Parsing of UML Package Diagrams 2 UML

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1 Parsing of UM Package Diagrams akaaki Goto, adaaki Kirishima, etsuro Nishino, akeo Yaku and Kensei suchida Graduate chool of Informatics and Engineering, he University of Etro-Communications, Chofu, okyo, Japan College of Cornerstone Education, Oberlin University, Machida, okyo, Japan Department of Information cience, Nihon University, etagaya, okyo, Japan Faculty of Information cience and rts, oyo University, Kawagoe, aitama, Japan {gototakaaki, bstract Program diagrams are used when we develop software. Unified Modeling anguage (UM) is also used in software development. Package diagram is one of a diagram used in UM. Package diagram plays an important role to design or analyze structures of systems. o far we posed a graph grammar for package diagram in order to formalize manipulation of package diagram. In this paper, we pose a parsing method of posed a graph grammar for package diagram. keywords: diagram 1 Introduction graph grammar, parsing, UM, package he Unified Modeling anguage (UM) for modeling in software development was posed relatively recently, and in 2005 it was standardized as the IO/IEC standard. UM has already been used in the analysis, design and implementation of many systems. It makes use of various types of diagrams, such as class and sequence diagrams, for designing processes in system development, from upstream processes to downstream processes. utomation of the processing of these graphical representations using computers first requires definition of a syntax for program diagrams. ome tools for drawing UM diagrams have been posed in recent years. However, developers encounter difficulties when trying to draw UM diagrams using the UM tool because diagram layouts must be manually adjusted. Of course, some tools can automatically lay out diagrams, although sometimes these functions produce unexpected layouts. nalysis of the syntax of two-dimensional objects such as program diagrams also requires a description of the relationships between each of the elements. Graph grammars are one possible means for effective implementation of these methods. hey provide a formal method that enables rigorous definition of mechanisms for generating and analyzing graphs. ozenberg [] and others have conducted research on graph grammars. Other workers have focused on UM [5] and graph grammars and graph transformations with respect to UM [2, 4, 6]. However, these studies did not deal with syntax formalization for visual representation, and graph grammars for package diagram remain to be posed. We have previously provided a graph grammar for a UM package diagram to pose the theoretical fundamentals of UM [8]. In the present paper, we pose a parsing method for the posed graph grammar suitable for a package diagram. 2 UM UM is a notation for modeling object-oriented system development using diagrams. It can be divided into structural diagrams and behavioral diagrams. tructural diagrams are used to describe the structure of what is being modeled and includes class, object, and package diagrams. Behavioral diagrams are used to describe the behavior of what is being modeled and include use-case, activity, and state-machine diagrams. tructure diagrams include 1) class diagrams, which describe the static relationships between classes, and 2) package diagrams, which group classes and describe relationships between packages and package nesting relationships. In this paper, we target package diagrams. package indicates a namespace for its member. Package diagrams can describe dependencies among other packages. Package diagrams can describe dependencies among / copyright IC, C 2015 March 9-11, 2015, Honolulu, Hawaii, U

2 other packages. hey can also illustrate membership using membership notation [1]. Figure 1 depicts an example of a package diagram with members described in [1]. he middle representation shows a package with some of the members within the borders. he right representation shows a package diagram using alternative membership notation. In this paper, we target membership notation for our graph grammar and syntax-directed editor. Package1 Here, Σ P D = {,,,,, M,, sp,, rip, mip,, mic, ric } is a finite set of node labels, P D = {, sp,, rip, mip,, mic, ric } is a finite set of terminal node labels, Γ P D = { }, Ω P D = { }, P P D = { P 1,..., P 1 } is a finite set of production rules, and P D = { }, is the initial non-terminal. In Definition 1,, sp,, rip, mip,, mic, and ric, stand for root of package, single package, left package, right package, middle package, left class, middle class, and right class, respectively. he GGPD generates package hierarchy diagrams. It is a context-free grammar, and has 1 production rules. P P D has three types of production, as shown in Figure. Package2 Package Class1 Class2 Class Figure 2: n example of a package diagram Figure 2 shows an example of a package diagram using alternative membership notation. Boxes with rectangles at the upper left corners indicate the presence of a package. Boxes with three compartments represent classes, with each compartment representing its class name, its attributes, and its methods from top to bottom, respectively. plus sign in a circle is used to represent the components the package contains. Package 1 contains Package 2 and Package, and Package contains Class 2 and Class. 2 (a) ype (b) ype 2 0 Graph Grammar for UM Package Diagrams [8] (c) ype 0 In this section, we describe our Graph Grammar for Package Diagrams (GGPD), for UM package diagram membership notation. UM package diagrams using membership notation can be described as treestructured. We refer to our previous research on graph grammar for tree structures []..1 Grammar Overview Definition 1. he Graph Grammar for Package Diagrams (GGPD), for UM package diagrams, is a sixtuple GGP D = (Σ P D, P D, Γ P D, Ω P D, P P D, P D ). Figure : n example of a GGPD production rule In Figure, nodes with capitalized labels indicate nonterminal nodes, and nodes with uncapitalized labels indicate terminal nodes. ype 1 and ype 2 productions generate tree structures in a longitudinal and a transverse direction, respectively. ype productions substitute a nonterminal node for a terminal node. In Figure (a), the production rule can be applied to a node labeled, which is a non-terminal node, to generate a terminal node with the label, representing a

3 Figure 1: n Example of a package diagram with members [1] package, and a non-terminal node labeled. Our grammar generates directed graphs. However, the obtained graphs are drawn without arrows by assuming that the direction of each edge is from the top down. 4 Parsing In this section, we describe a parsing method for GGPD. he input of this method is a package hierarchy diagram. We can obtain a derivation tree by the parsing. Here we show the flow of parsing: (1) et the root node of the input diagram as the current node..2 Example of Derivation Figure 4 shows an example of a GGPD derivation. In this example, G 0 is a graph with a node labeled. he node ID is 1 (to the lower right of the node). he production rule P 1 is then applied to a nonterminal node labeled with the node ID 1, which is the initial nonterminal node. hat is, a mother node with label and node ID 1 is removed, and then a daughter graph is embedded in the P 1. In this case, the daughter graph is the node with the label. his produces the nonterminal node labeled with a node ID 2, to which the P production rule is applied. In other words, a graph G 1, consisting of a node with the node ID 2, is obtained. fter application of the production P, the terminal node labeled and a non-terminal node labeled are generated. We apply production rules to obtain a graph that corresponds to the UM package diagrams. We can obtain a derivation tree from the derivation sequence of production. Figure 5 shows the derivation tree corresponding to Figure 4. In Figure 5, the labels show the names of the production rules. nother example of a package diagram resulting from application of the production rules is shown in Figure 6. (2) If the current node is a node with node label, go to. Otherwise, shift the current node to the right-most node of the input diagram, and then set the right-most node as a handle. () he parser searches for a production rule in which the right-hand side is isomorphic to the handle. If the parser finds a production, then the parser reduces the handle to the left-hand side of the production. hen go to 2. (4) If the parser cannot find productions in step, the parser sets the right-most node and its immediate left node as a handle, and then searches for a production rule. If the parser finds a production, then the parser reduces the handle to the left-hand side of the production. hen go to 2. (5) If the parser cannot find productions in step 4, the parser sets the right-most node and its parent as a handle, and then searches for a production. If the parser find a production, then the parser reduces the handle to the left-hand side of the production. hen go to 2. (6) If the parser can not find productions in step 5, the parser outputs an error. () he parser finishes parsing, and outputs a derivation tree.

4 G0: P1 P 1 G1: 1, P1' P1 P8 P6 P12 G2: 2 2, P' P Figure 5: derivation tree corresponding to the tree in Figure 4 + rip sc ric 4, P6' P6 G: Figure 6: n example of package diagram resulting from derivation 5 6 5, P8' P8 G4: 6 6, P12' rip P12 G5: rip 8 Figure 4: n example of a GGPD derivation Next we show an example of parsing. Figure shows an example of parsing of a package diagram. In the Figure, G 6 is the input of this example. he root node of the input is the initial location of this parser. First of all, the parser shifts the current node to the right-most node 11 with ric label. Here,node 11 is the handle; the parser then searches for a production. In this case, the parser is able to find Production 14, so the parser then reduces node11 with the found production rule. s a result, we obtain G after the reduction. Node 12 is generated by the reduction. In the same way, we can obtain G 1 after a reduction. One node has the node label. he parser then succeeds in parsing for the input diagram G 6. 5 Conclusion In this paper, we posed a parsing method for our posed a graph grammar for a package diagram of UM. In the future, we will implement this parsing method, and realize formalisms of other UM diagrams. Our method can be used for generating diagrams with aesthetic drawings but is also useful for understanding source code.

5 G6: mic ric , P14' P14 ric {14,15}, P6' P6 G: G11: mic , P1' P1 G8: M mic G11: 16, P' 16 1 P M 1 12 P11 {12,1}, P11' M 1, P1' P1 G9: G12: 18 14, P10' P10 G10: Figure : n example of parsing of a package diagram

6 cknowledgment his work was partially supported by JP KK- ENHI Grant Number eferences [1] Object Management Group. Omg unified modeling language (omg uml), infrastructure, v Infrastructure/PDF/, 200. [2] Frank Hermann, Hartmut Ehrig, and Gabriele aentzer. yped ttributed Graph Grammar with Inheritance for the bstract yntax of UM Class and equence Diagrams. Etron. Notes heor. Comput. ci., 211: , pril []. Kirishima,. Goto,. Yaku, and K. suchida. n attribute graph grammar enabling narrower drawings of trees. In Computer and Information cience (ICI), 2010 IEEE/CI 9th International Conference on, pages 41 46, [4] Kong, Jun and Zhang, Kang and Dong, Jing and Xu, Dianxiang. pecifying behavioral semantics of UM diagrams through graph transformations. J. yst. oftw., 82:292 06, [5] eszek Kotulski and Dariusz Dymek. On the Modeling iming Behavior of the ystem with UM(V). In Computational cience ICC 2008, volume 5101 of ecture Notes in Computer cience, pages 86 95, [6] Dorina Petriu and Hui hen. pplying the UM Performance Profile: Graph Grammar-Based Derivation of QN Models from UM pecifications. In Computer Performance Evaluation: Modelling echniques and ools, volume 224 of ecture Notes in Computer cience, pages , [] Grzegorz ozenberg. Handbook of Graph Grammar and Computing by Graph ransformation Volume 1. World cientific Publishing, 199. [8] akaaki Goto and adaaki Kirishima and etsuro Nishino and akeo Yaku and Kensei suchida. Generation of UM package diagrams based on an attribute graph grammar. Journal of Computational cience, 5(4): , 2014.