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Towa ds he Au oma ion o Me amo phic Tes ing in
Model T ans o ma ions
Ja ie T oya, Se gio Segu a, and An onio Ruiz-Co ´
es
Depa men o Compu e Languages and Sys ems
Uni e sidad de Se illa, Spain
{j oya, se giosegu a, a uiz}@us.es
Abs ac . Model ans o ma ions a e he co ne s one o Model-D i en Engi-
nee ing, and p o ide he essen ial mechanisms o manipula ing and ans o m-
ing models. Checking whe he he ou pu o a model ans o ma ion is co ec
is a manual and e o -p one ask, his is e e ed o as he o acle p oblem in he
so wa e es ing li e a u e. The co ec ness o he model ans o ma ion p og am
is c ucial o he p ope gene a ion o i s ou pu , so i should be es ed. Me amo -
phic es ing is a es ing echnique o alle ia e he o acle p oblem consis ing on
exploi ing he ela ions be ween di e en inpu s and ou pu s o he p og am un-
de es , so-called me amo phic ela ions. In his pape we gi e an insigh in o ou
app oach o gene ically de ine me amo phic ela ions o model ans o ma ions,
which can be au oma ically ins an ia ed gi en any speci ic model ans o ma ion.
Keywo ds: Me amo phic Tes ing, Model T ans o ma ion, Au oma ion, Gene ic
1 In oduc ion
Model T ans o ma ions (MTs) a e he co ne s one o Model-D i en Enginee ing (MDE).
They p o ide he essen ial mechanisms o manipula ing and ans o ming models.
Checking whe he he ou pu o a model ans o ma ion is co ec is a manual and
e o -p one ask, his is e e eed o as he o acle p oblem in he so wa e es ing li -
e a u e. Indeed, he quali y o he gene a ed so wa e a i ac s is highly a ec ed by he
co ec ness o he de eloped model ans o ma ions. Fo his eason, se e al app oaches
ha e been p oposed ha e i y he co ec beha io o he ans o ma ions using o mal
me hods [6,1] o ce i y hei beha io o a selec ed se o es models mainly o iden i y
bugs in a cos -e ec i e way [2,7].
Me amo phic Tes ing (MT’) [5] is a me hodology designed o alle ia e he o a-
cle p oblem. Di e en om con en ional es ing s a egies, MT’ consis s on exploi ing
he ela ions be ween di e en inpu s and ou pu s o he p og am unde es , so-called
Me amo phic Rela ions (MRs). In p ac ice, MRs de ine possible modi ica ions o a es
inpu and how hose changes a e p opaga ed o he p og am ou pu . A basic example
o MR can be de ined o he p og am ha compu es he sine unc ion. Le us suppose
we wan o know he exac alue o sin(5). Is an obse ed ou pu o 0.091 co ec ? A
ma hema ical p ope y o he sine unc ion s a es ha sin(x) = sin(π−x), and we
can use his o es whe he sin(5) = sin(π−5) wi hou knowing he conc e e alues
o ei he sine calcula ion. Cu en ly, he bigges limi a ion o MT’ has o do wi h he
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XXI Jo nadas de Ingenie ía del So wa e
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2 Towa ds he Au oma ion o Me amo phic Tes ing in Model T ans o ma ions
C1: es model
(sou ce model)
T1: esul model
( a ge model)
MTexecu ion
C2: ollow‐up es model
( ollow‐upsou ce model)
T2: ollow‐up esul model
( ollow‐up a ge model)
con olled
modi ica ion
MTexecu ion
Fig. 1: Me amo phic Tes ing in Model T ans o ma ions.
de ini ion o he MRs. In ac , he au oma ic gene a ion o MRs has been acknowledged
as one o he big challenges in MT’ [5].
Figu e 1 displays he scena io o MT’ in MTs. We ha e a es model (C1), which is
ypically he sou ce model. I we apply he MT, we ob ain he esul model (T1), i.e.,
he a ge model. By applying a con olled modi ica ion in he es model, we ob ain he
ollow-up es model (C2). I we now apply he same MT o C2, we ge he ollow-up
esul model (T2). In his con ex , a MR conside s he modi ica ion done in C2 wi h
espec o C1, and he consequences ha his has in T2 wi h espec o T1. We show an
example in nex sec ion.
As a as we a e conce ned, he e is only one app oach ha applies MT’ in MTs [3].
The au ho s demons a e he e ec i eness and easibili y o i s applica ion, al hough
hey apply i manually in a speci ic scena io, o which hey de ine he MRs. In ou
app oach, we p opose o au oma ically gene a e MRs o any model ans o ma ion, as
we explain in he nex sec ion. Then, in Sec ion 3 we desc ibe ou nex s eps.
2 App oach
The goal o ou app oach is o au oma e he p ocess o me amo phic es ing (MT’) in
model ans o ma ions (MTs). The eby, we p opose he au oma ic gene a ion o me a-
mo phic ela ions (MRs) o any model ans o ma ion. We wo k wi h ans o ma ions
w i en in he ATL T ans o ma ion Language due o i s impo ance bo h in academia
and indus y.
In o de o au oma ically ex ac in o ma ion ou o a ans o ma ion, we make use
o explici ace models. A ace model can be au oma ically ob ained om a ans o -
ma ion execu ion, e.g., by using Jouaul ’s T aceAdde [4], and is composed o a se o
aces, one o each ule execu ion. A ace cap u es he name o he applied ule and
he elemen s o he sou ce model (sou ceElems ela ionship) ha a e used o c ea e new
elemen s in he a ge model ( a ge Elems ela ionship). The e o e, by na iga ing he
ace model, we know which a ge elemen (s) ha e been c ea ed om which sou ce el-
emen (s) and by which ule. A simple example o a gene ic ace is shown in Figu e 2(a).
Please no e ha mo e han one elemen may appea as sou ceElems and a ge Elems.
We conside his ace as gene ic because each o he h ee elemen s appea ing in i
(Sou ceElemen ,T ace and Ta ge Elemen ) can be ins an ia ed in a pa icula scena io.
The idea o ou app oach is o de ine gene ic MRs o gene ic aces. These MRs
can hen be ins an ia ed oge he wi h he gene ic aces. Fo ins ance, conside ing he
gene ic ace o Figu e 2(a), we know ha i we ha e a es model (C1, Figu e 1) and
we add an elemen o ype Sou ceElemen in he ollow-up es model (C2), hen an
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© Ediciones Uni e sidad de Salamanca
Towa ds he Au oma ion o Me amo phic Tes ing in Model T ans o ma ions 3
T ace
uleName:Da aType2Type
Da aType
name:S ing
Type
name:S ing
sou ceElems a ge Elems
T ace
uleName
Sou ceElemen
sou ceElems a ge Elems
Ta ge Elemen
T ace
uleName:Class2Table
Class
name:School
Table
name:School
sou ceElems a ge Elems
Column
name:objec Id
key
ype
(a) Simple Gene ic T ace.
T ace
uleName:Da aType2Type
Da aType
name:S ing
Type
name:S ing
sou ceElems a ge Elems
T ace
uleName
Sou ceElemen
sou ceElems a ge Elems
Ta ge Elemen
T ace
uleName:Class2Table
Class
name:School
Table
name:School
sou ceElems a ge Elems
Column
name:objec Id
key
ype
(b) T aces o he ans o ma ion exce p o Lis ing 1.2.
Fig. 2: Gene ic and ins an ia ed aces
elemen o ype Ta ge Elemen is c ea ed o i in he ollow-up esul model (T2). This
means ha T2 has one mo e elemen o his ype han T1. Ha ing his in o ma ion in o
accoun , we can de ine he i s gene ic MR shown in Lis ing 1.1, w i en in he OCL
language. Besides, he numbe o elemen s o any o he ype should emain he same in
T1 and T2, so u he MRs can be de ined, such as he second one in he same lis ing.
Lis ing 1.1: Gene ic MRs o he addi ion o a Sou ceElemen
1T1_Ta ge Elemen .allIns ances()->size()=T2_Ta ge Elemen .allIns ances()->size()-1
2T1_AnyO he Type.allIns ances()->size()=T2_AnyO he Type.allIns ances()->size()
In o de o show an example o ins an ia ion o he gene ic MRs shown be o e, we
choose he well-known Class2Rela ional case s udy. We will ocus on he exce p o
he ans o ma ion, which has been sligh ly modi ied o simplici y in he explana ion,
shown in Lis ing 1.2. I we ha e a sou ce model wi h a Da aType and a Class and we
apply he ans o ma ion, he esul ing ace model is depic ed in Figu e 2(b). We can
see a ace ha e lec s he c ea ion o a Type om a Da aType and ano he one ha
s o es he c ea ion o a Table and a Column om a Class.
Lis ing 1.2: Exce p o Class2Rela ional ans o ma ion
1 ule Da aType2Type {
2 om
3d : Class!Da aType
4 o
5ou : Rela ional!Type (
6name <- d .name
7)
8}
9
10
11 ule Class2Table {
12 om c : Class!Class
13 o
14 ou : Rela ional!Table (
15 name <- c.name,
16 key <- key),
17 key : Rela ional!Column (
18 name <- ’objec Id’,
19 ype <- hisModule.objec IdType)
20 }
Since hese wo aces a e ins an ia ions o he gene ic one shown in Figu e 2(a), we
can also ins an ia e he MRs shown in Lis ing 1.1. In pa icula , we ha e wo scena ios.
The i s one consis s o adding an elemen o ype Da aType in C2, wha yields he
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XXI Jo nadas de Ingenie ía del So wa e
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4 Towa ds he Au oma ion o Me amo phic Tes ing in Model T ans o ma ions
MRs shown in Lis ing 1.3. In he second scena io we add an elemen o ype Class in
C2, ob aining he MRs shown in Lis ing 1.4.
Lis ing 1.3: MRs o he addi ion o a Da aType in C2
1T1_Type.allIns ances()->size()=T2_Type.allIns ances()->size()-1
2T1_Column.allIns ances()->size()=T2_Column.allIns ances()->size()
3T1_Table.allIns ances()->size()=T2_Table.allIns ances()->size()
Lis ing 1.4: MRs o he addi ion o a Class in C2
1T1_Column.allIns ances()->size()=T2_Column.allIns ances()->size()-1
2T1_Table.allIns ances()->size()=T2_Table.allIns ances()->size()-1
3T1_Type.allIns ances()->size()=T2_Type.allIns ances()->size()
3 Nex S eps and Obse a ions
In his pape we ha e gi en an insigh in o ou app oach o au oma e he gene a ion o
MRs o MTs. We iden i y gene ic pa e ns in he aces, om which we de ine gene ic
MRs o ganized as well in pa e ns. Fo ins ance, one pa e n is he gene ic ace and
MRs we ha e shown in his pape . Despi e i s simplici y, we a e pe o ming ongoing
wo ks de ining mo e pa e ns whe e elemen s, a ibu es and ela ionships a e aken in o
accoun , so ha we end up wi h a la ge se o MRs. One o he pu poses o he gene a ed
MRs is o au oma e eg ession es s, since hey can be checked as o whe he hey hold
in di e en e sions o he model ans o ma ion p og am and o any es model.
As men ioned, ou app oach akes as inpu one o mo e execu ions o a MT, i.e.,
he esul ing ace models. The numbe o execu ions o he MT ecei ed and hei size
in luence he comple eness o he MRs gene a ed. Fo ins ance, i a ule is ne e applied
in any o he execu ions ecei ed as inpu , no MRs will conside i s beha io .
Acknowledgmen s. This wo k has been pa ially unded by he Eu opean Commission
(FEDER) and Spanish Go . unde CICYT p ojec BELI (TIN2015-70560-R), and by
he Andalusian Go . p ojec s THEOS (TIC-5906) and COPAS (P12- TIC-1867).
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