Meta-Modelling and Graph Rewriting, Enablers for Domain...

SOCS Software Engineering Meeting23 September 2004

Meta-Modelling and Graph Rewriting,

Enablers for

Domain-Specific (Visual) Modelling

“model everything”

Hans Vangheluwe

Modelling, Simulation and Design Lab (MSDL)School of Computer Science, McGill University, Montreal, Canada

Hans Vangheluwe [email protected] MM, GG, DSVM 1/78

Overview

1. Domain-Specific (Visual) Modelling – DS(V)M� What/Why of DS(V)M (and DS(V)Ls) ?

� Examples

2. Building DS(V)M Tools Effectively

(a) Specifying textual/visual syntax of DS(V)Ls:

meta-modelling

(b) Specifying DS(V)L semantics

(c) Modelling (and executing) transformations:

graph rewriting

(d) Traffic, a domain-specific modelling formalism


3. AToM3, A Tool for Multi-formalism Meta-Modelling� Different “aspects” of AToM3

� A plethora of applications

� Current and future work


Domain-Specific (Visual) Modelling

DS(V)M “Domain-Specific (Visual) Modelling”

DS(V)Ls “Domain-Specific (Visual) Languages”

Some starting points:

� www.dsmforum.org

� OOPSLA Workshops on DSM

� Juan de Lara and Hans Vangheluwe. Defining visual notations and their manipulation

through meta-modelling and graph transformation. Journal of Visual Languages and

Computing, 15(3 - 4):309-330, June - August 2004. Special Issue on

Domain-Specific Modeling with Visual Languages.

� The OMG’s Model Driven Architecture (MDA) www.omg.org/mda


Why DS(V)M ?


DS(V)M Example 1: smart phones, the model

MetaEdit+ (www.metacase.com)


DS(V)M Example 1: smart phones, the application

MetaEdit+ (www.metacase.com)


Why DS(V)M ?� match the user’s mental model of the problem domain

� maximally constrains users

� separate domain-expert’s

from transformation expert’s work,

from target domain (e.g., code libraries) expert’s work

� re-use transformation knowledge

� model everything (nothing left implicit)


How to do DS(V)M ?


DS(V)M Example 2: Waste Water Treatment Plant

NATO’s Sarajevo WWTPhttp://www.nato.int/sfor/cimic/env-pro/waterpla.htm


WWTP Block Diagram (domain-specific) model

influentmixer

aeration_tanksettler effluent

f_influent f_mixed f_processed f_out

f_bacteria


Model of the Transformation from WWTP to . . .

influent

f_influent

f_influent

C_influent

0.0

OUT

mixer

f_influent

f_bacteria

f_mixed

f_bacteria

f_influent f_mixed

I OUT

C_aeration

0.9

aeration_tank

f_mixed

aeration_fraction

f_processed

f_processedf_mixed

TR

AN

SF

OR

M

TR

AN

SF

OR

M

TR

AN

SF

OR

M


... its meaning (in the steady-state abstraction):Causal Block Diagram (CBD)

C_influent

10.0 OUT

C_settling

0.6

I OUT

I OUT

−

1.0

OUT

effluentI OUT

f_influent

f_bacteria

f_mixed

settling_fraction

one

negated dump_fractionf_out

C_aeration

0.9

aeration_fraction

f_processed


Multi-step Transformation: meaning of the CBD��

��

�

C_influent

10.0 OUT

C_bacteria

1.0

C_settling

0.6

I OUT

I OUT

−

1.0

OUT

effluent

dump

I OUT

f_influent

f_bacteria

f_mixed

settling_fraction

one

negated

dump_fraction

f_dump

f_out

C_aeration

0.9

aeration_fraction

f_processed

� ��

� ��

��

�

f in f luent � C in f luent

f bacteria � C bacteria

f mixed � f in f luent f bacteria

aeration f raction � C aeration

f processed � aeration f raction� f mixed

settling f raction � C settling

negated � � settling f raction

one � 1

dump f raction � one negated

f dump � f processed� dump f raction

f out � settling f raction� f processed


WWTP Simulation Environment

www.hemmis.com/products/west/

Henk Vanhooren, Jurgen Meirlaen, Youri Amerlinck, Filip Claeys, Hans Vangheluwe, and

Peter A. Vanrolleghem. WEST: Modelling biological wastewater treatment. Journal of

Hydroinformatics, 5(1):27-50, 2003.


Building DS(V)M Tools Effectively� development cost of DS(V)M Tools may be prohibitive !

� we want to effectively (rapidly, correctly, re-usably, . . . )

specify and generate/execute:

– DS(V)Ls

– (reactive) behaviour of DS(V)M environments

– transformations

model everything


Building DS(V)M Tools Effectively

1. Specifying textual/visual syntax of DS(V)Ls:

meta-modelling

2. Specifying DS(V)L semantics

3. Modelling (and executing) transformations:

graph rewriting

4. Traffic, a domain-specific modelling formalism


Specifying textual/visual syntax of DS(V)Ls� abstract syntax:

– meta-model (� type graph)

– syntax grammar (SableCC text grammar, AToM3 Graph Grammar)

� concrete syntax:

– textual (SableCC lexing)

– visual (AToM3 “icons” + connections)


Meta-modelling


Meta-modelling: model-instance morphism

name type=String init.value=tokens type=Integer init.value=0

PNPlacename type=String init.value=PNTransition

mapping mapping mappingmapping

place10

place20

transition

level M2: model

a model of the Petri Net formalism,an INSTANCE of the Entity Relationship formalism

level M1: data

a Petri Net,an INSTANCE of the Petri Net formalism

tran2pl

pl2tran

mappingmapping


Meta-modelling: model-instance morphism ctd.

name type=String init.value=attributes type=List init.value=

ERentity

name type=String init.value=tokens type=Integer init.value=0

PNPlacename type=String init.value=PNTransition

level M3: meta−model

a model of the Entity Relationship formalism,an INSTANCE of the Core formalism(Core == Entity Relationship)

level M2: model

a model of the Petri Net formalism,an INSTANCE of the Entity Relationship formalism

level M1: data

a Petri Net,an INSTANCE of the Petri Net formalism

mappingmapping

mappingmapping

mapping

mapping mapping mappingmapping

mapping

place10

place20

transition

ERrelationship

tran2pl

pl2tran


How to break the meta-* chain ?

name type=String init.valattributes type=List init

ERentity

ERrelationship

bootstrap ER (Core == Entity Relationship)

note: interpret or compile meta-models


Example: the Traffic domain


a (domain-specific) model in the Traffic formalism

0bot_W2E

0turn1

0to_N_or_W

0turn2

0bot_N2S

2cars

1bot_CAP 1

turn1_CAP

1top_CAP

1turn2_CAP


A Traffic meta-model(an Entity Relationship model)

name type=String init.valnum_vehicles type=Integer

RoadSection

name type=String init.valnum_vehicles type=Integerinfinite_supply type=Enum

Source

name type=String init.valnum_vehicles type=Integer

Sink

capacity type=Integer ininame type=String init.val

Capacity

CapacityOf

FlowTo

Source2Section Section2Sink


Traffic meta-model notes

1. ER was extended with constraints

(OCL soon, now Python code)

2. alternative meta-formalisms: could use UML Class Diagrams

3. the given meta-model only specifies the Abstract Syntax of Traffic,

need to add Concrete (Visual) Syntax


Traffic Concrete Syntax (the Capacity Entity)


The generated Traffic visual modelling environment


Caveat: specifying the GUI’s Reactive Behaviour


The GUI’s reactive behaviour in action

current work: what is the optimal formalism to specify GUI reactive behaviour ?


Modelling Traffic’s Semantics� choices: timed, un-timed, . . . (level of abstraction)

� “denotational”: map onto known formalism (TTPN, PN)

good for analysis purposes

� “operational”: procedure to execute/simulate model

may act as a reference implementation

� note: need to prove that denotational and operational semantics

correspond if both are given !


Traffic, the Big Picture

neglect time

Timed Transition Petri Nets

Traffic (timed)

Traffic (un-timed)

Place-Transition Petri Nets

Coverability Graph

desc

ribe

sem

antic

s

by m

appi

ng o

nto

describe semanticsby mapping onto

compute allpossible behaviours

simulate

simulate

simulate

analyze:reachability,coverability, ...

simulateanalyze


Traffic’s semantics in terms of Petri Nets (PN)� need a meta-model of Traffic (shown before)

� need a meta-model of Petri Nets (shown before)

� need a model of the mapping: Traffic � Petri Nets


Graph Grammars to Specify Model Transformations

References:

Ehrig, H., G. Engels, H.-J. Kreowski, and G. Rozenberg. 1999. Handbook

of graph grammars and computing by graph transformation. World

Scientific.

. . .

Tools:

AGG, PROGRES, GME, AToM3, Fujaba, . . .


Traffic to Petri Net Graph Grammar rules

INITIAL ACTION:for node in graph.listNodes["RoadSection"]: node.vehiclesPNPlaceGenerated=False


A very simple Traffic model

2segment1

1segment2

4capacity



<ANY><ANY>

1

LHS

rule1: RoadSection2PNPlace

CONDITION:node = LHS.nodeWithLabel(1)return not node.vehiclesPNPlaceGenerated

ACTION:node = RHS.nodeWithLabel(1)node.vehiclesPNPlaceGenerated = True

<COPIED><COPIED>

<SPECIFIED><SPECIFIED>

1

2

3

RHS

LHS.nodeWithLabel(1)).name

LHS.nodeWithLabel(1)).num_vehicles


Road Sections converted to Petri Net Places

2segment1

1segment2

4capacity

segment12

segment21



<ANY><ANY>

<ANY><ANY>

<ANY><ANY>

<ANY><ANY>

1 27

3 4

5 6

LHS

<COPIED><COPIED>

<COPIED><COPIED>

<COPIED><COPIED>

<COPIED><COPIED>

0

1 2

103 4

9

5 6

8

RHS

rule 2: Flow2PNTransition

CONDITION:node = getMatched(LHS.nodeWithLabel(1))return node.in_connections_ == []

ACTION:node = RHS.nodeWithLabel(1)node.capacityPNPlaceGenerated = True


Traffic Flow to Petri Net Transitions

2segment1

1segment2

4capacity

segment12

segment21



rule 3: Capacity2PNPlace<COPIED>

<COPIED> <SPECIFIED><SPECIFIED>

1 23

RHS LHS.nodeWithLabel(1)).name

LHS.nodeWithLabel(1)).capacity

<ANY><ANY>

1

LHS


Traffic Capacity to Petri Net Place

2segment1

1segment2

4capacity

segment12

segment21

capacity4



<ANY><ANY>

<ANY><ANY> <ANY>

<ANY>

4

1

5

23

LHS

<COPIED><COPIED>

<COPIED><COPIED> <COPIED>

<COPIED>

4

1

6

23

RHS

rule 4: Capacity2PNPlaceLinks


Traffic Capacity to Petri Net Place (links)

2segment1

1segment2

4capacity

segment12

segment21

capacity4



<ANY><ANY> <ANY>

<ANY>1 2

3

LHS <COPIED><COPIED>

2

RHS

rule 5: Capacity2PNPlaceCleanup


Traffic Capacity to Petri Net Place cleanup

2segment1

1segment2

segment12

segment21

capacity4



<ANY><ANY>

<ANY><ANY>

<ANY><ANY>

<ANY>

<ANY>

17

2

6

5

3

4

LHS

<COPIED><COPIED>

<COPIED><COPIED>

<COPIED><COPIED>

<COPIED>

<COPIED>

1

8

7

2

6

5

3

4

RHS

rule 6: CapacityConstraintOnPl2Tr

CONDITION:cap_place = LHS.nodeWithLabel(6)out_trans = LHS.nodeWithLabel(4)capacity_transition_absent = Truefor in_link in cap_place.in_connections_: for out_link in out_trans.out_connections_: if (in_link == out_link) and isinstance(in_link,tran2pl): capacity_transition_absent = False breakreturn capacity_transition_absent


Capacity Constraint on Place to Transition

2segment1

1segment2

segment12

segment21

capacity4



<ANY><ANY>

<ANY><ANY>

<ANY>

<ANY><ANY>

<ANY>

1

5

7

2

6

4

3

LHS

<COPIED><COPIED>

<COPIED><COPIED>

<COPIED><COPIED>

<COPIED>

1

5

7

2

6

4

8

3

RHS

rule 7: CapacityConstraintOnTr2Pl

CONDITION:cap_place = LHS.nodeWithLabel(6)in_trans = LHS.nodeWithLabel(4)capacity_transition_absent = Truefor out_link in cap_place.out_connections_: for in_link in in_trans.in_connections_: if (in_link == out_link) and isinstance(in_link, pl2tran): capacity_transition_absent = False breakreturn capacity_transition_absent


Capacity Constraint on Transition to Place

2segment1

1segment2

segment12

segment21

capacity4



rule 8: InitialCapacity

<COPIED><COPIED> <COPIED>

<SPECIFIED>1

2

RHS

initial_num_vehicles = LHS.nodeWithLabel(1).num_vehiclescapacity_tokens = LHS.nodeWithLabel(2).tokensreturn capacity_tokens-initial_num_vehicles

<ANY><ANY> <ANY>

<ANY>1

32

LHS


Model Initial Capacity (applied rule twice)

2segment1

1segment2

segment12

segment21

capacity1



<ANY><ANY>

1

2LHS RHS

rule 9: RemoveRoadSection


Removed Traffic Road Section, now only Petri Net

segment12

segment21

capacity1


Static Analysis of the Transformation Model

The transformation specified by the Graph Grammar model must satisfy

the following requirements:

� Convergence: the transformation process is finite

� Uniqueness: the transformation results in a single target model

� Syntactic Consistency: the target model must be exclusively in the

target formalism


Traffic, the Big Picture

neglect time

Timed Transition Petri Nets

Traffic (timed)

Traffic (un-timed)

Place-Transition Petri Nets

Coverability Graph

desc

ribe

sem

antic

s

by m

appi

ng o

nto

describe semanticsby mapping onto

compute allpossible behaviours

simulate

simulate

simulate

analyze:reachability,coverability, ...

simulateanalyze


A less trivial Traffic model

0bot_W2E

0turn1

0to_N_or_W

0turn2

0bot_N2S

2cars

1bot_CAP 1

turn1_CAP

1top_CAP

1turn2_CAP


the Petri Net describing its behaviourobtained by Graph Rewriting

bot_W2E0

turn10

to_N_or_W0

turn20

bot_N2S0

cars2

bot_W2E_dep

top_S2W_dep

bot_N2S_dep

top_arrbot_N2S_arr

bot_W2E_arr

top_S2N_dep

bot_CAP1

turn1_CAP1

top_CAP1

turn2_CAP1


Analysis: a Coverability Graph for the Petri Net[turn1_CAP, cars(2), bot_CAP, top_CAP, turn2_CAP]

[turn1_CAP, cars, bot_W2E, top_CAP, turn2_CAP]

bot_W2E_arr

[cars, turn1, bot_CAP, top_CAP, turn2_CAP]

bot_W2E_dep

[turn1_CAP, cars, bot_CAP, turn2_CAP, to_N_or_W]

top_arr

[turn1_CAP, turn2, cars, bot_CAP, top_CAP]

top_S2W_dep

[turn1_CAP, cars, top_CAP, turn2_CAP, bot_N2S]

bot_N2S_arrbot_N2S_dep

[turn1_CAP, turn2, bot_W2E, top_CAP]

bot_W2E_arr

[turn2, turn1, bot_CAP, top_CAP]

bot_W2E_dep

[turn1_CAP, turn2, bot_CAP, to_N_or_W]

top_arr

[turn1_CAP, turn2_CAP, bot_N2S, to_N_or_W]

bot_N2S_arr

[turn1_CAP, turn2, top_CAP, bot_N2S]

top_S2W_dep

bot_N2S_dep

bot_N2S_dep

top_S2N_dep

top_S2N_dep

[turn1, top_CAP, turn2_CAP, bot_N2S]

bot_N2S_arrbot_N2S_dep

top_arr

[turn1_CAP, bot_W2E, turn2_CAP, to_N_or_W]

bot_W2E_arr

[turn1, bot_CAP, turn2_CAP, to_N_or_W]

bot_W2E_dep

top_S2W_dep

top_S2N_dep

top_S2W_dep

top_S2N_dep

top_S2N_dep

[turn1, bot_W2E, top_CAP, turn2_CAP]

bot_W2E_arr

top_arr


Conservation Analysis

1.0 x[turn1_CAP] + 1.0 x[turn1] = 1.0

1.0 x[cars] + 1.0 x[bot_W2E] + 1.0 x[turn1] +

1.0 x[to_N_or_W] + 1.0 x[turn2] + 1.0 x[bot_N2S] = 2.0

1.0 x[top_CAP] + 1.0 x[to_N_or_W] = 1.0

1.0 x[turn2_CAP] + 1.0 x[turn2] = 1.0

1.0 x[bot_CAP] + 1.0 x[bot_W2E] + 1.0 x[bot_N2S] = 1.0


Model-Based Development, Modify the Model

model

model’ app’

apptransformation

transformation

small modification


Model-Based Development, Modify theTransformation

model

model app’

apptransformation

small modification

transformation’


AToM3, A Tool for Multi-formalism Meta-Modelling

atom3.cs.mcgill.ca


Forrester System Dynamics modelof Predator-Prey behaviour

Predator Prey

Grazing_efficiency

uptake_predatorloss_prey

predator_surplus_DR

prey_surplus_BR

2−species predator−prey system


Causal Block Diagram modelof a Harmonic Oscillator

x0

0.0

y0

1.0

ICx

ICy

− I OUT

K

1.0

0.0

PLOT


Petri Net model of a Producer-Consumer system

P.Calculating1

Wait4Cons0

Buffer0

Buffer−p1

Wait4Prod1

C.Calculating0

Produce

Put in Buffer

Rem.from buffer

Consume


Statechart model of a Producer-Consumer system

Empty

Full

Producing Wait4Prod

Wait4Cons

Computing

Buff Producer Consumer

buffer++

buffer−−

Produce

/ buffer++

[in Buff.Empty]

/ buffer−−

[in Buff.Full]Consume


GPSS model of a Telephone Exchange

FN112

0

2V2

V1 PH1

LR PH1

V1 H2

P2NEP1

S PH1

LNKS

R PH1

1

LR PH2 R PH1

LNKS

1

S PH2

FN1120

Function: 1LNKS10


Generated GPSS code

1 FUNCTION RN1,C24

0.0,0.0/0.1,0.104/0.2,0.222/0.3,0.355/0.4,0.509/0.5,0.69

0.6,0.915/0.7,1.2/0.75,1.38/0.8,1.6/0.84,1.83/0.88,2.12

0.9,2.13/0.92,2.52/0.94,2.81/0.95,2.99/0.96,3.2/0.97,3.5

0.98,3.9/0.99,4.6/0.995,5.3/0.998,6.2/0.999,7.0/0.9997,8.0

*

L1 GENERATE 12,FN1

L3 TEST G V2,2,OUT

L4 ASSIGN 1,V1,H

L5 GATE LR PH1,L4 L17 ADVANCE 120,FN1

L6 ASSIGN 2,V1,H L18 LOGIC R PH1

L7 TEST NE P1,P2,L6 L19 LOGIC R PH2

L0 LOGIC R PH1 L20 LEAVE LNKS

L8 TRANSFER BOTH,L9,L11 L21 TERMINATE 1

L9 LOGIC R PH1 L13 LOGIC R PH1

L10 TERMINATE 1 L14 LEAVE LNKS

OUT TERMINATE 0 L15 TERMINATE 1

L11 ENTER LNKS LNKS STORAGE 10

L12 GATE LR PH2,L13 1 VARIABLE XH1*RN1/1000+1

L16 LOGIC S PH2 2 VARIABLE XH1-2*S$LNKS


HS=ES+ODE, a Hybrid Formalism� To demonstrate the ease with which an HS-specific modelling

environment can be built

� HS combines

– Event Scheduling (ES)

to describe discrete-event behaviour

– Ordinary Differential Equations (ODEs)

to describe continuous-time behaviour

– Constructs to link ES and ODE


Example: Personalized Rapid Transit (PRT)� Discrete-event behaviour: loading and unloading passengers

� Continuous-time behaviour: accelerating, decelerating

� Control: keep velocity between boundaries

by switching between continuous “modes”


Passenger Arrival

Train_at_rest

START EVENT

x = x_0v = v_0passengers = 0

Initialize_Model

passengers = passengers Passenger_arrive

print "Train is leaving iTrain_is_full

IFpassengers < 10

AFTERrandom.uniform ( 1 , 10 )

IF1

AFTER0

IF1

IFpassengers >= 10

AFTER0


Train Motion

AcceleratingODE

xv

vk * ( v − v_init + 5 )

FrictionODE

xv

v− k * ( v − 20 )

BrakingODE

xv

v− k * ( v + 3 )

print "Train is leaving a

Train_starts

Stop_Accelerating

Start_Accelerating

Start_Braking

monitoring fct.:

v_max − v

+−

testmax

monitoring fct.:

stopping_x − x

+−

test_arrival

monitoring fct.:

v − v_min

+−

testmin

AFTER5


Train Arrival and Unloading

Train_at_rest

BrakingODE

xv

v− k * ( v + 3 )

print "Train arrived at t

DepartureStartpassengers = passengers −

Departure_EventIF

passengers > 0

AFTER5

IF1

AFTER0

monitoring fct.:

v

+−

Test_zerospeed


The Complete Model

Train_at_rest

AcceleratingODE

xv

vk * ( v − v_init + 5 )

FrictionODE

xv

v− k * ( v − 20 )

BrakingODE

xv

v− k * ( v + 3 )

START EVENT

x = x_0v = v_0passengers = 0

Initialize_Model

passengers = passengers Passenger_arrive

print "Train is leaving iTrain_is_full

print "Train is leaving a

Train_starts

Stop_Accelerating

Start_Accelerating

Start_Braking

print "Train arrived at t

DepartureStartpassengers = passengers −

Departure_Event

IFpassengers < 10

AFTERrandom.uniform ( 1 , 10 )

IF1

AFTER0

IFpassengers > 0

AFTER5

monitoring fct.:

v_max − v

+−

testmax

monitoring fct.:

stopping_x − x

+−

test_arrival

monitoring fct.:

v − v_min

+−

testmin

IF1

AFTER5

IF1

AFTER0

IFpassengers >= 10

AFTER0

monitoring fct.:

v

+−

Test_zerospeed


Simulating the (compiled) Model


Train Passengers


Train Velocity


Date post:	04-Sep-2019
Category:	Documents
Upload:	others
View:	4 times
Download:	0 times

Meta-Modelling and Graph Rewriting, Enablers for Domain...

Documents