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26.2 TheGeneratedCode
337
nullifthereisnone).Theselistsallowtoquicklyretrieveallincomingoralloutgoingedges
ofanode. The e edge objects containelds sourceandtarget referencingthesource and
thetargetnode. Theygiveinstantaccesstothesourceandtargetnodesofanedge. Edges
furthermorecontainaeldinNexttogivethenextedgeintheincomingringlistandaeld
outNexttogivethenextedgeintheoutgoingringlisttheyarecontainedin.Allthe3ringlists
(type,in,out)aredoublylinked(toallowforfastinsertionanddeletion),soforevery next
eldthereisalsoapreveldavailable. Thegure26.3givestheringlistimplementationof
theexamplegraphdepictedingure26.2.
Figure26.2: Incidenceexamplesituation
outHead
outNext
outNext
inHead
outHead
outNext
inNext
inNext
inNext
source
source
target
source
target
target
Figure26.3:Ringlistimplementationofincidenceexample
Incaseattributeindicesweredeclared,abalancedsearchtree(anAA-tree)iscreatedfor
eachofthem.Thetreeismaintainedbyeventhandlersthatlistentographelementcreation
anddeletion,butesp. forattributeassignment.
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338
UnderstandingandExtendingGrGen.NET
PatternMatchingandSearchPrograms
Thepatternofarule(ortest)ismatchedwithabacktrackingalgorithmbindingonepattern
elementafteranothertoagraphelement,checkingifittstothealreadyboundparts. If
itdoestsearchcontinuestryingtobindthenextpatternelement(orsucceedsbuildingthe
matchobjectfromalltheelementsboundifthelastchecksucceeds),ifitdoesnottsearch
continueswiththenextgraphelement;ifallgraphelementcandidatesforthispatternelement
areexhausted,searchbacktrackstothepreviousdecisionpointandcontinuestherewiththe
next element. . For r every pattern n to matcha search programimplementingthis s algorithm
is generated, , basically y consistingof nestedloops iteratingthe available graphelementsfor
eachpatternelement andconditioncheckingcodecontinuingsearchwiththenextelement
toinvestigate.Figure26.4showsapatternandasearchprogramgeneratedforit.
Figure26.4:Patterntosearch
1
foreach(v1:A ingraph) {
2
foreach(e1inoutgoing(v1)) {
3
if(type(e1)!=a)continue;
4
v2 =e1.tgt;
5
if(type(v2)!=B)continue;
6
foreach(e3in outgoing(v2)) {
7
if(type(e3)!=b)continue;
8
v3 =e3.tgt;
9
if(type(v3)!=C)continue;
10
foreach(e2 inoutgoing(v3)) {
11
if(type(e2)!=a)continue;
12
if(e2.tgt!=v2) continue;
13
//v1,e1,v2,e3,v3,v2constituteamatch
14
}
15
}
16
}
17
}
Ifanon-leaf-type(regardinginheritancehierarchy)istobematchedwithagraphlookup
(theoutermostloopintheexample),thenanadditionalloopisusediteratingallsubtypes
ofthe type ofthe patternelement. . If f a patternis given one or more parameters,search
normallyfollowsthegraphstructurebyiteratingtheincomingoroutgoingedgesofanodeor
determiningthesourceortargetnodeofanedge,insteadoflookingupatypeinthegraph.Ifa
patternconsistsofseveralunconnectedcomponents,severallookupsareneeded. Undirected
or arbitrary y directed pattern edges s are searched d in both, , the e incoming and the outgoing
ringlist;undirectededgesareimplementedbynormaldirectededgeswhichcangetmatched
inbothdirections.Constraintswhichmightcauseancandidatetogetrejectedarethetypeof
theelementasshownintheexample,structuralconnectionstoalreadyboundelementsand
theisomorphy constraint. . Furthermorethere e arenegativechecking,independent checking,
andattributechecking,whicharenormallydependingonmultipleelements. Othermatching
operationsarestorageaccess,storageattributeaccessandstoragemapping.
Comparedtopatternmatchingwhichmayneedalongtime,patternrewritingisavery
simple task following asimple sequence of node or edge operations, rst creating all new
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26.2 TheGeneratedCode
339
nodes thenedges,followedbyanevaluationof theattributes, , thendeleting alledges s and
nodes,nallyexecutingembeddedsequences(seetable8.1formoreonthis).
Anotableperformance optimizationallowedby the graphmodelis search state space
stepping: after r a a pattern was matched, the e list t heads of f the e type lookup p ring g lists, , the
incomingringlistsandtheoutgoingringlistsaremovedtothepositionofthematchedentries
withMoveHeadAfter, MoveInHeadAfter r and d MoveOutHeadAfter. . With h this s optimization
thepatternmatchingduringaniterationr*willstartwherethepreviousiterationstepleft
of,savingthe cost ofiteratingagainthroughalltheelements whichfailedinthe previous
iteration.
PushdownMachineforNestedandSubpatterns
Everysubpattern(asintroducedinchapter8)ishandledwithasearchprogramcorrespond-
ing to its s pattern as introduced in the e previous section. . The e interesting part is how the
subpatternsusedgetcombined,whichhappenswitha2+npushdownmachine. Itconsists
ofacallstack,containingthesubpatterninstancesfoundwith the boundelementsinthe
localvariablesofthesearchprogramframe,anopentasksstackcontainingthesubpatterns
tomatch(whenasubpatternwasmatcheditscontainedsubpatternsarepushedtothatopen
tasks stack, , then the topof the stack k gets processed), , and n n result stacks containing the
(partial)matchobjecttrees;for anormalruleapplicationn=1,for anall-bracketedrule
thenumberofmatchesisunbound. Asimulationofthismachine,i.e. thematchingprocess
ofapatternusingsubpatternsisshownonthefollowingpages.
Alternativesarehandledlikeasubpatternwithseveralpossiblepatternswhicharetried
out,therstonematchingisaccepted.Iteratedsarehandledlikesubpatternswhosetasksare
notremovedwhenthey getmatched,but onlyif matchingfailedorthemaximumamount
ofmatches was reached. . In n case ofa failure theminimumrequired amount t of matches is
inspected,iftheamountoffoundmatchesislargerorequalthenmatchingpartiallysucceeds
andcontinues withthe next opentask (orplainsucceeds ifthere areno opentasksleft),
otherwisematching ofthegivenpartialmatchfails causingmatchingtobacktrack (tothe
previousdecisionpointofin uence).
Theadvantagesofthisdesignlinearizingthepatterntreeonthecallstackaretherather
low usage of f heap memory, , the e ability y to reuse the e match programs for r the e patterns s as
introducedintheprevioussection,andtheabilitytondallmatches(thenin2+npushdown
machinestandsforthenumberofmatchesfound).
Rewritingiscarriedoutbyadepth-rsttraversalofthematchobjecttree,creatingnew
elementsbeforedescending,evaluatingattributesanddeletingoldelementsbeforeascending.
Foreachpatternpiecematchedthemodicationspeciedintherewritepartiscarriedout,
i.e. theoverallrewritegetscombinedfromtherewritesofthepatternpieces(cf. table8.1
fortheorderofrewriting).
Thesubpatternusageparametersarecomputedduringmatchingfrommatchedelements
and call expressions (inherited attribution), LHS S yielding g is s carried out t after r the e match
wasfoundduringmatchobject buildingwithinyieldstatements (synthesizedattribution),
RHSyieldingiscarriedoutduringmatchobjecttreerewritingwithinevalstatements(left
attribution,withauserdenedleft-relation).
Inthefollowing,anexamplerunofthe2+npushdownmachineisgiven:
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340
UnderstandingandExtendingGrGen.NET
:A
:D1
Open tasks stack
Call stack holding partial match
State of matching
:B
:C
:D2
:B
:C
:D
Result building stack(s)
Pattern
Match storage
Search state
Figure26.5:1.Startstate
:A
:D1
:B
:C
:D2
:B
:C
:D
:A
Pattern
State of matching
Open tasks stack
Call stack holding partial match
Result building stack(s)
Search state
Match storage
Figure26.6: 2. TheterminalpartofpatternAwasmatched
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26.2 TheGeneratedCode
341
:A
:D1
:B
:C
:D2
:B
:C
:D
:C
:B
:A
Pattern
State of matching
Open tasks stack
Call stack holding partial match
Result building stack(s)
Search state
Match storage
Figure26.7:3.ThetasksforsubpatternsBandCarepushed
:A
:D1
:B
:C
:D2
:B
:C
:D
:A
:C
:B
Pattern
State of matching
Open tasks stack
Call stack holding partial match
Result building stack(s)
Search state
Match storage
Figure26.8: 4. ThetaskforBgetsexecuted,theterminalpartofBwasmatched
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342
UnderstandingandExtendingGrGen.NET
:A
:D1
:B
:C
:D2
:B
:C
:D
:A
:B
:C
:D
Pattern
State of matching
Open tasks stack
Call stack holding partial match
Result building stack(s)
Search state
Match storage
Figure26.9: 5. ThetaskforalternativeDispushed
:A
:D1
:B
:C
:D2
:B
:C
:D
:A
:B
:C
:D1
Pattern
State of matching
Open tasks stack
Call stack holding partial match
Result building stack(s)
Search state
Match storage
Figure26.10:6. ThetaskforDgetsexecuted,D1istried,butmatchingfails
26.2 TheGeneratedCode
343
:A
:D1
:B
:C
:D2
:B
:C
:D
:A
:B
:C
:D2
Pattern
State of matching
Open tasks stack
Call stack holding partial match
Result building stack(s)
Search state
Match storage
Figure26.11: 7. ThetaskforDgetsexecuted,D2wasmatched
:A
:D1
:B
:C
:D2
:B
:C
:D
:A
:B
:D2
:C
Pattern
State of matching
Open tasks stack
Call stack holding partial match
Result building stack(s)
Search state
Match storage
Figure26.12:8. ThetaskforCgetsexecuted,Cwasmatched,amatchfortheoverallpattern
wasfound,butiscontainedonlyonthecallstack
344
UnderstandingandExtendingGrGen.NET
:A
:D1
:B
:C
:D2
:B
:C
:D
:A
:B
:D2
:C
:C
Pattern
State of matching
Open tasks stack
Call stack holding partial match
Result building stack(s)
Search state
Match storage
Figure26.13:9.ThematchofCispoppedfromthecallstackandpushedtotheresultstack
:A
:D1
:B
:C
:D2
:B
:C
:D
:A
:B
:C
:C
:D2
:D
Pattern
State of matching
Open tasks stack
Call stack holding partial match
Result building stack(s)
Search state
Match storage
Figure26.14: 10. ThematchofD2is s poppedfromthecallstackandpushedtotheresult
stack
26.2 TheGeneratedCode
345
:A
:D1
:B
:C
:D2
:B
:C
:D
:A
:C
:C
:B
:B
:D2
Pattern
State of matching
Open tasks stack
Call stack holding partial match
Result building stack(s)
Search state
Match storage
Figure26.15: 11.ThematchofBispoppedfromthecallstack,D2fromtheresultstackis
added,thecombinedmatchispushedtotheresultstack
:A
:D1
:B
:C
:D2
:B
:C
:D
:A
:B
:C
:D1
Pattern
State of matching
Open tasks stack
Call stack holding partial match
Result building stack(s)
Search state
Match storage
Figure26.16: 12. . ThematchofAis s poppedfromthecallstack,BandCfromtheresult
stackareadded,nowwegotthecombinedmatchoftheoverallpattern
346
UnderstandingandExtendingGrGen.NET
Figure26.17: Patterntosearch
Figure26.18:Hostgraphtosearchin
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