Precedence Graph Grammar for Hierarchical Program Diagram

1

Precedence Graph Grammar for Hierarchical Program Diagram

○Takaaki Goto (Toyo University) Kenji Ruise (Kirigaoka School for the

Physically Challenged, University of Tsukuba )

Kensei Tsuchida (Toyo University) Takeo Yaku (Nihon University)

2

1. Introduction2. Hichart/DXL3. Preliminaries4. Graph Grammar for Hichart/DXL5. Parsing of precedence graph grammar for

Hichart/DXL6. Hichart Editor7. Conclusion

Contents

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1. Introduction

1.1 Background1.2 Motivation1.3 Purpose1.4 Results

4

1.1 Background

Various researches have been done on graph grammars and their application

We have been developing a software development environment based on graph grammars to formalize of diagram’s structure and layout information to formalize of diagram processing method

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1.1 Background (cont.)

The program diagram called Hichart (HIerachical flowCHART description language) in this environment is treated

We have already developed bidirectional translators that translatePascal, C, or DXL to Hichart 　Hichart 　 to Pascal, C, or DXL

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1.2 Motivation

A parser plays a key role in our processing system and needs to be efficient as large-scale program diagrams are parsed

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1.3 Purpose

To adopt a precedence relation of graph grammar for Hichart/DXL to parse Hichart diagram efficiently

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1.4 Results Adapted a precedence relation of

graph grammar for Hichart/DXL productions 　 70semantic rules 　 888precedence relations 　 256

Implemented graphical editor with parser in JAVA

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2. Hichart/DXL

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2. Hichart/DXL (cont.)

Characteristics of Hichart(1) Diagram is a tree-flowchart with the

same flow control lines as a Neumann program flowchart

(2) The hierarchy of the data structure and the control flow are displayed on a plane simultaneously

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DXL(1) Diagram eXchange Language for

tree-structure charts, DXL, was specified in the 1997 ISO

(2) Purpose of DXL is to facilitate the interchange of different tree-structure charts between CASE tools


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Data exchange between various tree-structure diagrams through DXL


(Hitachi)

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3. Preliminaries

3.1 edNCE Graph Grammar3.2 Precedence Graph Grammar

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3.1 edNCE Graph Grammar [Rozenberg, 1997]

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3.1 edNCE Graph Grammar (cont.)

(c) Result

Example of production & derivation

(a) Host

(b) Production

X:=

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3.2 Precedence Graph Grammar

A graph grammar that is ・ confluent

・ symmetric・ uniquely invertible・ has no reflexive nonterminals・ no precedence conflicts

is called precedence graph grammar [Kaul, 1986].

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3.2 Precedence Graph Grammar (cont.)

derivation specifications , where

is an isomorphic graph of the left hand side of a production

is an isomorphic graph of the right hand side of a production

is an isomorphism

)~

,~

,~

,( bDXps

X~

D~

b~

RRVV ~

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derivation sequences

　 precedes if The reflexive and transitive closure of this

relation is denoted are incomparable if neither nor

iS jS j iL R

D

)~

,~

,~

,(,),1|( 1 iiiiiis

i bRLpsNnniGGDi

ji ss , iDj ss jDi ss

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DD v D wv w s s

An ordering of the nodes in Gn is

,,, are the precedence relation between nodes

The precedence relations between labels

,,,,R

is the set of all )}(),,(),,(),({),( wλvwEwvEvλwvlab GGG

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4. Graph Grammar for Hichart/DXL

4.1 Attribute Graph Grammar for Hichart/DXL

4.2 Derivation of GGHD

4.3 Precedence Relation for GGHD

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4.1 Attribute Graph Grammar for Hichart/DXL

GGHD (Graph Grammar for Hichart/DXL)

GG Type Productions

Semantic rules

GGHD Context-free

70 888

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4.1 Attribute Graph Grammar for Hichart/DXL (cont.)

Fig. Example of production and semantic rules of GGHD

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4.2 Derivation of GGHD

We substitute (D’,C’) for a node X’ in H as follows.(1) Remove a mother node X’ , and edges that

connect with X’ from host graph H,(2) Embed the daughter graph D’ into H- , and(3) Establish edges between the nodes of D’ and

the nodes that were connected to the mother node in the H of H− using the connection instructions of C’.

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4.2 Derivation of GGHD 　

(cont.)

Remove mother node and edges that connect

with [profile_module_list]

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(cont.)

Embed the daughter graph

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(cont.)

Establish edges using the connection instructions

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4.3 Precedence Relation for GGHD

We adopted a precedence relation of graph grammar for Hichart/DXL using Kaul’s definitions

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4.3 Precedence Relation for GGHD (cont.)

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s1=(P1, [module_packet], D1, b)

sD(2)=s1

sD(3)=s1

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32


s2=(P3, [profile_module_list], D2, b)

sD(4)=s2

sD(5)=s2

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34


s3=(P4, [profile], D3, b)

sD(6)=s3

sD(7)=s3

35


36


s4=(P5, [module_list], D4, b)

sD(8)=s4

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432104321

GGGGGssssderivation

sequence ：

sD(6)=s3, sD(7)=s3, s3 =D s3, 6 = 7

6 7 ⇔ sD(6) D sD(7)

lab(6, 7) = ("profile", #, , "explanation") R ∈ =

[The precedence relation between 6 and 7 ]

421321 ,, ssssss DDDD

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4.3 Precedence Relation for GGHD (cont.) We defined all the precedence relations

between labels for grammar GGHD

We call this grammar the Precedence Graph Grammar for Hichart/DXL (PGGHD)

[Property 1]PGGHD is a precedence graph grammar

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5. Parsing of Precedence Graph Grammar for Hichart/DXL

5.1 Algorithm for parsing5.2 Example of Parsing

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5.1 Algorithm for parsing

uses a stack for storing traversed nodes Starts parsing from the root node of an input graph

[parsing]1. shift as long as possible2. If there is no ascending node, the parser searches

a production where the right-hand-side is isomorphic to the precedence handle.

3. reduce the precedence handle to lhs of the production

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“m_packet” “profile”

“identifier_is”

“explanation”

“module_algorithm”

“BoxEmpty1”

<

< <

<

M_Packet

0

G

K※

5.2 Example of ParsingAn input

graph

An ordered listof G

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“identifier_is”

“explanation”


“BoxEmpty1”

<

< <

<

“m_packet”

0

G

K

※

5.2 Example of Parsing (cont.)

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“identifier_is”

“explanation”


“BoxEmpty1”

<

< <

<

“m_packet”

0

G

K

TOP(G,K)

※


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“m_packet”

0

“profile”

1

G

K



“identifier_is”

“explanation”


“BoxEmpty1”

<

< <

<

※

45

G

K

TOP(G,K)



“identifier_is”

“explanation”


“BoxEmpty1”< <

※“m_packet”

0

“profile”

1

< <

46

G

K “explanation”

2



“identifier_is”

“explanation”


“BoxEmpty1”< <

※

< <

“m_packet”

0

“profile”

1

47

G

K “explanation”

2



“identifier_is”

“explanation”


“BoxEmpty1”< <

※

< <

“m_packet”

0

“profile”

1

TOP(G,K)

48

G

K “explanation”

2



“identifier_is”

“explanation”


“BoxEmpty1”< <

※

< <

“m_packet”

0

“profile”

1

TOP(G,K)

find_production

P10

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G

K [explanation]

2



“identifier_is”

[explanation]


“BoxEmpty1”< <

※

< =

“m_packet”

0

“profile”

1

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G

K [explanation]

2



“identifier_is”

[explanation]


“BoxEmpty1”< <

※

< =

“m_packet”

0

“profile”

1

TOP(G,K)

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G

K [explanation]

2



“identifier_is”

[explanation]


“BoxEmpty1”< <

※

< =

“m_packet”

0

“profile”

1

TOP(G,K)

find_production

P04

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G

K


“m_packet”

“identifier_is”


“BoxEmpty1”< <

<

“m_packet”

0

[profile]

1

[profile]

<

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G

K


“m_packet”

“identifier_is”


“BoxEmpty1”< <

<

“m_packet”

0

[profile]

1

[profile]

<

TOP(G,K)

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G

K


“m_packet”

“identifier_is”


“BoxEmpty1”< <

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”

2

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G

K


“m_packet”

“identifier_is”


“BoxEmpty1”< <

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”

2

TOP(G,K)

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G

K


“m_packet”

“identifier_is”


“BoxEmpty1”< <

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”

2“module_algorithm”

3

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G

K


“m_packet”

“identifier_is”


“BoxEmpty1”< <

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”


3

TOP(G,K)

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G

K


“m_packet”

“identifier_is”


“BoxEmpty1”< <

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”


3

“BoxEmpty1”

4

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G

K


“m_packet”

“identifier_is”


“BoxEmpty1”< <

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”


3

“BoxEmpty1”

4

TOP(G,K)

60

G

K


“m_packet”

“identifier_is”


“BoxEmpty1”< <

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”


3

“BoxEmpty1”

4

TOP(G,K)

find_production

P14

61

G

K


“m_packet”

“identifier_is”


[statement_list]

< =

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”


3[statement_

list]

4

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G

K


“m_packet”

“identifier_is”


[statement_list]

< =

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”


3[statement_

list]

4

TOP(G,K)

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G

K


“m_packet”

“identifier_is”


[statement_list]

< =

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”


3[statement_

list]

4

TOP(G,K)

find_production

P11

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G

K


“m_packet”

“identifier_is”

<

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”

2[module_algorithm]

3

[module_algorithm]

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G

K


“m_packet”

“identifier_is”

<

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”

2[module_algorithm]

3

[module_algorithm]

TOP(G,K)

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G

K


“m_packet”

“identifier_is”

<

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”

2[module_algorithm]

3

[module_algorithm]

TOP(G,K)

find_production

P08

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G

K


“m_packet”

“identifier_is”

=

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”

2

[explanation_modue_algorithm]


3

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G

K


“m_packet”

“identifier_is”

=

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”

2



3

TOP(G,K)

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G

K


“m_packet”

“identifier_is”

=

<

“m_packet”

0

[profile]

1

[profile]

<

“identifier_is”

2



3

TOP(G,K)

find_production

P07

70

G

K


“m_packet”<

“m_packet”

0

[profile]

1

[profile]

<

[module]

[module]

2

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G

K


“m_packet”<

“m_packet”

0

[profile]

1

[profile]

<

[module]

[module]

2

TOP(G,K)

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G

K


“m_packet”<

“m_packet”

0

[profile]

1

[profile]

<

[module]

[module]

2

TOP(G,K)

find_production

P05

73

G

K


“m_packet”<

“m_packet”

0

[profile]

1

[profile]

=

[module_list]

[module_list]

2

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G

K


“m_packet”<

“m_packet”

0

[profile]

1

[profile]

=

[module_list]

[module_list]

2

TOP(G,K)

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G

K


“m_packet”<

“m_packet”

0

[profile]

1

[profile]

=

[module_list]

[module_list]

2

TOP(G,K)

find_production

P03

76

G

K


“m_packet”=

“m_packet”

0

profile_module_list

profile_module_list

1

77

G

K


“m_packet”=

“m_packet”

0

profile_module_list

profile_module_list

1

TOP(G,K)

78

G

K


“m_packet”=

“m_packet”

0

profile_module_list

profile_module_list

1

TOP(G,K)

find_productionP01

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[module_packet]

[module_packet]

0

G

K


80

[module_packet]

[module_packet]

0

G

K


finish parsing

TOP(G,K)

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6. Hichart Editor【 Outline 】Hichart Editor Supports non-syntax-directed editing has parserJava （ 10,000steps ）【 features 】

1. To check the correctness of diagrams2. To draw Hichart diagrams aesthetically3. To generate an SVG file

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Input: Hichart diagrams

Output: Hichart code with derivation tree

SVG files with aesthetically drawing

6. Hichart Editor (cont.)

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DEMO

Parsing on Hichart Editor Generating SVG file on Hichart Editor

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7. ConclusionSummary Adapted a precedence relation of graph

grammar for Hichart/DXL productions 　 70 semantic rules 　 888 precedence relations 　 256

Implemented graphical editor with parser in JAVA

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7. Conclusion (cont.)

Our graph grammar based method would be able to apply to other visual programming systems that treat tree-like graphs

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7. Conclusion (cont.)

Future workTo apply our method of graph grammar

to Object-Oriented Language

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Precedence Graph Grammar for Hierarchical Program Diagram

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