aangemaakt? (In Calc.hs, regel 332)") ,A_Markup English ReST (string2Blocks ReST "Why is this rule created? (In Calc.hs, line 333)")] --TODO Stef, gaarne de explanations aanvullen/verwijderen. Dank! Han. , rrmsg = [] , rrviol = Nothing , rrtyp = sign neg' {- (neg `meet` pos) -} , rrdcl = Nothing , r_env = "" , r_usr = Multiplicity , isSignal = fatal 352 $ "illegal reference to isSignal in rule ("++showADL neg'++") |- ("++showADL pos'++")" , srrel = fatal 353 $ "illegal reference to srrel in rule ("++showADL neg'++") |- ("++showADL pos'++")" } showOp expr' = case expr' of EEqu{} -> "=" EImp{} -> "|-" EIsc{} -> "/\\" EUni{} -> "\\/" EDif{} -> "-" ELrs{} -> "/" ERrs{} -> "\\" EDia{} -> "<>" ECps{} -> ";" ERad{} -> "!" EPrd{} -> "*" EKl0{} -> "*" EKl1{} -> "+" EFlp{} -> "~" ECpl{} -> "-" _ -> "" {- The purpose of function lambda is to generate a derivation. Rewrite rules: -r;-s -> -(r!s) -} lambda :: InsDel -> Expression -> Expression -> [Proof Expression] lambda tOp' e' expr' = [reversePrf[(e'',txt,op) | (e'',_,txt,op)<-prf] | prf<-lam tOp' e' expr' ] where lam :: InsDel -> Expression -> Expression -> [[(Expression,Expression -> Expression,[String],String)]] lam tOp e3 expr = case expr of EIsc{} | e3==expr -> [[(e3,id,[],"")]] | length (const' expr)>0 -> [(expr,\_->expr, [derivtext tOp "mono" (inter' expr) expr],"<--") :prf | prf<-lam tOp e3 (inter' expr) ] | and [isNeg f |f<-exprIsc2list expr] -> let deMrg = deMorganEIsc expr in [(expr, deMorganEIsc, [derivtext tOp "equal" deMrg expr],"==") :prf | prf<-lam tOp e3 deMrg] | or[null p |p<-fPrfs] -> [] | otherwise -> [(expr,\_->expr, [derivtext tOp "mono" (first lc) expr],"<--") : lc] EUni{} | e3==expr -> [[(e3,id,[],"")]] | length (const' expr)>0 -> [(expr,\_->expr, [derivtext tOp "mono" (inter' expr) expr],"<--") :prf | prf<-lam tOp e3 (inter' expr) ] | and [isNeg f |f<-exprUni2list expr] -> let deMrg = deMorganEUni expr in [(expr, deMorganEUni, [derivtext tOp "equal" deMrg expr],"==") :prf | prf<-lam tOp e3 deMrg] | or[null p |p<-fPrfs] -> [] | otherwise -> [(expr,\_->expr, [derivtext tOp "mono" (first lc) expr],"<--") : lc] ECps{} | e3==expr -> [[(e3,id,[],"")]] | and [isNeg f |f<-exprCps2list expr] -> let deMrg = deMorganECps expr in [(expr, deMorganECps, [derivtext tOp "equal" deMrg expr],"==") :prf | prf<-lam tOp e3 deMrg ] -- isNeg is nog niet helemaal correct. | or[null p|p<-fPrfs] -> [] | otherwise -> [(expr,\_->expr, [derivtext tOp "mono" (first lc) expr],"<--"): lc] ERad{} | e3==expr -> [[(e3,id,[],"")]] | and [isNeg f |f<-exprRad2list expr] -> let deMrg = deMorganERad expr in [(expr, deMorganERad, [derivtext tOp "equal" deMrg expr],"==") :prf | prf<-lam tOp e3 deMrg] -- isNeg is nog niet helemaal correct. | or[null p |p<-fPrfs] -> [] | otherwise -> [(expr,\_->expr, [derivtext tOp "mono" (first lc) expr],"<--"): lc] EKl0 x -> [(expr,\e->EKl0 e,[derivtext tOp "mono" x expr],"<--") :prf | prf<-lam tOp e3 x] EKl1 x -> [(expr,\e->EKl1 e,[derivtext tOp "mono" x expr],"<--") :prf | prf<-lam tOp e3 x] ECpl x -> [(expr,\e->ECpl e,["invert"],"<--") :prf | prf<-lam (inv tOp) e3 x] EBrk x -> lam tOp e3 x _ -> [[(e3,id,[],"")]] where sgn = sign expr fPrfs = case expr of EUni{} -> [lam tOp e3 f |f<-exprUni2list expr, isVar f e3] EIsc{} -> [lam tOp e3 f |f<-exprIsc2list expr, isVar f e3] ECps{} -> [lam tOp e3 f |f<-exprCps2list expr, isVar f e3] ERad{} -> [lam tOp e3 f |f<-exprRad2list expr, isVar f e3] _ -> fatal 428 ("fPrfs is not defined.Consult your dealer!") lc = longstcomn vars++concat (drop (length rc-1) (sortWith length rc)) rc = remainders vars vars vars = map head fPrfs const' e@EUni{} = [f |f<-exprUni2list e, isConst f e3] const' e@EIsc{} = [f |f<-exprIsc2list e, isConst f e3] const' expr'' = fatal 440 $ "'const'("++ show expr''++")' is not defined.Consult your dealer!" inter' e@EUni{} = foldr (.\/.) (notCpl (EDcV sgn)) [f |f<-exprUni2list e, isVar f e3] inter' e@EIsc{} = if and [sgn==sign f | f<-exprIsc2list e, isVar f e3] then foldr (./\.) (EDcV sgn) [f | f<-exprIsc2list e, isVar f e3] else fatal 532 ("signature error in inter' "++show [(showADL f,showSign (sign f)) | f<-exprIsc2list e, isVar f e3]) inter' expr'' = fatal 443 $ "'inter'("++ show expr''++")' is not defined.Consult your dealer!" -- lam tOp e f = [] -- longstcomn determines the longest prefix common to all xs in xss. longstcomn :: (Eq a) => [[(a, b, c, d)]] -> [(a, b, c, d)] longstcomn xss | or [null xs | xs<-xss] = [] | length (eqCl first xss)==1 = head [head prf | prf<-xss]: longstcomn [tail prf | prf<-xss] | otherwise = [] -- remainders determines the remainders. remainders :: (Eq a) => [[(a, b, c, d)]] -> [[(a, b, c, d)]] -> [[(a, b, c, d)]] remainders _ xss | or [null xs | xs<-xss] = xss | length (eqCl first xss)==1 = remainders xss [tail prf | prf<-xss] | otherwise = xss isConst :: (ConceptStructure a, ConceptStructure b) => a->b->Bool isConst e f = null (relsUsedIn e `isc` relsUsedIn f) isVar :: (ConceptStructure a, ConceptStructure b) => a->b->Bool isVar e f = not (isConst e f) derivtext :: InsDel -> String -> Expression -> Expression -> String derivtext tOp "invert" e'' expr = sh tOp++showADL e''++" means "++sh (inv tOp)++showADL expr++"." derivtext tOp "mono" e'' expr = "("++showADL e''++"->"++showADL expr++") is monotonous, so "++sh tOp++showADL e''++" means "++sh tOp++showADL expr++"." derivtext _ txt _ _ = txt sh :: InsDel -> String sh Ins = "insert into " sh Del = "delete from " inv :: InsDel -> InsDel inv Ins = Del inv Del = Ins first :: [(a,b,c,d)] -> a first ((e'',_,_,_):_) = e'' first _ = fatal 472 "wrong pattern in first" ruleType :: Rule -> RuleType ruleType r = case rrexp r of EEqu{} -> Equivalence EImp{} -> Implication _ -> Truth -- | Action semantics for inserting a delta into a relation dcl. actSem :: InsDel -> Expression -> Expression -> Expression actSem Ins dcl delt | sign dcl/=sign delt = fatal 598 "Type error in actSem Ins" | dcl==delt = dcl | otherwise = disjNF (dcl .\/. delt) actSem Del dcl delt | sign dcl/=sign delt = fatal 598 "Type error in actSem Del" | dcl==delt = notCpl (EDcV (sign dcl)) | otherwise = conjNF (dcl ./\. notCpl delt) -- | assembleECAs assembles larger chunks of code, because it combines acts that are triggered by the same event. assembleECAs :: Fspc -> [(ECArule,Blocks)] assembleECAs fSpec = [eca i | (eca,i) <- zip ecas [(1::Int)..]] where ecas :: [Int->(ECArule,Blocks)] ecas = [ (\ruleNr->( ECA ecaEvt delt normEcaAct ruleNr , para ("Let us analyse what happens "<>str (show (On ev rel))<>".")<> bulletList [ txt | (_,_,_,txt)<-acts]<> ( if length ecaProof>1 then para ("The resulting action is:\n ")<> showProof (codeBlock . ("\n "++) . showECA "\n ") ecaProof else fromList [] )<> para ("These results lead to the following ECA-rule:\n ")<> (codeBlock . ("\n "++) . showECA "\n ".ecaRule) ruleNr ) ) | rel <- allDecls fSpec ++ [ Isn c | c<-allConcepts fSpec, c/=ONE] -- This is the relation in which a delta is being inserted or deleted. , let relEq = [ q | q<-vquads fSpec, qDcl q==rel] -- Gather the quads with the same declaration (qDcl). A quad has a declaration (qDcl) and clauses (qClauses) , let quadClauses = (nub.map qClauses) relEq -- these are the clauses , let EDcD delt = delta (sign rel) -- delt is a placeholder for the pairs that have been inserted or deleted in rel. , ev<-[Ins,Del] , let acts = [ -- go through all the events that affect that clause: (normPA act, conj, rule, para ("Let us analyse clause "<>str (showADL expr)<>" from rule "<>(singleQuoted.str.name) rule<>".")<> para ("event = "<>str (show ev)<>space<>str (showREL rel)<>" means doing the following substitution")<> para (str (showADL clause<>"["<>showREL rel<>":="<>showADL (actSem ev (EDcD rel) (delta (sign rel)))<>"] = clause'"))<> para ("clause' = "<>str (showADL ex')<> if clause'==ex' then ", which is already in conjunctive normal form."<>linebreak else ", which has conjunctive normal form: "<>linebreak<>str (showADL clause') )<> para ("Let us compute the violations to see whether invariance is maintained."<>linebreak<> "This means to negate the result (notClau = notCpl clause'): ")<> (showProof (para.str.showADL). cfProof showADL) notClau<> para ("So, notClau has CNF: "<>str (showADL viols )<>linebreak<> ( if viols==viols' then "This expression is in disjunctive normal form as well." else str ("In DNF, notClau is: "<>showADL viols'<>".")))<> ( if isTrue clause' then para ("This result proves the absence of violations, so a reaction of doing nothing is appropriate."<>linebreak <>"Just for fun, let us try to derive whether clause |- clause' is true... ")<> (showProof (para.str.showADL). cfProof showADL) (expr .|-. clause') else para ("This result does not prove the absence of violations, so we cannot conclude that invariance is maintained."<>linebreak<> "We must compute a reaction to compensate for violations..."<>linebreak<> "That would be to reinsert violations that originate from "<> ( if ev==Ins then str (showADL (conjNF negs))<>" into "<> str (showADL (disjNF poss))<>"." else str (showADL (disjNF poss))<>" into "<> str (showADL (conjNF negs))<>"." )<>linebreak<>"deltFr: ")<> (showProof (para.str.showADL). dfProof showADL) deltFr<> ( let pr=proofPA act in if length pr>1 then para "Now let us remove redundancy from the ECA action:\n "<> showProof (codeBlock . ("\n "++) . showECA "\n ") (proofPA act) else fromList [] ) {- <> "To finish the analysis of case "<>str (show ev)<>space<>str (showADL rel) <>", let us compute the contents of "<>str (showADL toExpr)<>" after insertion of viols."<>linebreak <> ( if length (nub [sign viols, sign viols', sign toExpr])>1 then fatal 248 ("viols"<>showSign (sign viols) <>" "<>showADL viols <>"\n"<> "viols'"<>showSign (sign viols')<>" "<>showADL viols'<>"\n"<> "toExpr"<>showSign (sign toExpr)<>" "<>showADL toExpr) else if ev==Ins then (showProof (para.str.showADL). cfProof showADL) (viols'.\/.toExpr)<>linebreak else (showProof (para.str.showADL). dfProof showADL) (notCpl viols./\.toExpr)<>linebreak ) -} )) | Clauses ts rule<-quadClauses, conj<-ts -- get conjuncts from the clauses , clause@(Dnf antcs conss) <- rc_dnfClauses conj -- the DNF form of each clause , let expr = dnf2expr clause -- Note that this differs from: rc_conjunct conj , let vee = EDcV (sign expr) , let ex' = subst (rel, actSem ev (EDcD rel) (delta (sign rel))) expr -- the clause after the edit action , let clause' = conjNF ex' -- its CNF , not (isTrue clause') , let notClau = notCpl clause' -- the violations after the edit action , let viols = conjNF notClau -- the violations after the edit action , let viols' = disjNF notClau -- the violations after the edit action , let negs = if (length.nub.map sign) (vee:antcs)>1 then fatal 265 ("type inconsistencies in antcs: "++show (map showADL (vee:antcs))) else foldr (./\.) vee antcs , let poss = if (length.nub.map sign) (vee:conss)>1 then fatal 265 ("type inconsistencies in conss: "++show (map showADL (vee:conss))) else foldr (.\/.) (notCpl vee) conss , let frExpr = case ev of Ins -> disjNF (notCpl negs) Del -> disjNF poss , let deltFr = if sign poss/=sign negs then fatal 274 ("type inconsistencies in deltFr: "++showADL clause) else if ev==Ins then (subst (rel, actSem ev (EDcD rel) (delta (sign rel)))) negs ./\. notCpl poss else (notCpl . subst (rel, actSem ev (EDcD rel) (delta (sign rel)))) poss ./\. negs , let deltFr' = disjNF deltFr , rel `elem` relsMentionedIn frExpr , let toExpr = if ev==Ins then disjNF poss else disjNF (notCpl negs) , let visible _ = True , if length (nub (map sign [toExpr, deltFr', expr]))>1 then fatal 285 "type problem" else True , let act = genPAclause visible Ins toExpr deltFr' [(expr,[rule])] ] , let ecaAct = ALL (map fst4 acts -- The following acts add the implicit rules, which allows the user to add and delete atoms from concepts in a safe way. ++ [act' | (ev',rel',act')<-rulesDecls++rulesGens rel, ev==ev', rel==rel' ] ) [ (rc_conjunct conj,[rule]) | (_,conj,rule,_)<-acts] --motivation is of type [(Expression,[Rule])] , let normEcaAct = normPA ecaAct , let ecaProof = proofPA ecaAct , let ecaEvt = On ev rel , let ecaRule = ECA ecaEvt delt normEcaAct ] -- the following eca-rules are derived from the typing rules, rather than explicit rules specified by users. -- This concerns the following rules: -- Each declaration "RELATION r[A*B]" represents the rule "RULE r[A*B] |- V[A*B]" -- Besides, for every A, B: "RULE I[A]*I[B] = V[A*B]" -- For every "CLASSIFY A ISA B" we get "RULE I[A] |- I[B]" -- For every "CLASSIFY A IS B /\ C" we get "RULE I[A] |- I[B]" and "RULE I[A] |- I[C]" -- The results of both classify statements are available through vgens. -- Finally, for every Atom c a there is a rule "RULE 'a' |- I[c]" -- The eca-rules that can be derived from these rules are produced by ecasFromTypes {- V[A*B] is implicit, so we don't generate ECA (On Ins rel) delt (Do Ins (Vs (Sign a b)) delt motive). Neither do we generate ECA (On Del (Vs (Sign a b))) delt (Do Del rel delt motive). However, we do generate: ECA (On Ins rel) delt (Do Ins (Isn a) ((dlt.<>.flp dlt).-.EDcI a) motive) and: ECA (On Ins rel) delt (Do Ins (Isn b) ((flp dlt.<>.dlt).-.EDcI b) motive), because the delta to be inserted might contain new atoms. Similarly, upon deletion of an atom from a concept we must delete the appropriate links from relations that share this concept. So, we generate ECA (On Del (Isn a)) delt (Do Del rel (delt.:.V[A*B]) motive) and: ECA (On Del (Isn b)) delt (Do Del rel (V[A*B].:.delt) motive) ECA-rules that are derivable from relation declarations are generated by rulesDecls -} rulesDecls :: [(InsDel, Declaration, PAclause)] rulesDecls = concat [ [ (Ins, rel, Do Ins (Isn a) ((dlt.:.flp dlt ./\. EDcI a).-.EDcI a) []) , (Ins, rel, Do Ins (Isn b) ((flp dlt.:.dlt ./\. EDcI b).-.EDcI b) []) , (Del, Isn a, Do Del rel (delta (Sign a a).:.vee) []) , (Del, Isn b, Do Del rel (vee.:.delta (Sign b b)) []) ] | rel <- allDecls fSpec, let dlt = delta (sign rel) , let a=source rel, let b=target rel , let vee = (EDcV . sign) rel ] {- We generate: for every "RULE I[A] |- I[B]": ECA (On Ins (Isn a)) delt (Do Ins (Isn b) (EDcD delt) motive) and: ECA (On Del (Isn b)) delt (Do Del (Isn a) (EDcD delt) motive) for every "RULE 'a' |- I[c]": ECA (On Del (Isn c)) ('a','a') (Blk motive) -} rulesGens :: Declaration -> [(InsDel, Declaration, PAclause)] rulesGens rel = concat [ [ (Ins, Isn s, Do Ins (Isn g) dlt []) , (Del, Isn g, Do Del (Isn s) dlt []) ] | let dlt = delta (sign rel), (s,g) <- fsisa fSpec ] fst4 (x,_,_,_) = x -- | de functie genPAclause beschrijft de voornaamste mogelijkheden om een expressie delta' te verwerken in expr (met tOp'==Ins of tOp==Del) -- TODO: Vind een wetenschappelijk artikel waar de hier beschreven transformatie uitputtend wordt behandeld. -- TODO: Deze code is onvolledig en misschien zelfs fout.... genPAclause :: (Declaration->Bool) -- ^True if a relation may be changed (i.e. is editable) -> InsDel -- ^the type of action: Insert or Delete -> Expression -- ^the expression in which a delete or insert takes place -> Expression -- ^the delta to be inserted or deleted -> [(Expression,[Rule])] -- ^the motivation, consisting of the conjuncts (traced back to their rules) that are being restored by this code fragment. -> PAclause genPAclause editAble tOp' expr1 delta1 motive = genPAcl delta1 tOp' expr1 where testPA i l r ex = if (source l,target r)/=(source ex,target ex) then fatal i ("test with sign deltaX = ["++show (source l)++"*"++show (target r)++"], and sign expr = "++show (sign ex)++":\ndeltaX = "++showADL (l.:.r)++"\nexpr = "++show ex) else if source r/=target l then fatal i ("test with source r = "++show (source r)++", and target l = "++show (target l)++":\nl"++showSign (sign l)++" = "++showADL l++"\nr"++showSign (sign r)++" = "++showADL r++"\nexpr = "++show ex) else id genPAcl deltaX tOp expr = case (tOp, expr) of (_ , EEqu{}) -> Blk [(expr, nub [r |(_,rs)<-motive, r<-rs])] (_ , EImp{}) -> Blk [(expr, nub [r |(_,rs)<-motive, r<-rs])] (_ , EFlp x) -> genPAcl (flp deltaX) tOp x (_ , EBrk x) -> genPAcl deltaX tOp x (Ins, ECpl x) -> genPAcl deltaX Del x (Del, ECpl x) -> genPAcl deltaX Ins x (Ins, EUni{}) -> CHC [ genPAcl deltaX Ins f | f<-exprUni2list expr{-, not (f==expr1 && Ins/=tOp') -}] motive -- the filter prevents self compensating PA-clauses. (Ins, EIsc{}) -> ALL [ genPAcl deltaX Ins f | f<-exprIsc2list expr ] motive (Del, EUni{}) -> ALL [ genPAcl deltaX Del f | f<-exprUni2list expr {-, not (f==expr1 && Del/=tOp') -}] motive -- the filter prevents self compensating PA-clauses. (Del, EIsc{}) -> CHC [ genPAcl deltaX Del f | f<-exprIsc2list expr ] motive (Ins, EDif (l,r)) -> CHC [ genPAcl deltaX Ins l, genPAcl deltaX Del r ] motive (Del, EDif (l,r)) -> CHC [ genPAcl deltaX Del l, genPAcl deltaX Ins r ] motive (Ins, EDia (l,r)) -> CHC [ ALL [ genPAcl (testPA 986 (deltaX) (flp r) l $ deltaX.:.flp r ) Ins l , genPAcl (testPA 987 (flp l) (deltaX) r $ flp l.:.deltaX ) Ins r] motive , ALL [ genPAcl (testPA 988 (deltaX) (notCpl (flp r)) l $ deltaX.:.notCpl (flp r)) Del l , genPAcl (testPA 989 (deltaX) (flp r) l $ deltaX.:.flp r ) Ins l] motive , ALL [ genPAcl (testPA 990 (notCpl (flp l)) (deltaX) r $ notCpl (flp l).:.deltaX) Del r , genPAcl (testPA 991 (flp l) (deltaX) r $ flp l.:.deltaX ) Ins r] motive , ALL [ genPAcl (testPA 992 (deltaX) (notCpl (flp r)) l $ deltaX.:.notCpl (flp r)) Del l , genPAcl (testPA 993 (notCpl (flp l)) (deltaX) r $ notCpl (flp l).:.deltaX) Del r] motive ] motive (Del, EDia (l,r)) -> GCH [ (Del, (testPA 995 (deltaX) (flp r) l $ deltaX.:.flp r), genPAcl (EMp1 "a" (source l).*.EMp1 "b" (target l)) tOp l) , (Ins, (testPA 996 (deltaX) (flp (notCpl r)) l $ deltaX.:.flp (notCpl r)), genPAcl (EMp1 "a" (source l).*.EMp1 "b" (target l)) tOp l) , (Del, (testPA 997 (flp l) (deltaX) r $ flp l.:.deltaX), genPAcl (EMp1 "a" (source r).*.EMp1 "b" (target r)) tOp r) , (Ins, (testPA 998 (notCpl (flp l)) (deltaX) r $ notCpl (flp l).:.deltaX), genPAcl (EMp1 "a" (source r).*.EMp1 "b" (target r)) tOp r) ] motive (Ins, ERrs (l,r)) -> CHC [ genPAcl (testPA 1000 (notCpl r) (flp deltaX) l $ notCpl r.:.flp deltaX) Del l , genPAcl (testPA 1001 (l) (deltaX) r $ l.:.deltaX) Ins r ] motive (Del, ERrs (l,r)) -> GCH [ (Ins, (testPA 1003 (notCpl r) (flp deltaX) l $ notCpl r.:.flp deltaX), genPAcl (EMp1 "a" (source l).*.EMp1 "b" (target l)) tOp l) , (Del, (testPA 1004 (l) (deltaX) r $ l.:.deltaX), genPAcl (EMp1 "a" (source r).*.EMp1 "b" (target r)) tOp r) ] motive (Ins, ELrs (l,r)) -> CHC [ genPAcl (testPA 1006 (flp deltaX) (notCpl l) r $ flp deltaX.:.notCpl l) Del r , genPAcl (testPA 1007 (deltaX) (r) l $ deltaX.:.r ) Ins l ] motive (Del, ELrs (l,r)) -> GCH [ (Ins, (testPA 1009 (flp deltaX) (notCpl l) r $ flp deltaX.:.notCpl l), genPAcl (EMp1 "a" (source r).*.EMp1 "b" (target r)) tOp r) , (Del, (testPA 1010 (deltaX) (r) l $ deltaX.:.r), genPAcl (EMp1 "a" (source l).*.EMp1 "b" (target l)) tOp l) ] motive (Ins, ECps (l,r)) -> CHC [ GCH [ (Ins, (testPA 1012 (deltaX) (flp r) l $ deltaX.:.flp r), genPAcl (EMp1 "a" (source l).*.EMp1 "b" (target l)) tOp l) , (Ins, (testPA 1013 (flp l) (deltaX) r $ flp l.:.deltaX), genPAcl (EMp1 "a" (source r).*.EMp1 "b" (target r)) tOp r) ] motive , New (source r) (\x->ALL [ genPAcl (deltaX.*.EMp1 x (target l)) Ins l , genPAcl (EMp1 x (source r).*.deltaX) Ins r] motive) motive ] motive (Del, ECps (l,r)) -> CHC [ genPAcl (testPA 1018 (deltaX) (flp r) l $ deltaX.:.flp r) Del l , genPAcl (testPA 1019 (flp l) (deltaX) r $ flp l.:.deltaX) Del r ] motive (Ins, ERad (l,r)) -> CHC [ genPAcl (testPA 1021 (deltaX) (notCpl (flp r)) l $ deltaX.:.notCpl (flp r)) Ins l , genPAcl (testPA 1022 (notCpl (flp l)) (deltaX) r $ notCpl (flp l).:.deltaX) Ins r ] motive (Del, ERad (l,r)) -> CHC [ GCH [ (Del, (testPA 1024 (deltaX) (flp r) l $ deltaX.:.flp r), genPAcl (EMp1 "a" (source l).*.EMp1 "b" (target l)) tOp l) , (Del, (testPA 1025 (flp l) (deltaX) r $ flp l.:.deltaX), genPAcl (EMp1 "a" (source r).*.EMp1 "b" (target r)) tOp r) ] motive , New (source r) (\_->Nop motive) motive ] motive (Ins, EPrd (l,r)) -> ALL [ genPAcl (EDcV (Sign ONE (source deltaX)).:.deltaX) Ins (EDcV (Sign ONE (source r)).:.r) , genPAcl (deltaX.:.EDcV (Sign (target deltaX) ONE)) Ins (l.:.EDcV (Sign (target l) ONE)) ] motive (Del, EPrd (l,r)) -> ALL [ genPAcl (EDcV (Sign ONE (source deltaX)).:.deltaX) Del (EDcV (Sign ONE (source r)).:.r) , genPAcl (deltaX.:.EDcV (Sign (target deltaX) ONE)) Del (l.:.EDcV (Sign (target l) ONE)) ] motive (_ , EKl0 x ) -> genPAcl (deltaK0 deltaX tOp x) tOp x (_ , EKl1 x ) -> genPAcl (deltaK1 deltaX tOp x) tOp x (_ , EDcD d) -> if editAble d then Do tOp d deltaX motive else Blk [(expr, nub [r |(_,rs)<-motive, r<-rs])] (_ , EDcI c) -> if editAble (Isn c) then Do tOp (Isn c) deltaX motive else Blk [(expr, nub [r |(_,rs)<-motive, r<-rs])] (_ , EDcV{}) -> Blk [(expr, nub [r |(_,rs)<-motive, r<-rs])] (_ , EMp1{}) -> Blk [(expr, nub [r |(_,rs)<-motive, r<-rs])] (_ , EEps{}) -> Nop [(expr, nub [r |(_,rs)<-motive, r<-rs])] {- (_ , _) -> fatal 767 ( "(Stef?) Non-exhaustive patterns in the recursive call\n" ++"doCod ("++showADL deltaX++") -- deltaX\n "++show tOp++" -- tOp\n ("++showADL expr++") -- expr\n"++ "within function\ndoCode "++show tOp'++" -- tOp'\n ("++showADL expr1++") -- expr1\n ("++showADL delta1++") -- delta1\n"++ concat [ "while trying to maintain conjunct "++showADL conjunct++ "\nfrom rule "++intercalate "\n " [show r | r<-rs] | (conjunct,rs)<-motive ] ++ if null motive then "null motive" else "" ) -} deltaK0 :: t -> InsDel -> t1 -> t deltaK0 delta' Ins _ = delta' -- error! (tijdelijk... moet berekenen welke paren in x gezet moeten worden zodat delta |- x*) deltaK0 delta' Del _ = delta' -- error! (tijdelijk... moet berekenen welke paren uit x verwijderd moeten worden zodat delta/\x* leeg is) deltaK1 :: t -> InsDel -> t1 -> t deltaK1 delta' Ins _ = delta' -- error! (tijdelijk... moet berekenen welke paren in x gezet moeten worden zodat delta |- x+) deltaK1 delta' Del _ = delta' -- error! (tijdelijk... moet berekenen welke paren uit x verwijderd moeten worden zodat delta/\x+ leeg is)