NECSIS Workshop March 10

NECSIS Workshops 1

Source-to-target model transf.

B…

A T(B)…

Space of M’s instances (models), [[

M]]

T(A)

…

Space of N’s instances (models),

[[ N]]

Metamodel M Metamodel NTransf. def. T

Color Legend:given datacomputed data

NECSIS Workshops

2

:execute T

:execute T

Space mapping [[T]]: [[M]] --> [[N]]

Towards Relational Algebra for Model Translations (just started)

McMaster:Hamid Gholizadeh, Sahar Kokaly, Tom Maibaum

Waterloo: Krzysztof Czarnecki, Michal Antkiewicz, Peiyuan Sun

Zinovy Diskin

NECSIS Workshops 3

Content

• New view of model translation– more abstract– transf. becomes a formal object

manipulateanalyze…..

NECSIS Workshops 4

Source-to-target model transf.

B…

A T(B)…

Space of M’s instances (models), [[

M]]

T(A)

…

Space of N’s instances (models),

[[ N]]

Metamodel M Metamodel NTransf. def. T

Color Legend:given datacomputed data

NECSIS Workshops

5

:execute T

:execute T

Space mapping [[T]]: [[M]] --> [[N]]

Model translation w/out traceability mappings

Model T(A)

Metamod. M

Car

Boat

lv’:LV

Transf. T1:Car -> CV*LV Boat -> LV

and

lv:LV

cv:CV

Metamod. N

Commut.Vehicle

LeisureVehicle

physical objects object roles

Model A

c:Car

b:Boat

NECSIS Workshops 6

up to iso

Model translation w/out traceability mappings

Model T(A)

Metamod. M

Car

Boat

lv’:LV

Transf. T1:Car -> CV*LV Boat -> LV

and

lv:LV

cv:CV

Theorem. [[ T1]] ≅ [[ T2 ]], where [[T1,2]]: [[M]] --> [[N]] are space functions generated by T1,2

Metamod. N

Commut.Vehicle

LeisureVehicle

physical objects object rolesTransf. T2:Car -> LVBoat -> CV*LV

R 11

Model A

c:Car

b:Boat

cb:R

lv:LV

cv:CV

lv’:LV

T1(A) ≅ T2(A)

NECSIS Workshops 7

up to iso

Model translation with traceability mappings

Model T(A)

Metamod. M

Car

Boat

lv’:LV

Transf. T1:Car -> CV*LV Boat -> LV

and

lv:LV

cv:CV

Theorem. [[ T1]] ≅ [[ T2 ]], where T1,2: [[M]] --> [[N]] are space functions generated by T1,2

Metamod. N

Commut.Vehicle

LeisureVehicle

physical objects object rolesTransf. T2:Car -> LVBoat -> CM*LV

R 11

Model A

c:Car

b:Boat

cb:R

lv:LV

cv:CV

lv’:LV

T1(A) ≅ T2(A)

Traceability linksTraceability mappingsTr1(A) ≠ Tr2(A)

Theorem. [[ T1]] ≠ [[ T2 ]], where T1,2: [[M]] --> ([[N]] x Map([[ N]] ,

[[ M]] )) are two-valued (instance x map) functions generated by T1,2

NECSIS Workshops 8

Summary 1: Mappings

• Traceability mappings are a semantic rather than just technological component of MTs

• Provide several benefits:– hold useful info about MTs • carry basic Boolean operations

– help to understand MTs

• Should be treated as first-class citizens

NECSIS Workshops 9

Model T(A)

Metamod. M

Car

Boat

Model A

c:Car

b:Boat lv’:LV

Transf. T1:Car -> CV*LV, Boat -> LV

lv:LV

cv:CV

Metamod. N

Commut.Vehicle

LeisureVehicle

physical objects object roles

cb:R

Traceability mapping

Typing mapping

Typing: What we have

Typing mapping

??

NECSIS Workshops 10

Color Legend:given datagiven datacomputed data

Model T(A)

Metamod. M

Car

Boat

Model A

c:Car

b:Boat lv’:LV

Transf. T1: Car -> CV*LV, Boat -> LV

lv:LV

cv:CV

Metamod. N

Commut.Vehicle

LeisureVehicle

physical objects object roles

cb:R

Traceability mapping

Typing mapping

Typing: What we want

Transf. definition mappings

Typing mapping

NECSIS Workshops 11

Issues to manage

NECSIS Workshops 12

Model T(A)

Metamod. M

Car

Boat

Model Ac:Car

b:Boat lv’:LV

Transf. T1: Car -> CV*LV, Boat -> LV

lv:LV

cv:CV

Metamod. N

Commut.Vehicle

LeisureVehicle

physical objects

object roles

cb:R

Traceability mapping

Typing mappin

g

Transf. definition mappings

Typing mappin

g

NECSIS Workshops 12

• Dynamic thing (a transf.) is encoded by a structural thing (a set of links)

• The mapping that encodes a transf. [[M]]-->[[N]] is directed from N to M

• We need associations between associations (beyond UML?)

Model T(A)

Metamod. M

Car

Boat

Model A

c:Car

b:Boat 3:LV

Transf. T: Car -> CV*LV, Boat -> LV

2:LV

1:CV

Metamod. NCommut.Vehicle

LeisureVehicle

Traceability mapping

map.TCar+Boat LVinM

c’: Car+Boat

b’: Car+Boat

CVinM

Given data:metamodels & modesltrans. definitionComputable data:queriesrelabeling

3:LVinM2:LVinM

1:CVinM

Dynamics via mappings: Queries

NECSIS Workshops13

:relabel

Metamod. T

same

12:same

Algebra and reuse

T1 Q(M)

M N

[[Q]] (A)A

Definitions

Instances

Typing :PB

Relabeling as “pulling Q(M) back” (pullback)

T2

NECSIS Workshops 14

Model T(A)

Metamod. M

Car

Boat

Model A

c:Car

b:Boat

3:LV2:LV

1:CV

Metamod. N

Commut.Vehicle

LeisureVehicle

Traceability mapping

map.T

Car+Boat

c’: Car+Boat

b’: Car+Boat

[=]

Algebra of MTs: T1 \/disj T2

NECSIS Workshops 151’:CV

2’:LV 3’:LV

T1

T2

T1 \/disj T2

Model T(A)

Metamod. M

Car

Boat

Model A

c:Car

b:Boat3:LV

Transf. T: Car -> CV*LV, Boat -> LV

2:LV

1:CV

Metamod. N

Commut.Vehicle

LeisureVehicle

Traceability mapping

map.T

Typing mapping

Car+Boat

c’: Car+Boat

b’: Car+Boat

[=]

Algebra of MTs: T1 /\ T2 and T1 \/ T2

NECSIS Workshops 161’:CV

2:LV 3:LV

T1

T2

T1 \/ T2

T1/\ T2

Model T(A)

Metamod. M

Car

Boat

Model A

c:Car

b:Boat

1:CV

Metamod. N

Commut.Vehicle

LeisureVehicle

Traceability mapping

Car+Boat

c’: Car+Boat

b’: Car+Boat

Algebra of MTs: T1 /\ T2 and T1 \/ T2

T1

T2

NECSIS Workshops 17

T1 \/ T2

T1/\ T2

1’:CV

2:LV 3:LV

T1 (A) \/ T2 (A)

T1(A) /\ T2(A)

T1(A) T2(A)

T1 \/ T2

T1/\ T2

T1 T2

Algebra of MTs. Chaining (seq. composition)

...

Q1(M)

[[Q1]] (A)

Definitions

Instances

Typing:PB

Q2(N)

[[Q2]] (..)

:PB

T1oT2

T2 T1

A

M ON

:PB

NECSIS Workshops 18

Chaining transf. via mapping composition

...

Q1(M)

[[Q1]] (A)

Definitions

Instances

Typing:PB

Q2(N)

[[Q2]] (..)

:PB

T1oT2

T2 T1

A

M ON

How?

Chaining trans. via query substitution

...

Q1(M)

[[Q1]] (A)

Definitions

Instances

Typing:PB

Q2(N)

[[Q2]] (..)

:PB

T1*T2

T2 T1

A

M ON

Q2(Q1(M))

Q2(T1)

T1oT2 Kleisli mapping composition

:PB

Example of chainingMetamod. Q2(N)Metamod. Q1(M)

CommVehicle

Leisure Vehicle

S

Car+Boat

CVinM

LVinM

SinMCar

Boat

CV+LV

Metamod. O

Vehicle

T1 T2

VinN

S’ U

UinN

Metamod. O

Vehicle

U

VinM

T1oT2

UinM

Boat

Metamod. Q2(Q1(M))

Car+Boat

Car

Car+(Car+Boat)

idCar’

Given data:metamodelstrafo definitiontrafo definitions

Computable data:applied query definition applied query definitionderived mapping

Model T(A)

Metamod. M

Car

Boat

Model A

c:Car

b:Boat 3:LV

Transf. T: Car -> CV*LV, Boat -> LV

2:LV

1:CV

Metamod. NCommut.Vehicle

LeisureVehicle

Traceability mapping

map.TCar+Boat LVinM

c’: Car+Boat

b’: Car+Boat

CVinM

Given data:metamodels & modesltrans. definitionComputable data:queriesrelabeling

3:LVinM2:LVinM

1:CVinM

Constraint transfer

NECSIS Workshops22

:relabel

Metamod. T

same

12:same

[0..1][1] [0..1]

[1]

[0..1]

[1]

[cover][disj]

Constraint transfer Metamod. NMetamod. Mclass X

(commV)

class Y(leisV)

S

A+BidA +R [2] *

XinM

YinM

SinM

class A(Car)

class B(Boat)

RR~+ idB [2]

*X+Y

idX

idY

Metamod. O

class Z(Vehicle)

T1 T2

ZinN

S’U

UinN

Metamod. M

A+B

idA + R [2]

class A(Car)

class B(Boat)

R

R~ + idB [2]

ZinMA+(A+B)

idA

idA+B

T1oT2

R’

idA’ + R’

Metamod. O

class Z(Vehicle)

U

UinM

**

[2] [2]

R’

*

[1]

[2]

[2]

[1]

[2][1]

[1]

[1]

[1]

[1]

[1]Given data:metamodelstrafo definitiontrafo definitionsconstraints

Computable data:applied query definition applied query definitionderived constraintderived constraintderived mapping

[1]*

Transf. = Querying + Relabeling (=View computation)

• Separation of concern• Reuse of the same queries • Analysis

NECSIS Workshops 24

Content

• Intro• Model merge (BM: choice) via colimit• Model join (BM: concurrency) via limit• Model translation via Cartesian monads :) • Composing operations into workflows

NECSIS Workshops 25

Composing operations into workflows

NECSIS Workshops 26

V1+V2T

embed1

embed2

traceability

2:merge 4:transf.

1:meet

V2

V1

• The diagram above (a megamodel) is an algebraic term in diagram algebra -- continuity is to be respected!

• Can be executed• Allow term rewriting (based on laws), hence, optimization

T /\ V2 view def. 2

view def. 1

System

5:meet

integrated view

3:univ.property