aclass: ClassDeclaration (name=name) aspectstatement: Statement (place=name) methods method: MethodDeclaration

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1 Asect Weaving with Grah Rewriting Uwe A mann and Andreas Ludwig Institut f r Programmstrukturen und Datenorganisation Universit t Karlsruhe, RZ, Postfach 6980, Karlsruhe, Germany (assmannjludwig)@id.info.uni-karlsruhe.de Abstract. This aer introduces GRS-based AOP which exlains a large subclass of AOP weavers as grah rewrite systems (GRS). The corresonding class of AOP roblems has a formal background since it inherits all features of grah rewrite systems such as criteria for termination, conuence, and unique normal forms. In articular, it it shown that dierent kinds of rewrite rules form dierent weaver classes. At least two of them (EARS and XGRS weavers) have simle semantics since they always yield unique weaving results. Aasect-oriented rogramming (AOP) allows to secify arts and behaviors of comonents using dierent views, or asects. These asects can be seci- ed indeendently from each other and are combined to the nal form by a weaver tool. This comosition rocess yields software that is better readable (since secications are modular) and better reusable (since asects can be recombined). However, although single instances of AOP such as Adative Programming [Lie96] or Comositon Filters [AWB + 94] rely on formal rinciles the technique as such does not yet have a formal background. This aer introduces GRS-based AOP which exlains a large subclass of weavers as grah rewrite systems (GRS). Hence it has a formal background, inheriting all features of grah rewrite systems such as criteria for termination, conuence, and unique normal forms. In articular, it it shown that dierent kinds of rewrite rules form dierent weaver classes. Although GRS-based AOP does not cover all ossible incarnations of AOP, it rovides a simle formalism for asects relying on roerties that can be recognized directly from the their syntactical structure. We start with a simle examle which demonstrates that grah rewrite rules can describe simle weavings. After introducing some basic terminology we resent a rened classication concering comonents, join oints, and weavers (section 3). With GRS-based AOP, dierent kinds of rewrite rules form dierent weaver classes (section 3.1). Some of them have simle semantics since they always yield unique weaving results. For asects that are encoded into asect grahs, it is observed that GRS-based weaving must use context-sensitive grah rewriting (section 3.1). In articular, GRS-based AOP simlies the construction of AOP weavers. Since tools exist which generate code for the grah rewriting secications weavers can be generated automatically. We demonstrate this with an examle with the grah rewrite tool OPTIMIX (section 4). A table comaring the dierent classes of GRS-based AOP concludes the aer.

2 1 An Informal Examle: Weaving into Method Entries Suose we want to weave some statements into all of a class that exress a debugging asect, e.g. the statements could rint a message when a method is entered. To this end, a weaver should insert the corresonding statements exressing the asect into all entries of the. For examle, ublic doit () { /* here comes the method body */ }... should be extended with a statement which rints the name of the class: ublic doit () { System.out.rintln("entering class " + this.getclass().getname()); // debugging asect /* here comes the method body */ }... The rule in Fig. 1 deicts a simle simle weaver, consisting of a simle grah rewrite system with only one rule. The weaver rule contains in its left-hand side two atterns, one that matches a class and its method (later on called the comonent attern), and another one which matches a statement exressing the asect (later on called the asect attern). Whenever a redex in the classes and asect statements is found whose class name corresonds to the name mentioned in the asect statement the statement is linked to the method as entry statement. The lower art of Fig. 1 shows two redexes in an examle grah which the rule matches. The entries of the corresonding are extended by the statement that carries the asect. If the statements consist of rinting debugging outut, and the rule system is arametrized with the aroriate class name, it transforms our examle as desired. The examle hints to the insight that certain weave roblems can be exressed with grah rewritings over comonents and asect grahs. Before we detail this, the next section resents some basic terminology. 2 Basic Terminology In AOP, only some basic terminology seems to be standardized [KLM + 97]. The area is new and quickly develoing; it is not yet known how far AOP reaches, and a reliminary xing of the terms could hinder the develoment. Hence this aer relies on some basic denitions for AOP terms that seem to be generally consistent with the literature; this does not reclude that other denitions can be considered: Comonents contain the rimary structure of a rogram [Cza98]. They have a meaning of their own, i.e. do not refer to other asects. They carry the core functional semantics of an alication. Asects form the secondary structure of the alication and refer to comonents or other asects. A join oint is a oint

3 aclass: ClassDeclaration (name=name) method: MethodDeclaration asectstatement: Statement (lace=name) aclass: ClassDeclaration (name=name) method: MethodDeclaration entry asectstatement: Statement (lace=name) o o c entry c c c entry Fig. 1. Weaving a statement which realizes an asect into a class'. Classes are deicted in gray, in gray without shade, statements in white. On to, the grah rewrite rule is deicted. Two redexes are found in this examle host grah. in a comonent where asects are integrated. A weaver integrates asect into comonents to arrive at the nal rogram. AOP literature distinguishes dierent ways how asects are secied. This leads to dierent classes of asects and asect-oriented systems: Scrit-based AOP In this oerational aroach, asects are weaved in by scrits which modify the comonent exlicitly. They are executed at weaving time in a redened order. RG is one of those systems [MKL97]: its memoization, fusion and memory management asect are reresented by rules which are alied to the algorithmic comonent. Language-based AOP In this declarative aroach, asects are described by asect languages. [KLM + 97] claims that asect languages rovide more abstraction than scrit-based AOP and increase the exressive ower of asect secications. However, to interret asects weavers must be full-edged comilers. AsectJ is one of these systems [Lo97]. Rewriting-based AOP It has been roosed to regard a weaver as a rewriting system which rewrites comonents and asects [A m97] [FS98]. This aroach relies on the reresentation of asects in data or abstract syntax (in case the asect was secied with an asect language) and weaves asects by rogram transformations. In consequence, it is a kind of amalgamation between scrit-based and language-based AOP. In rewriting-based AOP, A comonent/asect grah is an abstract syntax grah of a comonent/asect, i.e. an instance of the comonent/asect data model.

4 A variant of this kind of AOP relies on meta models of comonents and asects and weaves asects by meta-rogramming. This classication need not be comlete other weavers and weaving mechanisms are likely to be invented. In this aer, we will concentrate on a variant of rewriting-based AOP, GRS-based AOP; this aroach describes weavers as grah rewrite systems, gives them a formal background, and emloying grah rewrite tools an automatic imlementation method. Before we detail GRS-based AOP, some basic terminology of grah rewriting has to be resented. 2.1 Grah Rewrite Systems From the many variants of grah rewrite system in the literature, we choose relational grah rewriting, in which grahs uniformly reresent comonents and asects [A m96a]. Nodes reresent entities of comonents and asects, and are linked by multile relations. As oosed to general grah rewriting [EKL90], it is not required to deal with multigrahs since relations reresent redicates over the entities, and a redicate holds or does not hold [A m96a]. Relational grah rewriting relies on the following denitions. A context-free attern is a nite connected grah. A context-sensitive attern is a grah of at least two disconnected subgrahs. A host grah is the grah to be rewritten by a grah rewrite system. A redex is a subgrah of the host grah injectively homomorhic to a attern. A grah rewrite rule r = (L; R) consists of a lefthand side attern L and a right-hand side grah R. r is matched against the host grah, i.e. its redex is located in the host grah. A rewriting ste which relaces a redex with arts secied in the right-hand side of the rule is called direct derivation. A sequence of direct derivation is a derivation. A terminating derivation ends in a normal form of the host grah. All these denitions can be formalized recisely [A m96a] [RV94]; due to sace restrictions, we kee them abstract. It is well-known that several dierent semantics for grah rewrite rules exists [BFG94]. Our examles here only deal with left hand sides that match a xed number of nodes in a 1-context embedding [SWZ95]. There are more owerful aroaches which allow to match sets of nodes and arbitrary embeddings. 3 GRS-based AOP GRS-based AOP does not cover all ossible incarnations of AOP, but rovides a simle formalism for the weaving of asects which rely on roerties directly recognizable from the structure of the asect secication and the comonents. Based on the denitions in the revious section, certain weaving rocesses can be modelled with grah rewriting which gives several imortant AOP terms a recise and clear meaning. In the following, all dened terms should be rexed with the rex GRS-based-. This is omitted for brevity. A join oint is a redex of a attern in the comonent grah. An asect fragment is a redex of a attern in an asect grah. An asect comoser (an

5 asect comosition oerator) is a grah rewrite rule. Nodes and edges in this rule are tyed with the comonent and asect data model. Most often, the left-hand side contains at least one comonent attern and one asect attern. A comonent attern is a attern in the left-hand side of an asect comoser matching a join oint. An asect attern is a attern in the left-hand side of an asect comoser matching an asect fragment. A weave oeration (weaving transformation) is a direct derivation in a system of asect comosers, attaching an asect fragment to a join oint. A weaver is a grah rewrite system with asect comosers, working on the comonent grah and a set of asect grahs. The weaving stos when a normal form of the system is found. Once weaving is described with grah rewriting, several classes of weavers can be dened. Weavers inherit several formal features such as termination or conuence from the kind of rule system which secies them. 3.1 Asect Fragment Matching Rule Systems Weaving systems of this class matchcomonent join oints as well as asect fragments in their left-hand sides. Due to the nature of asects, comonents and asect grahs are disconnected. Rewriting relates asect subgrahs to comonent subgrahs. In consequence, comonent atterns and asect atterns in asect comosers must also be disconnected atterns in left-hand sides. This yields the following insight: An asect comoser matching asect fragments in asect grahs must be a context-sensitive grah rewrite rule, consisting of at least two disconnected subgrahs in its left-hand side, a comonent attern and an asect attern. Asect fragment matching systems have the advantage that one join oint can be matched multile times with one rule, together with dierent asect fragments. Hence several asect fragments can be related to one join oint with one rule, and comlex weave oerations can be exressed easily. Asect fragment matching systems can be classied at least in the following subclasses which show dierent behavior in termination and congruence, thus yielding dierent weaving behavior. Asect-relating Rules (EARS Weavers) One of the simlest classes of grah rewrite systems only constructs relations, i.e. adds edges to a set of nodes. These systems are called edge-addition rewrite systems (EARS) and are always congruent (i.e. terminating and conuent) [A m94]. Such secications have a simle semantics: there will be always one unique result. If such a system is used to secify a weaver, the weaver is deterministic, and hence a function from the domains of rules, comonents, and asect grahs to the weaved rograms. EARS weavers are useful when items in the comonent grah need to be related to asects: the nodes in the comonent grah are not modied but related to asect fragments. This is ideal for simle roerty asects. Binary roerties as ersistence or distribution can be exressed by relating a comonent node to an aroriate asect fragment (Fig. 2).

6 Clearly, our examle in section 1 is an EARS weaver. Hence the weaver is terminating and deterministic, i.e. the generated rogram is uniquely determined. o o c c Fig. 2. Above: EARS rule, relating items of the comonent grah to an asect roerty. Here, means ersistence. Above left: comonent attern. Above right: asect attern. Down: a direct derivation. Afterwards, the item in the comonent grah is related to the ersistence roerty. Asect-additive Rules Extend Comonents (XGRS Weavers) Asectadditive rules add asect fragments to join oints but do not modify the join oints (Fig. 3). They match a comonent attern as well as an asect attern but do not modify the comonent redex. In consequence, redexes are never destroyed. Such systems are strongly conuent since their direct derivations are commutative [A m96a]. If the system terminates, it yields a unique result and the weaving rocess is deterministic as in the case of EARS weavers. Termination for additive grah rewrite systems has been roven in [A m96b]. When a system comletes a subgrah of the host grah and does not add nodes to it, it terminates. Those systems are called exhaustive GRS (XGRS). For weaving, this means that the asect-additive rule system comletes a subgrah in the comonent grah to which it does not add nodes. In consequence, a weaver consisting of an XGRS is congruent and always yields a unique weaving result. We call such systems XGRS weavers. Similar to EARS weavers, they have a simle and deterministic semantics.

7 Fig. 3. Additive asect weaving rules are context-sensitive grah rewrite rules which do not destroy join oints since comonents are not modied. Comonent-modifying Rules Weaving may require to exchange arts of comonents. Then an asect comoser needs to modify its comonent attern, i.e. the comonent attern is not rule invariant (Fig. 4). Also with comonent-modifying rules, termination may be rovable with the XGRS criterion, but conuence is lost. Modifying rules destroy join oints in comonents. If two rules refer to the same arts of a join oint, such a rule system roduces overlas, i.e. non-commutative direct derivations. In consequence, the system cannot be strongly conuent nor yields unique normal forms. Then, the weaving rocess is indeterministic since several normal forms may exist. Indeterministic weaver secications only make sense if all normal forms are semantically equivalent which may be roved for a articular secication 1. Otherwise it has to be roved that a weaver secication is conuent. 3.2 Asects in Rules Only Asect weavers can also rely on rules which do not contain disconnected comonent and asect atterns. For instance, asects can be encoded in rules themselves. Then the asect fragments which are to be introduced in join oints are encoded in the right-hand sides of rules (R n L) and a secication of asects aart from the weaving rules is not necessary. Hence these systems are very similar to scrit-based AOP systems (section 2). 1 Also rogram otimization is an indeterministic rocess. However, there are always variants of the rogram with the same semantics. If the otimization only yields such equivalent variants, it is semantically sound.

8 Fig. 4. A rule modifying a comonent with an asect fragment. The comonent attern is not rule-invariant. Fig. 5. Asects secied in right hand sides of rules. Above: rule with asect in R n L. Down: asect is introduced into the comonent grah by executing the right hand side of the rule

9 3.3 Intra-comonent Weaving Rules One class of weavers results when rules rewrite the comonent grah only (intracomonent rules), i.e. contain only comonent atterns. Such systems may modify join oints, may add arts of join oints to other join oints, or may move code from one lace of the comonent to another (Fig. 6). Hence they can also be classied as EARS-based, additive or modifying, inheriting the same formal features. An examle for such a code-motion weaver is RG, which otimizes the control- and data-ow asect in a comonent [MKL97]. Such systems resemble standard code motion otimizations in comilers since they move code within the comonent [A m96b]. Their join oints corresond to code statements in the comonent grah. n n? Fig. 6. Rules weaving intra-comonently. Here, the rule moves a node n to another lace. This concludes our classication of GRS-based AOP weavers. It is likely that more classes will be found, which dier in their weaving semantics since they have dierent formal features as grah rewrite systems. 4 Weaving with GRS Tools In GRS-based AOP, weaver secications can be fed into a grah rewrite tool to generate a weaver imlementation. One examle for such a tool is OPTI- MIX which roduces C and Java code from rule secications in textual form [A m96b] [A m99]. Figure 1 would be secied as follows:

10 grs WeaveAsectStatement(ClassDeclarationList classdeclarations, Identifier Name, StatementList asectstatements) { range aclass <= classdeclarations; // instantiation of aclass, comonent data asectstatement <= asectstatements; // instantiation of asectstatement, asect data rules if // look for join oint (aclass,method) in all classes (comonent attern) aclass.name == Name and method in aclass. // asect attern and asectstatement.lace == Name then // add the statement to the method of the class asectstatement in method.entry; } grs The rule system WeaveAsectStatement consists of one rule. Its recondition (between if and then) consists of a list of conjunctive redicates which corresond to the edges of the left-hand side from Fig. 1. The generated algorithm searches all redices (join oint and asect fragment airs) starting from a range of nodes (all classes in list classdeclarations and statements in asectstatements). The rule rewrites a redex, adding the asectstatement to the entry of the method. Hence in the modied class grah, each time a method from class with name Name from list classdeclarations is called, the asect statement is executed. For the rule system, OPTIMIX generates a Java method which contains the weaver. Basically, this weaver alies the rules until a xoint is reached. Also, OPTIMIX nds out that WeaveAsectStatement is an EARS and alies certain otimizations to imrove the eciency of the generated weaver. The generated weaver can be alied for weaving of arbitrary asects into method entries, such as mixing in diagnostic rint statements as in our examle, or event signalling statements for rogram animation. Also, the system can be extended with more rules so that more comlex asect weavings are ossible, e.g. comlete method wraings. Not all asect weavings can be reduced to GRS-based AOP. However, we believe that we have identied an imortant subclass of AOP which has a recise semantics: the weaving is based on grah rewriting, join oints are redices, the weaver consists of the grah rewrite system, and weaver imlementations can be generated automatically. 5 Related Work It is well-known that AOP can be modeled with meta-rogramming [KLM + 97]. Although GRS-based AOP also relies on a data model (meta model) of both asects and comonents, it has not been realized yet that asect comosers can be modeled by grah rewrite rules. [Zim97] develos the idea to use design atterns as transformation oerators on the class grah. In [A m97], we have extended this work: design atterns are regarded as grah rewrite rules modifying class grahs. Since design atterns refer to certain asects of systems it is only a small ste towards the work resented in this aer.

11 The most closely related work is [FS98]. Here asect comosition is exlained as a rogram transformation on abstract syntax trees, i.e. as term rewriting system. This is similar to our aroach, however, we claim that grah rewriting is more at for asect comosition since it has to deal with class grahs. Secondly, whenever asects are reresented exlicitly in an asect grah, term rewriting is not sucient since context-sensitive rules are required. Fradet and S dholt also claim that asect comositions that reserve semantics are closely related to rogram otimizations. This is suorted by our aroach since we use essentially the same grah-rewriting aroach that has been found useful as a uniform framework for rogram otimizations [A m96b]. In this aer, we have considered automated, i.e. chaotic grah rewriting. In contrast, rogrammed grah rewriting a la PROGRES [SWZ95] allows to rogram a control-ow on rewrite rules. This hels to structure otherwise nonconuent or non-terminating rule systems, but sacrices the declarative semantics of general grah rewriting. 6 Conclusion This aer resented GRS-based AOP, an aroach in which asects, join oints, and weavings have a well-dened and recise semantics since they are all dened in terms of grah-rewriting. Asect comosition is described by grah rewrite rules, weave oerations are direct derivations, and weaved rograms are normal forms of the rewrite systems. Formal features, such as termination or conuence criteria are inherited to weaving. A classication of the asect comosers leads to two classes of simle weaving systems which have a deterministic semantics (EARS weavers and XGRS weavers). Asect comoser systems can be fed into grah rewrite tools such as OPTIMIX which generate weavers automatically. Hence for GRS-based AOP, it is not necessary to write weavers by hand. The following table summarizes our classication of GRS-based AOP and the features of its classes. System terminating? deterministic? Asect grah Asect Fragment Matching Asect-relating (EARS) yes yes yes Asect-additive if XGRS yes yes Comonent-modifying if XGRS normally not yes Asects in Rules deends deends no Intra-comonent deends deends no Clearly, GRS-based AOP does not cover all AOP incarnations. Also, secic instances may have more aroriate formalizations. In articular, it should be investigated how secic formalizations, e.g. of Adative Programming, relate to GRS-based AOP. In general, AOP requires more research: How are asects described which do not only rely on syntactical roerties? How can we relate, reuse, modify, (de)comose asects? To answer these questions, GRS-based AOP rovides a good starting oint.

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13 [RV94] [SWZ95] [Zim97] Jean-Claude Raoult and Fr d ric Voisin. Set-theoretic grah rewriting. In Hans J rgen Schneider and Hartmut Ehrig, editors, Grah Transformations in Comuter Science, volume 776 of Lecture Notes in Comuter Science, ages , Andreas Sch rr, Andreas J. Winter, and Albert Z rndorf. Grah Grammar Engineering with PROGRES. In Euroean Software Engineering Conference ESEC 5, volume 989 of Lecture Notes in Comuter Science, ages , Heidelberg, Setember Sringer. Walter Zimmer. Frameworks und Entwurfsmuster. PhD thesis, Universit t Karlsruhe, February 1997.