Foundations of Model Transformation

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Foundations of Model Transformation
ARTIST2 - MOTIVESTrento - Italy, February 19-23,
2007 Model Transformation and UML Reiko
Heckel University of Leicester, UK
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Motivation Model-driven Engineering

• Focus and primary artifacts are models instead of
  programs
• Core activities include
• maintaining consistency
• evolution
• translation
• execution
• of models
• These are examples of model transformations

• A math. foundation is needed for studying
• expressiveness and complexity
• execution and optimisation
• well-definedness
• preservation of semantics
• of transformations
• Graph transformations can be one such foundation

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Outline

• Graph Transformation
• why it is fun
• how it works
• Semantics-preserving Model Transformation

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Why it is fun Programming By Example

• StageCast (www.stagecast.com) a visual
  programming environment for kids (from 8 years
  on), based on
• behavioral rules associated to graphical objects
• visual pattern matching
• simple control structures (priorities, sequence,
  choice, ...)
• external keyboard control
• intuitive rule-based behavior modelling
• Next abstract from concrete visual presentation

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States of the PacMan GameGraph-Based
Presentation
Ghost
Field
Field
PacMan marbles3
Field
Field
Field
Marble
Field
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Rules of the PacMan GameGraph-Based
Presentation, PacMan
pmPacManmarblesm
pmPacManmarblesm1
Marble
collect
f1Field
f2Field
f1Field
f2Field
pmPacMan
pmPacMan
movePM
f1Field
f2Field
f1Field
f2Field
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Rules of the PacMan GameGraph-Based
Presentation, Ghost
gGhost
PacMan
gGhost
kill
f1Field
f2Field
f1Field
f2Field
gGhost
gGhost
moveGhost
f1Field
f2Field
f1Field
f2Field
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Graph Transformation
Field
Field
Ghost
collect kill
PacMan marbles3
PacMan marbles4
Field
Field
Field
Field
typing
PacManmarblesint
1
1


Field
Ghost
1

Marble
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Outline

• Graph Transformation
• why it is fun
• how it works
• Semantics-preserving Model Transformation

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A Basic Formalism Typed Graphs

• Directed graphs
• multiple parallel edges
• undirected edges as pairs of directed ones
• Graph homomorphism as mappings preserving source
  and target
• Typed graphs given by
• fixed type graph TG
• instance graphs G typed over TG by
  homomorphism g

Field
Field
gGhost
Field
Field
fField
Field
G
g
PacManmarblesint
Field
Ghost
Marble
TG
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Rules

• p L ? R with L ? R well-defined, in different
  presentations
• like above (cf. PacMan example)
• with L ? R explicit DPO L ? K ? R

movePM
pmPacMan
pmPacMan
f1Field
f2Field
f1Field
f2Field
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Rules

• p L ? R with L ? R well-defined, in different
  presentations
• like above (cf. PacMan example)
• with L ? R explicit DPO L? K ? R
• with L, R integrated UML, Fujaba L ? R and
  marking
• L - R as destroyed
• R - L as new

movePM
pmPacMan
destroyed
new
f1Field
f2Field
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Transformation Step
G
f1Field
m1Marble
pmPacMan marbles3
f2Field
m2Marble
f3Field

1. select rule p L ? R occurrence oL L ? G
2. remove from G the occurrence of L\ R
3. add to result a copy of R \ L

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Semantic Questions Dangling Edges

• conservative solution application is forbidden
• invertible transformations, no side-effects
• radical solution delete dangling edges
• more complex behavior, requires explicit control

?
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A bit of History
Chomsky Grammars
Term Rewriting
PetriNets
Graph Transformation and Graph Grammars
Diagram Languages
Behaviour Modelling and Visual Programming
Models of Computation
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Outline

• Graph Transformation
• why it is fun
• how it works
• Semantics-preserving Model Transformation
• operational
• denotational

transformation
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Example Executable Business Process

• refactoring of business processes, replacing
  centralised by distributed execution
• How to demonstrate preservation of behaviour?
• specify operational semantics of processes
• define transformations
• show that transformations preserve semantics

Warehouse
Office
Receiveorder
Undoorder
Shipment
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Operational Semantics Idea
operational
semantics
Abstract
Syntax

• diagram syntax plus runtime state
• GT rules to model state transitions

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Operational Semantics Formally

• GTS (TG, P) with start graph G0
• defines transition system
• LTS(GTS, G0) (S, L, ?)
• taking
• as states S all graphs reachable from G0
• observations on rules as labels
• transformations as transitions

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Type Graph Metamodel
Abstract
response
Syntax
Msg op String id String
with runtime state
request
to
from
current
Orch name String
Elem
partner
responsible
src
Edge
Node
tar
corresponds
Basic op String
Structured
Switch
Invoke
Reply


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Rules Invoke another Service
operational
semantics
Abstract
Syntax
tar
partner
eEdge
iInvoke
current
o1Orch
o2Orch
partner
tar
eEdge
iInvoke
current
request
req(i.id, m.id)
from
mMsg idnew() opi.op
to
o1Orch
o2Orch
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Rules Answer the Invocation
operational
semantics
Abstract
tar
src
Syntax
eEdge
rReply
eEdge
current
m1Msg opr.op
from
to
o1Orch
o2Orch
tar
src
eEdge
rReply
eEdge
current
m1Msg opr.op
from
to
reply(r.id, m1.id, m2.id)
o1Orch
o2Orch
response
from
to
m2Msg idnew() opr.op
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Rules Receive the Response
operational
semantics
Abstract
src
Syntax
iInvoke
eEdge
current
partner
request
to
from
o1Orch
o2Orch
m1Msg
response
to
from
m2Msg
src
iInvoke
eEdge
resp(i.id, m2.id)
partner
current
o1Orch
o2Orch
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Simulation
Edge
Edge
tar
tar
current
current
partner
iInvoke
o1Orch
o2Orch
rReply
src
src
Edge
Edge
Observations
req(i.id, m1.id)
reply(r.id, m1.id, m2.id)
resp(i.id, m2.id)
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Refactoring Executable Processes
Orch 1
Orch1
Orch 2
Orch 2
ltltreceivegtgt op
delegate




ltltinvokegtgt Orch2.op




ltltreplygtgt op

• replace local control flow by message passing

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Semantic Compatibility

• Processes P1 and P2 are semantically compatible
  if they are weakly bisimilar after hiding labels
  not in alph(P1) ? alph(P2)
• Show for trafo P1 ? P2 that P2 simulates P1, i.e.
• P1?obs Q1 implies P2 ?obs Q2
• Q2 simulates Q1
• and vice versa.
• Approach
• mixed (local) confluence
• critical pair analysis

obs
P1
Q1
obs
P2
Q2
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Critical Pairs and Local Confluence

• a pair of rules (p1, p2) in a minimal conflict
  situation
• constructed by overlapping their left-hand sides
  so that they intersect in items to be deleted
• system is locally confluent if all critical
  pairs are

G
p2
p1
G2
G1


H
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Critical Pair Analysis in AGGdelegate vs
operational rules
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Critical Pair
LHS ofinvoke vs delegate
delete-use-conflict
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Outline

• Graph Transformation
• why it is fun
• how it works
• Semantics-preserving Model Transformation
• operational
• denotational

transformation
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Process Improvement

• Motivation
• transform process to increase flexibility,
  performance, ...
• preserve behaviour!
• Aim rule-level verification

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Rule-level Verification
r
r/o
H
G
s(L)
s(R)
s(H)
s(G)
semantic domain

• Approach
• check for each rule r if s(L) R s(R)
• make sure that s(L) R s(R) implies s(G) R s(H)

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Works if

• we select semantic domain SD where relation R is
  compositional
• trace or failures equivalence or refinement in
  CSP is closed under context
• we can show that semantic mapping s AS ? SD is
  compositional
• maps union of graphs to composition of CSP
  processes
• ? use GT to define mapping s

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Context-Free Graph Grammar
Abstract
Syntax
Concrete syntax of well-structured activity
diagrams
Productions in EBNF-like notation
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Analysis
0
1
3
receive order
4
check availability
product available
2
product not available
5
6
calculate prize
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notify client
7
send receipt
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Pair Grammar
Abstract
AAct
Syntax
Source well-structured activity diagrams
denotational
semantics
Semantic
Domain
in
not c
c
do something

out
if c then Proc(A1) else Proc(A2)
do something
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Synthesis

• Proc(A0)
• Proc(A1) Proc(A2)
• Proc(A3) Proc (A4) if product available
  then Proc(A5) else Proc(A8)
• receive order check availability if product
  available then calculate prize
  send receipt else notify client

receive order
check availability
product available
product not available
calculate prize
notify client
send receipt
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Good Enough ?

• Visual
• abstract syntax or concrete syntax templates
• Bi-directional
• swap source and target grammars
• Declarative

• Expressive ?
• context-free graph languages only
• Traceable ?
• through naming conventions
• Efficient ?
• NP complete parsing problem

? Triple Graph Grammars (see Andys
lecture) Challenge verify compositionality for
more complex mappings
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Relevant Theory
Chomsky Grammars
Term Rewriting
PetriNets
Graph Transformation and Graph Grammars

• Concurrency theory
• Causality and conflict
• Processes, unfoldings
• Event-structures
• Stochastic concepts
• Verification,

• Formal language theory of graphs
• Diagram compiler generators

• Well-definedness
• Termination
• Confluence
• Semantics of process calculi