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8.3 LocalVariables,OrderedEvaluation,andYieldingOutwards
97
TherstexampleforLHSyieldingfollowswithinanindependentachainpiecebypiece
tosomeaprioriunknownendnode,andyieldsthisendnodechainpiecebychainpieceagain
outwards tothechainstart. . Thereit t is usedasinputtoanother chain n (maybe thesame
chain,maybeoverlappingduetotheindependent),linkingallthenodesofthischaintothe
endnodeoftheformer.
Whenyieldingfromaniteratedpatternthere’stheproblemthateachyieldingassignment
fromaniteratedinstancewouldoverwritetheonedefvariablefromoutsidetheiterated,while
oneisinterestedmostofthetimeinsomeaccumulationofthevalues,e.g. summingintegers
orconcatenatingstrings. Thiscanbeachievedwithaforloopiteratingadefvariableinside
aniteratedforallthematchesoftheiteratedpatternreferencedbyname,allowingtoassign
toanoutsidedefvariableavaluecomputedfromthedefvariableandthevalueoftheiterated
defvariable.
ThisisshowninthesecondexampleforLHSyielding,summingtheintegerattribute a
ofnodesoftypeNadjacenttoastartnode,matchedwithaniterated.
EXAMPLE(49)
1
testsumOfWeight(start:Node): (int,int)
2
{
3
defvarsum:int =0;
4
defvarv:int=0;
5
6
iteratedit{
7
defvari:int;
8
9
start--> n:N;//nodeclassN {a:int;}
10
11
yield {
12
yieldi = n.a;
13
yieldv =42; // visassigned 42multipletimes
14
}
15
}
16
17
yield {
18
for(iinit)
19
{
20
yieldsum= sum+ i;
21
}
22
}
23
24
return(sum,v);
25
}
Incasenoaccumulationisneededbutasimplecountoftheiteratedmatchesissucient,
onecanemploythecountoperatoronaniterated(thatmusthavebeennamedbefore),as
displayedinthefollowingexample(thecountisonlyavailableinayieldorevalblock).
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98
SubpatternsandYielding
EXAMPLE(50)
1
testcountOfEdges(start:Node) :(int)
2
{
3
defvarsum:int =0;
4
5
iteratedit{
6
start-->;
7
}
8
9
yield {
10
yieldsum= count(it);
11
}
12
13
return(sum);
14
}
8.4 FlowExample,RegularExpressionSyntax,andLocking
Patternmatchingandrewritingoccursintwocompletelydistinctpasses,separatedbythe
part-patternmatches tree of thecombinedpatterns. . During g each pass, input andoutput
parametersmaybecomputedandpassed;withexplicitpassingforsubpatterns,andimplicit
passingfornestedpatterns(whichcandirectlyaccessthecontentoftheircontainedpattern).
Firstthepatternis matchedwithrecursivedescent alongside patternnesting andsub-
patterncalling, employingsomehelper r stacksinadditiontothecallstack(thepushdown
machineisexplainedinmoredetailin26.2). Matchingoccursstrictlytop-down(orfromthe
outsidetothenestedinsidepatterns),rstthegraphletsofthecurrentpatternarematched,
thencontroldescends tothenestedandsubpatterns. . Duringmatching,input t parameters
maybepassed,esp. forwardingjustmatchedelementsorattributesfromthem;theyallow
toin uencethematchingprocess.
Whenacompletematchisfound,whileascendingagain,unwindingthecallstack,output
pattern-defparametersarepassedbottom-up(orfromtheinsidetothecontainingoutside
patterns)withyieldblocksandyieldassignmentswithinthoseblocks,oryieldbindings
of def parametersinasubpatterncall. . Duringthis s ascent,thepart-patternmatchestree
isassembled,eachmatchofapatterncontainsthematchesofitsnestedpatternsandused
subpatternswhenitisleft.
Intherewritestep,thematchestreeisvisitedrecursivelyagain,creatingthenewnodes
ofthecurrent pattern,thendescending tothe nestedpatternsandsubpatterns,executing
theirchanges,andaftertheyreturned,executingallotherchanges ofthepattern. . During
thisvisit,rewriteinputparametersmaybepassed,forforwardingjustcreatedelements(or
computedvalues).
Onascendingagainfrom apattern,the rewrite-defelements s areassignedfromyield
assignmentsintheevalblocks,oryieldbindingsofdefrewriteparametersinasubpattern
rewritecall.(Technically,nestedpatternsarehandledlikesubpatterns,withparameterpass-
ingforaccessedelementsofthecontainingpatternautomaticallyinsertedbythecompiler.)
Let’stakealookatanexample,withFigure8.1depictingtheinputandoutputparameter
passingduringthematchingofExample8.4,andFigure8.2depictingtheinputandoutput
parameter passing g during the rewriting of Example 8.4 (which is s an extended version of
Example8.1).
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8.4 FlowExample,RegularExpressionSyntax,andLocking
99
EXAMPLE(51)
1
rule r(a:Node): (Node, int)
2
{
3
a--> b:Node;
4
5
defvari:int;
6
optional o{
7
a--> .-->c:N;
8
yield {yieldi= c.i;}
9
10
modify {
11
}
12
}
13
14
defd:Node;
15
p:P(b, yield d);
16
17
modify{
18
b--> u:Node;
19
return(d, i);
20
}
21
}
22
23
patternP(n:Node,defrm:Node)
24
{
25
n--> .-->m:Node;
26
yield {yieldrm =m;}
27
}
Figure8.1:Parameter owinmatching
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100
SubpatternsandYielding
EXAMPLE(52)
1
rule r(a:Node): (Node, int,Node,int) {
2
a--> b:Node;
3
defvari:int;
4
optional o{
5
a--> .-->c:N;
6
yield { { yieldi i =c.i; }
7
8
modify {
9
eval{yieldj = i+ u.i;}
10
}
11
}
12
defd:Node;
13
p:P(b, yield d);
14
15
modify{
16
defe:Node;defvar j:int;
17
b--> u:N;
18
p(u,yielde);
19
return(d, i, e,j);
20
}
21
}
22
patternP(n:Node,defrm:Node) modify(k:Node,def x:Node) {
23
n--> .-->m:Node;
24
yield { { yieldrm= = m; }
25
26
modify{
27
m--> k;m -->l:Node;
28
eval{ yield x= l; }
29
}
30
}
Figure8.2: Parameter owinrewriting
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8.4 FlowExample,RegularExpressionSyntax,andLocking
101
InExample8.4,arulerismatched,whichcontainsanestedoptionalpatternoanduses
asubpatternP.Therulematchesfromitsinputnodeaonaneighbouringnodebandhands
itintothesubpatternp.Intheoptionalpatternitmatchesatwo-stepneighbouringnodec
fromaon.ThesubpatternPmatchesfromitsinputparameternonatwo-stepneighbouring
nodem.
Adefvariableiisdeclaredinthepattern,andyieldassignedfromtheoptionaloan
attributeofthecfoundthere.Anotherdefvariabledisdeclaredinthepattern,andassigned
fromthesubpatterncallpwithayieldparameterpassing. Thetwopatterndefvariables
arethenreturnedoutofruler. ThesubpatternPyieldstoitsoutputdefparameterrm
themfoundinitsbody.
IntheextendedExample8.4,therewritepartoftherulercreatesanodeu,linksittob,
andhandsitintothesubpatternrewriteemploymentof p. Therewritepartofsubpattern
Pcreatesanodelandlinksittom. Additionally,anedgeisinsertedinbetweenmandthe
rewriteinputparameterk.
Adefvariablejisdeclaredintherewritepartof r,andyieldassignedfromtheeval
insidetherewritepartoftheoptionalo. Anotherdef f variableeisdeclaredintherewrite
part, and assigned fromthe subpatternrewrite callp. . Thetworewrite-def f variables are
thenreturnedoutoftherule,inadditiontothetwopattern-defvariables. Thesubpattern
yieldsfromitsevalparttoitsoutputdefrewriteparameterxtheljustcreated.
Bottomline:youcan exiblycombinepatternswithnestedandsubpatterns,includingin-
putandoutputparameters.Youcanpassparametersinduringmatchingalongsidematching
order.Whenmatchingcompleted,duringmatch-treebuilding,youcanyieldelementsfound
incontainedpatterns out. . Whentherewriteisapplied,youcanpassparametersinalong-
sidethebuildupofthepatterns,andyieldelementsoutoncemore. Butnotonlyarethose
twopasses strictly distinct,but alsoarethe parameterpassingdirections strictly distinct,
rstisallinputparameterpassingcarriedoutduringdescent,thenisalloutputparameter
synthesizingcarriedoutduringascent.
RegularExpressionSyntax
In addition n to the already y introduced d syntax x for r the e nested patterns s with the e keywords
negative,independent,alternative,iterated,multipleandoptional,thereisamore
lightweight syntax x resembling g regular expressions available; when n used together r with h the
subpatternsityieldsgraphrewritespecicationswhichlooklikeEBNF-grammarswithem-
beddedactions. Besides s reducing syntacticalweight, , they y oer constructs for matchinga
patternaboundednumberoftimes(samenotationastheonefortheboundediterationin
thesequences).
iterated f P g
(P)*
multiple f P g
(P)+
optional f P g
(P)?
alternative f l1 f P1 g .. . lk k f Pk g g
(P1|..|Pk)
negative f P g
(P)
independent f P g
&(P)
modify f R g
f+ R R g
replace f f R g
f- R R g
-
(P)[k] / / (P)[k:l] ] / / (P)[k:*]
Table8.2:Mapofnestedpatternsinkeywordsyntaxtoregularexpressionsyntax
UnderstandingGrGen.NET-subpatternsmaybeeasiergivenknowledgeaboutEBNF-
grammars when n we compare them to those. . We e nd then that t rules resemble e grammar
axioms,subpatternsresemblenonterminals,andgraphletsresembleterminalsymbols;nested
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102
SubpatternsandYielding
patterns aresimilar toEBNF operators,andtherewrite partcorresponds tothesemantic
actions of syntax directedtranslation. . Negative e andindependent patterns are usedto ex-
plicitlycheckcontextconstraints(everygraphletassuchisalreadyabletomatchpiecesthat
onewouldorcouldclassifyascontext,graphrewritingallowsforderivationsthatarehighly
adaptabletothesurroundingparts). See[Jak11]formoreonthis.
EXAMPLE(53)
1
testmethod
2
{
3
m:Method<--n:Name; //signatureofmethodconsisting ofname
4
(m <-- :Variable;)* // and0-nparameters
5
6
:AssignmentList(m);//bodyconsistingof alistofassignmentstatements
7
}
8
9
patternAssignmentList(prev:Node)
10
{
11
(//nothingora linkedassignmentandagainalist
12
prev--> a:Assign; //assignmentnode
13
a-:target-> v:Variable;//whichhasa variableastarget
14
:Expression(a); //andanexpressionwhichdefinesthelefthandside
15
:AssignmentList(a); // nextone, plz
16
)?
17
}
18
19
patternExpression(root:Expr)
20
{
21
(//expressionmaybea binaryexpressionofan operatorand two expresions
22
root<--expr1:Expr;
23
:Expression(expr1);
24
root<--expr2:Expr;
25
:Expression(expr2);
26
root<--:Operator;
27
|//or aunaryexpressionwhichisavariable(readingit)
28
root<--v:Variable;
29
)
30
}
IsomorphyLocking
When matching a program graph as in the e introductory example 19 one e might t be satis-
edwithmatchinga tree structure. . Butonother r occasionsonewantstomatchbacklinks
andespecially thetargetsofthebacklinks,too,fromuses s nestedsomewhereinthesyntax
graphtodenitionswhosenodeswerealreadymatchedearlierinthesubpatternderivation
(subpatternscanbeseenasanequivalentofgrammarrulesknownfromparsergenerators).
Unfortunatelytheseelementsarealreadymatchedandthusisormorphylockedfollowingthe
defaultsemantics ofisomorphicmatching. . Andunfortunately y theseelements can’tbede-
clared homomorphic c as s they y are e unknown inthe nestedsubpattern. . Handing g them in as
parametersandthendeclaringthemhomomorphicisonlypossibleiftheyareofastatically
xednumber(asthenumberofparametersisxedatcompiletime),whichisnormallynot
thecasefore.g. theattributesofaclassinasyntaxgraph. Inordertohandlethiscasethe
independentoperator (cf. 5.3.1)was s addedtotherulelanguage|whenyoudeclarethe
8.4 FlowExample,RegularExpressionSyntax,andLocking
103
backlinktargetnodenasindependent(n)itcanbematchedonceagain.Thusitispossible
tomatche.g.aclassattributedenitionnodewhichwasalreadymatchedwhencollectingthe
attributesoftheclassagainlateroninasubpatternwhenmatchinganexpressioncontaining
ausageofthatattribute,allowingtoe.g. addfurtheredgestoit.
PatternpathLocking
As stated d inthe sections onthe negative and independent t constructs (7.17.2), they y get
matchedhomomorphicallytoallalreadymatchedelements. Byreferencinganelementfrom
outsideyoucanisomorphylockthatelementtopreventittogetmatchedagain.
Maybeyouwanttolockallelementsfromthedirectlyenclosingpattern,inthiscaseyou
canjustinsertpattern;inthepositionofagraphletintotheNACorPAC.
MaybeyouwanttolockallelementsfromthepatternsdynamicallycontainingtheNAC/-
PACofinterest,i.e. allsubpatternusages s andnestingpatternsonthepathleadingtothe
NAC/PACofinterest(butnottheirsiblings). Inthiscaseyoucaninsertpatternpath;in
thepositionofagraphletintotheNACorPAC.Youmightbeinterestedinthis construct
whenmatchingapiecewiseconstructedpattern,e.g. achain,whichrequirestocheckforan-
otherchain(iteratedpath)whichisnotallowedtocross(includeanelementof)theoriginal
one.
104
SubpatternsandYielding
CHAPTER 9
RULE APPLICATION CONTROLLANGUAGE
(SEQUENCES)
Graphrewritesequences(GRS),betterextendedgraphrewritesequencesXGRS,todistin-
guishthemfromtheoldergraphrewritesequences,areadomainspecicGrGen.NETlan-
guageusedforcontrollingtheapplicationofgraphrewriterules. Theyareavailable
 asanimperativeenhancementtotherulesetlanguage.
 forcontrolledruleapplicationwithintheGrShell.
 forcontrolledruleapplicationontheAPIleveloutofuserprograms.
Iftheyappearinrules,theygetcompiled,otherwisetheygetinterpreted.Iusedwithin
GrShell,theyareamenabletodebugging.
Graph rewritesequences s are built froma pure rule control l language, writtendownin
a syntax similar tobooleanandregular expressions,with ruleapplications as atoms,and
a computations sublanguage, noted down as a sequence of assignments, functioncalls, or
procedurecalls. Acomputationisgivenasanatomoftherulecontrollanguage,nestedin
curlybraces.
Thegraphrewritesequencesareameansofcomposingcomplexgraphtransformationsout
ofsinglegraphrewriterulesandfurthercomputations. Thecontrol owintherulecontrol
languageis determinedbytheevaluationorder ofthe operands. . Graphrewrite e sequences
haveabooleanreturnvalue;forasinglerule,truemeanstherulewassuccessfullyapplied
tothehostgraph. Afalsereturnvaluemeansthatthepatternwasnotfoundinthehost
graph.
In order r to store e and d reuse returnvalues of rewrite e sequences and d most t importantly,
forpassingreturnvalues ofrules tootherrules,variables s canbedened. . Avariableis s an
arbitraryidentierwhichcanholdagraphelementoravalueofoneoftheattributeorvalue
types GrGen.NET T knows. . There e are e two kinds s of f variables available in GrGen.NET,
i) graph h global variables s and d ii)sequence localvariables. . Avariable e isalivefromits rst
declarationon:graphglobalvariablesareimplicitlydeclareduponrstusageoftheirname,
sequencelocalvariablesareexplicitlydeclaredwithatypedvariabledeclarationoftheform
name:type. Graphglobalvariablesmustbeprexedwithadoublecolon::,localvariables
are referencedjustwiththeir name. . Graphglobalvariables s are untyped; ; their r values are
typed,though,sotypeerrorscauseanexceptionatruntime.Theybelongtoandarestored
inthegraphprocessingenvironment{ifyousavethegraphinGrShellthenthevariables
aresaved,too,andrestorednexttimeyouloadthesavedgraph.Furtheron,theyarenulled
ifthegraphelementassignedtothemgetsdeleted(evenifthishappensduetoatransaction
rollback),thussavingonefromdebuggingproblemsdueto zombieelements (youmayuse
thedef()operatortocheckduringexecutionifthishappened).Sequencelocalvariablesare
typed,sotypeerrorsarecaughtatcompiletime(parsingtimefortheinterpretedsequences);
anassignmentofanuntypedvariabletoatypedvariableischeckedatruntime.Theybelong
tothesequencetheyappearin,theirlifeendswhenthesequencenishesexecution(sothere
105
106
RuleApplicationControlLanguage(Sequences)
is nopersistence available for themas for thegraphglobalvariables; ; neither r dothey get
nulledonelementdeletionasthegraphdoesnotknowaboutthem).
Ifusedinsomerule,i.e. withinanexec,namedgraphelementsoftheenclosingruleare
availableasread-onlyvariables.
Notethatwehavetwokindsofreturnvaluesingraphrewritesequences. Everyrewrite
sequence returns a boolean n value, indicating whether the rewriting g could d be e successfully
processed,i.e. denotingsuccess s or failure. . Additionally y rules may return n graphelements.
Thesereturnvaluescanbeassignedtovariablesonthe y(seeexample54).
EXAMPLE(54)
Thegraphrewritesequences
1
(b,c)=R(x,y,z)=>a
2
a =((b,c)=R(x,y,z))
assignthetworeturnedgraphelementsfromruleRtovariablesbandcandtheinformation
whetherRmachedornottovariablea. Therstversionisrecommended.
9.1 RuleApplication
RewriteFactor
-
RuleExecution
-
SimpleVariableHandling
-
ExtendedControl
-
RewriteComputationUsage
-
Rewritefactorsare the buildingblocks ofgraphrewritesequences. . They y aresplitinto
fourmajorareas:rule(andsequence)application,simplevariablehandling,extendedcontrol,
andsequencecomputationusages. Herewestartwiththemostimportone,applyingrules.
Insection9.3wevisitsimplevariablehandling. Insection18.2wehavealookatadvanced
control,andinsection17.1atthesequencecomputations.
RuleExecution
-
(
-
Variable
,
-
)
-
=
-
RuleModier
-
Rule

-
RandomSelection
-
[
-
RuleModier
-
Rule
-
]
-
count
-
[
-
RuleModier
-
Rule
-
]
-
=
-
>
-
Variable
-
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