Towards Domain Completeness for Model Transformations Based on - - PowerPoint PPT Presentation

Nico Nachtigall, Frank Hermann, Benjamin Braatz, Thomas Engel (University of Luxembourg)

Towards Domain Completeness for Model Transformations Based on Triple Graph Grammars

VOLT 2014

21-JULY-2014

Source: SES - www.ses.com

Industrial Project: PIL2SPELL

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Source: SES - www.ses.com

ASTRA fleet

• f SES

Partner SES: 55 satellites Aim: Automated generation of test cases for static simulator Requirements: (1) Fully automated (2) Full coverage (3) High level of reliability: fidelity/precision, correctness, completeness

1. Symbolic execution 2. Model Transformation: Generation of test cases – inputs for each execution path: TM values, user inputs – automatic path traversal 3. Execution of test cases in simulator

Scenario for testing – static simulator

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Control procedure 1

def lift(target): current = GetTM('TM_HEIGHT') if current-target > 500: return False elif current-target < -500: Send('C_LIFT') return lift(target) else: return True while True: if Prompt('Abort?', YES_NO) break target=Prompt('Height:', NUM) if not lift(target): #Alert ...

SPELL Test input 2

<Test name="Lift Satellite"> <Test Case> <User> False, 23000 </User> <Telemetry name="TM_HEIGHT"> <Values> 22000,24000 </Values> </Telemetry> </Test Case> ... <Test>

XML Static simulator 3

• Challenge: Domain Completeness
• Conceptual Overview and TGGs
• Solution: C-Extension Completeness
• Evaluation
• Conclusion and Future Work

Outline

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Challenge: Domain Completeness

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A model transformation 𝑵𝑼: 𝑴𝑻 ⇛ 𝑴𝑼 from source language (DSL) 𝑀𝑇 to target language 𝑀𝑈 is a relation 𝑵𝑼 ⊆ 𝑴𝑻 × 𝑴𝑼.

Model Transformation (MT)

𝑁𝑈 is domain complete, if ∀𝑁𝑇 ∈ 𝑀𝑇: ∃ 𝑵𝑻, 𝑵𝑼 ∈ 𝑵𝑼 .

Domain Completeness

𝑀𝑇 𝑀𝑈

• DSL is specified by meta model (type graph) and constraints C1:

𝑀 = ℒ(𝐵𝑈𝐻𝐽, 𝐷)

• Source language: class diagrams
• Target language: data base models

Example: CD2RDBM

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[1]

• U. Golas, L. Lambers, H. Ehrig, F. Orejas: Attributed graph transformation with inheritance: Efficient conflict

detection and local confluence analysis using abstract critical pairs. Theor. Comput. Sci. 424: 46-68 (2012).

• Challenge: Domain Completeness
• Conceptual Overview and TGGs
• Solution: C-Extension Completeness
• Evaluation
• Conclusion and Future Work

Outline

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Translation Concept

• 3. Serialisation
• 1. Parsing

L1 Source Code L2 Source Code

• 2. TGGs

L1 EMF L2 EMF

General Concept: Language Conversion

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Key Idea of Triple Graph Grammars (TGGs)

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Translation (TGGs, Henshin)

Henshin

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Source Model Target Model Correspondence Model

Triple Graph

• Specify pattern by pattern how consistent integrated

models can be constructed simultaneously

Key Idea of Triple Graph Grammars (TGGs)

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Source Model Target Model Correspondence Model

Triple Graph

• Specify pattern by pattern how consistent integrated

models can be constructed simultaneously

• Generate operations for interoperability:

Model Translation/Integration/Synchronisation

Key Idea of Triple Graph Grammars (TGGs)

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Source Model Target Model Correspondence Model

Triple Graph

• Specify pattern by pattern how consistent integrated

models can be constructed simultaneously

• Generate operations for interoperability:

Model Translation/Integration/Synchronisation

Key Idea of Triple Graph Grammars (TGGs)

Triple type graph

Example: Type graph of TGG

21-JULY-2014 Domain Completeness for TGGs 13 TG TGS TG TGC TG TGT Attribute attrs type Table name:String

CT

ColumnType name:String

TT

Column name:String

AC

type colsref Classifier {abstract} Class PrimitiveType NamedElement {abstract} name:String 1 1 * * pkey

Class diagram Data base model

Example: Triple Rule for CD2RDBM

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Triple Rule

3: A2C = Attribute2Column(n:String)

:AC

:cols ++ :attrs ++ :Class :Table

:CT

:Attribute name = n ++ ++ :Column name = n ++ ++ ++ ++ ++ :Column name = n :cols NAC

Source Rule

3: A2CS = Attribute2ColumnS(n:String) :attrs ++ :Class :Attribute name = n ++ ++

Each TGG-model transformation 𝑁𝑈 is

• syntactically correct: for each 𝑁𝑈-sequence

there is 𝐻 = (𝐻𝑇 ← 𝐻𝐷 → 𝐻𝑈) ∈ 𝑀(𝑈𝐻𝐻)

• complete: for each source model 𝐻𝑇 ∈ 𝑀(𝑈𝐻𝐻)𝑇 there is an

𝑁𝑈-sequence

• terminating, if all rules are source creating

Theorem (Correctness, Completeness and Termination)

Results for MTs via TGGs

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[1,2]

[1]

• H. Ehrig, K. Ehrig, C. Ermel, F. Hermann, and G. Taentzer: Information Preserving Bidirectional

Model

• Transformations. Proc. FASE‘07. Springer (2007).

[2]

• F. Hermann, H. Ehrig, U. Golas, F. Orejas: Formal Analysis of Model Transformations Based on Triple Graph
• Grammars. MSCS (to appear 2014).

Each TGG-model transformation 𝑁𝑈 is

• complete: for each source model 𝐻𝑇 ∈ 𝑀(𝑈𝐻𝐻)𝑇 there is an

𝑁𝑈-sequence Theorem (Completeness)

Challenge: Domain Completeness

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[1,2]

𝑁𝑈 is domain complete, if ∀𝑁𝑇 ∈ 𝑀𝑇: ∃ 𝑵𝑻, 𝑵𝑼 ∈ 𝑵𝑼 .

Domain Completeness Need for extended results

𝑀𝑇 ⊆ 𝑀 𝑈𝐻𝐻 𝑇

Challenge

𝑴𝑻 ⊆ 𝑴 𝑼𝑯𝑯𝑻 ⊆ 𝑀 𝑈𝐻𝐻 𝑇

This talk

• Challenge: Domain Completeness
• Conceptual Overview and TGGs
• Solution: C-Extension Completeness
• Evaluation
• Conclusion and Future Work

Outline

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• 𝑀𝑇 = 𝑀 𝐵𝑈𝐻𝐽, 𝐷 , 𝐵𝑢𝑝𝑛𝑡 𝐻𝑇
• Show that ∀𝑏 ∈ 𝐵𝑢𝑝𝑛𝑡 𝐵𝑈𝐻𝐽 : 𝑏 can be

constructed via 𝑈𝐻𝐻𝑇 - either directly or for all extensions 𝐹𝑗 required by constraints 𝐷

• Ensure that creation sequences can be

merged to a single one for 𝐻

C-extensions

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𝑀𝑇 𝑭𝟐 𝑭𝟑 𝐻𝑇 𝐵𝑢𝑝𝑛𝑡(𝐻𝑇) 𝐷-extension completeness Conflict freeness

Main result for verifying language inclusion 𝑀 𝐵𝑈𝐻𝐽, 𝐷 ⊆ 𝑀 𝐵𝑈𝐻𝐽, 𝑈𝐻𝐻𝑇 :

Formal Result: C-Extension Completeness

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Let 𝑀1 = 𝑀 𝐵𝑈𝐻𝐽, 𝐷 , 𝑀2 = 𝑀 𝐵𝑈𝐻𝐽, 𝐻𝐻 with grammar 𝐻𝐻 = 𝐵𝑈𝐻𝐽, 𝑇𝐻, 𝑄 , non-deleting rules 𝑄, 𝑇𝐻 = ∅. If marking rules 𝑛(𝐻𝐻) are 𝑫-conflict-free and 𝑀2 is 𝑫-extension complete, then 𝑴𝟐 ⊆ 𝑴𝟑. Theorem (Language Inclusion) encoding of rules with markers

Tool Support

Marking rules

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Grammar Rule :attrs ++ :Class :Attribute name = n ++ ++ Marking Rule :attrs mark=[F => T] :Class mark=T :Attribute name = n mark=[F => T] mark_name=[F => T]

• Challenge: Domain Completeness
• Conceptual Overview and TGGs
• Solution: C-Extension Completeness
• Evaluation
• Conclusion and Future Work

Outline

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• 1. Conditions are sufficient, not necessary
• 2. Grammar 𝐻𝐻 is non-deleting
• 3. Start graph 𝑇𝐻 is empty
• 4. Morphisms in conditions have to be ℳ-morphisms

𝑏: 𝑄 → 𝐷

• 1. Merge of attribute values via 𝑏 is not allowed
• 2. Reason: check is performed on 𝐵𝑢𝑝𝑛𝑡(𝐵𝑈𝐻𝐽) to

ensure termination → no concrete attribute values, only terms

• 5. Conflict-freeness of marking rules:

sufficient, but not necessary to ensure confluence

Limitations

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• Term rewriting: DMS [1], TXL [2], Rascal [3], Spoofax [4]

→ standard approach to AST conversion – restriction to tree structures limits flexibility in preprocessing PIL2SPELL: non-treelike helper structures (simpler TGG) – Matching order of nodes: top-down/bottom up PIL2SPELL: manual search tree + automatic heuristic – Extended control structures to ensure efficiency → potential to extend TGG theory and tools

Related Work

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[1] Baxter, I., Pidgeon, P., Mehlich, M.: DMS: Program transformations for practical scalable software evolution. In: Software Engineering (ICSE 2004). IEEE Press (2004) [2] Cordy, J.R.: The TXL source transformation language. Science of Computer Programming 61(3), 190–210 (2006) [3] Klint, P., Vinju, J.J., van der Storm, T.: RASCAL: A domain specific language for source code analysis and

• manipulation. In: Source Code Analysis and Manipulation. pp. 168–177. IEEE Computer Society (2009)

[4] Kats, L.C.L., Visser, E.: The Spoofax language workbench. rules for declarative specification of languages and IDEs. In: Object-Oriented Programming, Systems, Languages, and Applications, OOPSLA 2010 (2010)

• Extension of existing results for TGGs concerning

completeness: first of two steps for domain completeness 𝑴𝒕 ⊆ 𝑴 𝑼𝑯𝑯𝑻 ⊆ 𝑀 𝑈𝐻𝐻 𝑇

• General result for graph grammars: Checkig language

inclusion 𝑀1 ⊆ 𝑀 𝐻𝐻 for non-deleting 𝐻𝐻 Future Work

• Second step: 𝑴 𝑼𝑯𝑯𝑻 ⊆ 𝑀 𝑈𝐻𝐻 𝑇 or adaptation
• Investigate possible extensions concerning “deleting”

grammars

Conclusion and Future Work

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Thank You! Questions …

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References

21-JULY-2014 Domain Completeness for TGGs 26

• Baxter, I., Pidgeon, P., Mehlich, M.: DMS: Program transformations for practical

scalable software evolution. In: Software Engineering (ICSE 2004). IEEE Press (2004)

• Bergmann, G., Horváth, Á., Ráth, I., Varró, D.: Incremental Evaluation of Model

Queries over EMF Models: A Tutorial on EMF-IncQuery. In: Proc. ECMFA 2011. (2011)

• Cordy, J.R.: The TXL source transformation language. Science of Computer

Programming 61(3), 190–210 (2006)

• H. Ehrig, K. Ehrig, C. Ermel, F. Hermann, and G. Taentzer: Information Preserving

Bidirectional Model Transformations. Proc. FASE‘07. Springer (2007).

• H. Ehrig, K. Ehrig, U. Prange, and G. Taentzer: Fundamentals of Algebraic Graph
• Transformation. EATCS Monographs in Theoretical Computer Science. Springer

(2006).

• Giese, H., Wagner, R.: From model transformation to incremental bidirectional

model synchronization. Software and Systems Modeling 8(1), Springer (2009).

• Hildebrandt, S., Lambers, L., Giese, H., Rieke, J., Greenyer, J., Schäfer, W., Lauder,

M., Anjorin, A., Schürr, A.: A survey of triple graph grammar tools. In: Proc. BX

• 2013. ECEASST, vol. 57. (2013)

References

21-JULY-2014 Domain Completeness for TGGs 27

• Kats, L.C.L., Visser, E.: The Spoofax language workbench - rules for declarative

specification of languages and IDEs. In: Object-Oriented Programming, Systems, Languages, and Applications, OOPSLA 2010 (2010)

• Klint, P., Vinju, J.J., van der Storm, T.: RASCAL: A domain specific language for

source code analysis and manipulation. In: Source Code Analysis and

• Manipulation. pp. 168–177. IEEE Computer Society (2009)
• Lauder, M., Anjorin, A., Varró, G., Schürr, A.: Bidirectional model transformation

with precedence triple graph grammars. In: Proc. ECMFA 2012. (2012)

• Plump, D.: Checking Graph-Transformation Systems for Confluence. ECEASST 26

(2010).

• Tichy, M., Krause, C., Liebel, G.: Detecting performance bad smells for Henshin

model transformations. In: Proc. AMT 2013 (2013)

Background Slides

Constraints

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A condition 𝑏𝑑𝑄 over graph 𝑄 is inductively defined by:

• true,
• ∃ 𝑏, 𝑏𝑑𝐷 , for morphism 𝑏: 𝑄 → 𝐷 and condition

𝑏𝑑𝐷 (P=Premise & C=Conclusion),

• ¬𝑏𝑑𝑄,∨𝑗∈ 𝐽 𝑏𝑑𝑄,𝑗 ,∧𝑗∈𝐽 𝑏𝑑𝑄,𝑗 , for conditions 𝑏𝑑𝑄 and

𝑏𝑑𝑄,𝑗 𝑗 ∈ 𝐽 , Graph Conditions

Constraints

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𝐻 ⊨ 𝑏𝑑𝑄, if:

• 𝑏𝑑𝑄 = true
• 𝑏𝑑𝑄 = ∃ 𝑏: 𝑄 → 𝐷, 𝑏𝑑𝐷 , for all occurrences 𝑞 ∶ 𝑄 →

𝐻 of 𝑄 in 𝐻 with 𝑞 ∈ 𝒫, also 𝐷 occurs in 𝐻 (∃𝑟 ∶ 𝐷 → Satisfaction