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6.9 OperatorPriorities
67
6.9 OperatorPriorities
Theprioritiesofallavailableoperatorsareshowninascendingorderinthetablebelow,the
dotsmarkthepositionsoftheoperands,thecommasseparatetheoperatorsavailableonthe
respectiveprioritylevel.
01
. ? ? . : : .
02
. || .
03
. && .
04
. | | .
05
. ^ ^ .
06
. & & .
07
. \ \ .
08
. ==,!= .
09
. <,<=,>,>=,in n .
10
. <<,>>,>>> > .
11
. +,- - .
12
. *,%,/ .
13
~,!,-,+ .
Table6.9:Alloperators,inascendingorderofprecedence
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BasicTypesandAttributeEvaluationExpressions
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CHAPTER 7
NESTED PATTERNS
Theextensionoftherulesetlanguagedescribedinthechapter5bynestedpatternsinthis
chapter7andthefollowingchapter8greatlyenhances the exibilityandexpressivenessof
patternmatchingandrewriting.Thefollowingpatternstomatchasimpliedabstractsyntax
treegivearoughpictureofthelanguageofnestedandsubpatterns:
EXAMPLE(19)
1
testmethod
2
{
3
m:Method<--n:Name; //signatureofmethodconsisting ofname
4
iterated{ // and 0-n parameters
5
m <-- :Variable;
6
}
7
8
:AssignmentList(m);//bodyconsistingof alistofassignmentstatements
9
}
10
11
patternAssignmentList(prev:Node)
12
{
13
optional{ //nothingor alinkedassignment and again alist
14
prev--> a:Assign; //assignmentnode
15
a-:target-> v:Variable;//whichhasa variableastarget
16
:Expression(a); //andanexpressionwhichdefinesthelefthandside
17
:AssignmentList(a); // nextone, plz
18
}
19
}
20
21
patternExpression(root:Expr)
22
{
23
alternative{ //expression maybe
24
Binary{ // abinaryexpressionofanoperatorandtwoexpresions
25
root<--expr1:Expr;
26
:Expression(expr1);
27
root<--expr2:Expr;
28
:Expression(expr2);
29
root<--:Operator;
30
}
31
Unary{//ora unaryexpressionwhichisa variable (readingit)
32
root<--v:Variable;
33
}
34
}
35
}
69
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70
NestedPatterns
Untilnowwehaveseenrulesandtestswithonelefthandsidestaticpatternspecication
in a direct t 1:1 correspondence with h its s dynamic match h in the host t graph h on a successful
application. Fromnowonwewillincreasetheexpressivenessofthepatternlanguage,and
dependentonittherewritelanguage,todescribemuchnerandmore exiblewhatpatterns
toaccept. Thiswillbedonebypatternspecicationsbuiltupfrommultiplestaticpattern
piece specications, where the pieces may be matched dynamically zero,one, or r multiple
times,orare forbiddentoexistsfor the entirepatterntobe matched. . These e rule setlan-
guageconstructs canbesplitintonestedpatterns(negativeapplicationcondition,positive
applicationcondition,nestedpatternwithcardinality,alternativepatterns)andsubpatterns
(subpatterndeclarationandsubpatternentitydeclaration,subrule declarationandusage),
inthischapterwewillfocusonthenestedpatterns:
NestedPattern
-
NegativeApplicationCondition
-
PositiveApplicationCondition
-
NestedPatternWithCardinality
-
AlternativePatterns
-
7.1 NegativeApplicationCondition(NAC)
NegativeApplicationCondition
-
negative
-
f
PatternStatement
-
g
-
Withnegativeapplicationconditions(keywordnegative)wecanspecifygraphpatterns
whichforbidtheapplicationofaruleifanyofthemispresentinthehostgraph(cf.[Sza05]).
NACspossessascopeoftheirown,i.e.namesdenedwithinaNACdonotexistoutsidethe
NAC.Identiers fromsurroundingscopesmustnot beredened. . Iftheyarenot t explicitly
mentioned,theNAC getsmatchedindependentfromthem,i.e. . elementsinsideanegative
arehom(everything from m the e outside)bydefault. Butreferencingtheelementfromthe
outsidewithinthenegativepatterncausesittogetmatchedisomorphically/distincttothe
otherelementsinthenegativepattern. Thisisabitunintuitiveifyouthinkofextendingthe
patternbynegativeelements,butcleanerandmorepowerful:justthinkofNACstosimply
specifyapatternwhichshouldnotbeinthegraph,withthepossibilityofforcingelements
tobethesameasintheenclosingpatternbynameequality.
EXAMPLE(20)
Wespecifyavariablewhichisnotbadlytyped,i.e. anodexoftypeVariablewhichmust
notbetargetofanedgeoftypetypewithasourcenodeoftypeBadType:
1
x:Variable;
2
negative{
3
x<-:type-:BadType;
4
}
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7.1 NegativeApplicationCondition(NAC)
71
BecauseNACshavetheir\own"binding,usingNACsleadstospecicationswhichmight
lookabitredundant.
EXAMPLE(21)
Let’scheckthesingletoncondition,meaningthere’sexactlyonenodeofthetypetocheck,for
thetypeRootNamespace. Thefollowingspecicationiswrong g (itwillneverreturnamatch):
1
x:RootNamespace;
2
negative{
3
y:RootNamespace;
4
}
InsteadwehavetospecifythecompleteforbiddenpatterninsidetheNAC.Thisisdoneby:
1
x:RootNamespace;
2
negative{
3
x;
4
y:RootNamespace;//nowitis ensuredthat ymust bedifferentfromx
5
}
Btw: thex;isnotaspecialconstruct,it’sanormalgraphlet(cf.5.1.1).
Ifthereareseveralpatternswhichshouldnot occur,useseveralnegatives. . Ifthereare
exceptionstotheforbiddenpattern,usenestednegatives. Asastraight-forwardgeneraliza-
tionofnegativeswithinpositivepatterns,negativesmay get nestedtoanarbitrarydepth.
Matchingofthenestednegativepatterncausesthematchingofthenestingpatterntofail.
EXAMPLE(22)
Afabricatedexampleusingparallelaswellasnestednegatives:
1
testonlyOneChildOrAllChildrenHaveExactlyOneCommonChild
2
{
3
root:Class;
4
negative{
5
root-:extending-> :Class; // rootdoes notextendanotherclass
6
}
7
root<-:extending-c1:Class; // aclassc1extendsroot
8
negative{
9
c1;
10
root<-:extending- c2:Class; //thereisnoc2 whichextendsroot
11
negative{
12
c1<-:extending- child:Class-:extending->c2;//exceptc1andc2have acommonchild
13
negative{ // andc1 hasno furtherchildren
14
child;
15
c1<-:extending-:Class;
16
}
17
negative{ // andc2 hasno furtherchildren
18
child;
19
c2<-:extending-:Class;
20
}
21
}
22
}
23
}
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72
NestedPatterns
7.2 PositiveApplicationCondition(PAC)
PositiveApplicationCondition
-
independent
-
f
PatternStatement
-
g
-
Withpositiveapplicationconditions(keywordindependent)wecanspecifygraphpat-
ternswhich,incontrasttonegativeapplicationconditions,mustbepresentinthehostgraph
tocausethematchingoftheenclosingpatterntosucceed. TogetherwithNACstheyshare
thepropertyofopeningascope,withelementsbeingindependentfromthesurroundingscope
(i.e. ahostgraphelementcaneasilygetmatchedtoapatternelementandaPACelement
withadierentname,unlessthepatternelementisreferencedinthePAC).Theyareusedto
improvethelogicalstructureofrulesbyseparatingapureconditionfromthemainpattern
oftheruleamenabletorewriting. Theyareusedwhenallmatchesofapatternarewanted,
anda part of that pattern is available inthe graph multiple times, but shouldnot cause
combinatoriallyadditionalmatches;thentheindependentcanbeusedtocheckonlyforthe
existenceofthatpart,limitingtheall-matchingtothecorepattern. Theyarereallyneeded
if subpatterns wanttomatchelementswhichwerealready matchedduringthesubpattern
derivation.
EXAMPLE(23)
Afurtherfabricatedexamplerathergivingtheintentionusingindependentpatternstocheck
someconditionswithonlythemainpatternavailabletorewriting:
1
rulemoveMethod
2
{
3
c:Class--> m:Method;
4
csub-:extending->c;
5
csub:Class -e:Edge-> msub:Method;
6
7
independent{
8
//acomplicatedpatterntofind outthatm andmsubhavesamesignatures
9
}
10
independent{
11
//acomplicatedpatterntofind outthatmsubis onlyusingvariablesavailable in c
12
}
13
independent{
14
//acomplicatedpatterntofind outthatm is notused
15
}
16
17
modify {//movemethodupwards
18
delete(m);
19
delete(e);
20
c --> msub;
21
}
22
}
7.3 PatternCardinality(iterated/multiple/optional)
73
7.3 PatternCardinality(iterated/multiple/optional)
NestedPatternWithCardinality
-
iterated
-
multiple
-
optional
-
f
-
NestedBody
-
g
-
NestedBody
-
PatternStatement
-
NestedRewriting
-
Theblocks allow to specify howoftenthenestedpattern n {openinga scope{is s tobe
matched.Matchingwillbecarriedouteagerly,i.e.iftheconstructisnotlimitingthenumber
ofmatchesandafurthermatchispossibleitwillbedone.(Thenestedbodywillbeexplained
inSection7.5.)
TheIteratedBlock
Theiteratedblockismatchingthecontainedsubpatternasoftenaspossible,succeedingeven
inthecasethecontainedpatternisnotavailable(thusitwillneverfail).Itwasincludedin
thelanguagetoallowformatchingbreadth-splittingstructures,asincapturingallmethods
ofaclassinaprogramgraph.
EXAMPLE(24)
1
testmethods
2
{
3
c:Class;
4
iterated{
5
c --> m:Method;
6
}
7
}
TheMultipleBlock
Themultipleblockisworkingliketheiteratedblock,butexpectsthecontainedsubpattern
tobeavailableatleastonce;ifitisnot,matchingofthemultipleblockandthusitsenclosing
patternfails.
EXAMPLE(25)
1
testoneOrMoreMethods
2
{
3
c:Class;
4
multiple{
5
c --> m:Method;
6
}
7
}
74
NestedPatterns
TheOptionalBlock
Theoptionalblockisworkingliketheiteratedblock,butmatchesthecontainedsubpatternat
mostonce;furtheroccurrencesofthesubpatternareleftunmatched.Ifthenestedpatternis
available,itwillgetmatched,otherwiseitwon’t;matchingoftheoptionalblockwillsucceed
eitherway.
EXAMPLE(26)
1
testvariableMaybeInitialized
2
{
3
v:Variable;//matchvariable
4
optional{ // and aninitializationwith adifferentoneifavailable
5
v <-- otherV:Variable;
6
}
7
}
IterationBreaking
Ifanapplicationconditioninsideaniterationblockfails,thenthatpotentialmatchofthe
iterated pattern is thrown away and d matching g continues s trying g to nd further r matches.
Sometimes adierent behaviour is wanted,with h anapplicationconditionterminatingthe
iteration and causing it t to fail. . This s wouldallowto check with h asinglerule that t "every
patternXmustalsosatisfyY"holds. Thisbehaviourissupportedwiththebreakkeyword
prependedtoanapplicationcondition,transformingitintoaniterationbreakingcondition.
EXAMPLE(27)
Ifthenegativematches,notonlythecurrentiterationinstanceispreventedfrommatching,
buttheentireiterated(andthusthetest)isfailingtomatch:
1
testforEachXMustNotBeTheCaseY
2
{
3
iterated{
4
<X>;
5
breaknegative {
6
<Y>;
7
}
8
}
9
}
Iftheindependentdoesnotmatch,notonlythecurrentiterationinstanceispreventedfrom
matching,buttheentireiterated(andthusthetest)isfailingtomatch:
1
testforEachXMustBeTheCaseY
2
{
3
iterated{
4
<X>;
5
breakindependent{
6
<Y>;
7
}
8
}
9
}
7.4 AlternativePatterns
75
NOTE(28)
Patterncardinalityconstructsarematch/rewrite-allenumerationblockers.Foreverypattern
instance,theiterated/...yieldsonlyonematch,evenifinallmode(usedin/fromall-bracketed
rules).
7.4 AlternativePatterns
AlternativePatterns
-
alternative
-
f
-
CaseName
-
f
-
NestedBody
-
g
-
g
-
Withthe alternative block youcanspecify severalnestedalternative patterns. . One e of
themmust get matchedfor the matching of thealternative (andthus its directly nesting
pattern)tosucceed,andonlyoneofthemismatchedpermatchofthealternative/overall
pattern. The e order ofmatchingthealternative patternsis unspecied,especiallyit is not
guaranteed that t a case gets s matched before e the case textually following { if you want to
ensurethatacasecannotgetmatchedifanothercasecouldbematched,youmustexplicitly
preventthat fromhappeningby addingnegativestothecases. . Incontrast t totheiterated
whichlocallymatcheseverythingavailableandinsertsthiscombinedmatchintothecurrent
match,thealternative decides for one case matchwhichit inserts intothe currentmatch
tree,ignoringotherpossiblematchesbyothercases.
EXAMPLE(28)
1
testfeature(c:Class)
2
{
3
alternative//afeatureof theclass iseither
4
{
5
FeatureMethod{ // amethod
6
c--> :Method;
7
}
8
FeatureVariable{//ora variable
9
c--> :Variable;
10
}
11
FeatureConstant{//ora constant
12
c---> :Constant;
13
}
14
}
15
}
76
NestedPatterns
EXAMPLE(29)
1
testvariableMaybeInitialized
2
{
3
v:Variable;//matchvariable
4
alternative{ //and aninitializationwitha differentoneifavailable
5
Empty{
6
// the emptypatternmatchesalways
7
negative{ // sopreventit to matchifinitializationisavailable
8
v <-- otherV:Variable;
9
}
10
}
11
Initialized {//initialization
12
v<--otherV:Variable;
13
}
14
}
15
}
EXAMPLE(30)
Whenworkingwiththesubtypinghierarchyonemaybeinterestedinmatchinginarststep
anabstractbaseclass,specifyingtherewritingbehaviourfor thisbaseclassonce,andina
renement stepinanalternativethedierent possiblesubtypes,thenbeingable toaccess
theirspecicattributesandbeingableofgivingdierentadditionalrewriteparts.
1
testrefineFeature
2
{
3
f:Feature; //matchabstractbaseclassFeature
4
5
alternative{
6
Variable{
7
v:Variable<f>;//trytocasttoconcreteVariable, if succeedswecanaccessthe
Variableattributes
8
}
9
Method{
10
m:Method<f>;//trytocastto aconcreteMethod,ifsucceedswe can accesstheMethod
attributes
11
}
12
}
13
14
modify {
15
//do stuffcommon to aFeaturehere
16
}
17
}
7.5 NestedPatternRewriting
Untilnowwe focusedonthepatternmatching ofnestedandsubpatterns {but we’re not
onlyinterestedinndingpatternscombinedfromseveralpatternpieces,wewanttorewrite
thepatternpieces,too. Sowewillextendthelanguageofthestructureparser r introduced
so far into alanguage for a structure transducer. . This s does not hold d for r theapplication
conditions,whicharepureconditions,butforalltheotherlanguageconstructs introduced
inthischapter.
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