Introduction to the Object Constraint Language (OCL) of UML. Here we just present this language as an expression language with the different operators and this independently from UML.

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OCL : An Expression LanguageOCL : An Expression Language
Basic Types, Enumerated Types, Types ConstructorsBasic Types, Enumerated Types, Types Constructors
Expressions, OperationsExpressions, Operations
Operations on collectionsOperations on collections

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OCL = An Expression LanguageOCL = An Expression Language
No side effectNo side effect
No explicit iterationNo explicit iteration
Like a functional languageLike a functional language
but no functions (in the standard)but no functions (in the standard)
Can serve as aCan serve as a query languagequery language
This first part,
« OCL : An Expression language » is
almost independent from UML

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TypesTypes
Basic typesBasic types
IntegerInteger
RealReal
BooleanBoolean
StringString
Enumerated typesEnumerated types
MetatypesMetatypes
OclTypeOclType
OclAnyOclAny
OclStateOclState
OclExpressionOclExpression
Types from UMLTypes from UML
classesclasses
associationsassociations
……
Type constructorsType constructors
TupleType( x : T, y : T … )TupleType( x : T, y : T … )
Set(T)Set(T)
OrderedSet(T)OrderedSet(T)
Sequence(T)Sequence(T)
Bag(T)Bag(T)
Collection(T)Collection(T)

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Syntax of ExpressionsSyntax of Expressions (Simplified)
<const> 12 'hello'
<id> children Residence
<expr> <op> <expr> age>18
self like in python, « this » in java
<exprobj> . <prop> self.chairman.age
<exprobj> . <objprop>(<expr>...) self.chairman.increaseSalary(10)
<exprcoll> -> <collprop>(<expr>...) self.employees->collect(salary)
<package>::<package> … :: <element> like in C++, « . » in python and java
if <expr> then <expr> else <expr> endif if age>18 then 1200 else 50*age endif
let <id> : <type> in <expr> .<expr> let e=x*x+y in (e-20)*1,5

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ExamplesExamples
self.salary - 100
self.children->isEmpty()
self.children->forall(age>20)
self.getTaxes(1998) / self.children->size()
self.children->select( sex= Sex::male )
self.children->collect(salary)->sum()
self.children.salary->sum()
self.children->union(self.parents)->collect(age)
children
*
Person
sex:Sex
salary:real
age:integer
parents
0..2
getTaxes()
<<enumeration>>
Sex
male
female

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To be Remembered !To be Remembered !
. to get access to properties of objects
->-> to get access to properties of collectionsto get access to properties of collections
+ some rules to mix collections and objects (see later)
self.taxes(1998) / self.children -> size()
because self
is an object
because self.children
is a collection of objects

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Integer et RealInteger et Real
IntegerInteger
values :values : 1, -5, 34, 243431, -5, 34, 24343, ..., ...
operations :operations : +, -, *, div, mod, abs, max, min+, -, *, div, mod, abs, max, min
RealReal
values :values : 1.5, 1.341.5, 1.34, ..., ...
operations :operations : +, -, *, /, floor, round, max, min+, -, *, /, floor, round, max, min
Integer type « conforms » to the type Real

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BooleanBoolean
BooleanBoolean
values :values : truetrue,, falsefalse
operations :operations : notnot,, andand,, oror,, xorxor,, impliesimplies,, if-then-else-endifif-then-else-endif
partial evaluation :partial evaluation :
true oror x always true, even when x is undefined
false andand x always false, even when x is undefined
(age<40 implies salaire>1000) and (age>=40 implies salaire>2000)
if age<40 then salaire > 1000 else salaire > 2000 endif
salaire > (if age<40 then 1000 else 2000 endif)

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StringString
name = nom.substring(1,1).toUpper().concat(
nom.substring(2,nom.size()).toLower())
Strings are not sequence of Sequence(char) (no char type)
Operations:Operations:
==
ss..sizesize()()
s1s1..concatconcat((s2s2))
s1s1..substringsubstring((i1i1,,i2i2))
ss..toUppertoUpper()()
ss..toLowertoLower()()
Values:Values:
''''
'a sentence''a sentence'

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EnumerationEnumeration
ValuesValues
Day::TuesdayDay::Tuesday (previous notation:(previous notation: #Tuesday#Tuesday ))
OperatorsOperators
==,, <><>
No ordering relation
<<enumeration>>
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday

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ExamplesExamples
spouse->notEmpty() implies spouse.sex = Sex::female
épouse.sexe < sexe
husband
0..1
Person
sex : Sex
spouse
0..1
No ordering relationNot always
defined
<<enumeration>>
Sex
male
female

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Element vs. singletonElement vs. singleton
In almost all languagesIn almost all languages
one elementone element ee
from singleton containing this elementfrom singleton containing this element Set{e}Set{e}
self->size() = 1
Implicit conversion in OCLImplicit conversion in OCL element => singletonelement => singleton
when an collection operationwhen an collection operation
is applied to an elementis applied to an element
elemelem ->-> propprop Set{Set{elemelem}->}->propprop
≠

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CollectionsCollections
General TypeGeneral Type CollectionCollection(( TT ))
Set(Set(TT ))
{unique}{unique} {nonunique}{nonunique}
{unordered}{unordered}
{ordered}{ordered} Sequence(Sequence(TT ))
Bag(Bag(TT ))
OrderedSet(OrderedSet(TT ))

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Use of collections for role navigationUse of collections for role navigation
object . nomderoleobject . nomderole type:type:
X
1 or 0..1
X
*
X
{ordered} *
X
Set(X)
OrderedSet(X)
X
*{nonunique}
Bag(X)
X
{ordered, nonunique} *
Sequence(X)

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Collection ExpressionsCollection Expressions
ExamplesExamples
SetSet {{ 'lundi''lundi',, 'mercredi''mercredi',, 'mardi''mardi' }}
BagBag {{ 'lundi''lundi',, 'lundi''lundi',, 'mardi''mardi',, 'lundi''lundi' }}
OrderedSetOrderedSet {{ 1010,, 2020,, 55 }}
SequenceSequence {{ 'lundi''lundi',, 'lundi''lundi',, 'mardi''mardi',, 'lundi''lundi' }}
To specify rangesTo specify ranges
SequenceSequence {{ 1..5, 2..41..5, 2..4 }}
Useful for 'loops' :
Sequence { 0 .. etagesnb-1 } -> forall( i | canStop(i) )

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Operations on CollectionsOperations on Collections
Cardinality: coll -> size()
Emptyness: coll -> isEmpty()
Non emptyness: coll -> notEmpty()
Occurrence number: coll -> count(elem)
Membership: coll -> includes( elem )
Non membership: coll -> excludes( elem )
Inclusion: coll -> includesAll(coll)
Exclusion: coll -> excludesAll(coll)
Sum (of numbers): coll -> sum()

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ExamplesExamples
Set { 3, 5, 2, 45, 5 }->size()
Sequence { 1, 2, 45, 9, 3, 9 } ->count(9)
Sequence { 1, 2, 45, 2, 3, 9 } ->includes(45)
Bag { 1, 9, 9, 1 } -> count(9)
c->asSet()->size() = c->size()
c->count(x) = 0
Bag { 1, 9, 0, 1, 2, 9, 1 } -> includesAll( Bag{ 9,1,9} )

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Operations on SetsOperations on Sets
UnionUnion ens ->ens -> unionunion( ens )( ens )
IntersectionIntersection ens ->ens -> intersectionintersection( ens )( ens )
DifferenceDifference ens1 - ens2ens1 - ens2
Adding an elementAdding an element ens ->ens -> includingincluding(elem)(elem)
Removing an elementRemoving an element ens ->ens -> excludingexcluding(elem)(elem)
Sequence conversionSequence conversion ens ->ens -> asSequence()asSequence()
Bag conversionBag conversion ens ->ens -> asBag()asBag()
Conversion to ordered setConversion to ordered set ens ->ens -> asOrderedSet()asOrderedSet()

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Filtering: select, reject and anyFiltering: select, reject and any
coll -> select( cond )
select elements satisfying the conditionselect elements satisfying the condition
coll -> reject( cond )
reject elementsreject elements
coll -> any( cond )
selectselect anyany element satisfying the conditionelement satisfying the condition
• non deterministnon determinist
• useful when there is only one elementuseful when there is only one element
• "undefined" if the collection is empty"undefined" if the collection is empty

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ExamplesExamples
self.children ->select( age>10 and sex = Sex::Male)
self.children ->reject(e : Person | e.children->isEmpty())->notEmpty()
members->any(title='president')
children*
Member
sex : Sexe
age : integer
title : string
parents0..2Club members
*

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Syntax AlternativesSyntax Alternatives
self.employees->select(age > 50)
self.employees->select( p | p.age>50 )
self.employees->select( p : Person | p.age>50)
Person
age : integer
Company
employees
*

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forall, exists, oneforall, exists, one
coll ->coll -> forallforall( cond )( cond )
coll ->coll -> existsexists( cond )( cond )
coll ->coll -> oneone( cond )( cond )
self.enfants->forall(age<10)
self.enfants->exists(sexe=Sexe::Masculin)
self.enfants->one(age>=18)
children*
Person
sexe : Sex
age : integer
parents0..2

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Syntax ComparisonSyntax Comparison
children->forall( p : Person | p.age<10)
∀ c ∈ children . c.age < 10

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Quantifiers: more about syntaxQuantifiers: more about syntax
It's possible toIt's possible to
give a name to a variablegive a name to a variable
explicit its typeexplicit its type
use various variables at the same timeuse various variables at the same time
self.children->forall( age < self.age )
self.enfants->forall( e | e.age < self.age - 7)
self.children->forall( e : Personne | e.age < self.age - 7)
self.children->exists( e1,e2 | e1.age = e2.age )
self.children->exists( e1,e2 | e1.age = e2.age and e1<>e2 )
self.children->forall( e1,e2 : Personne |
e1 <> e2 implies e1.firstname <> e2.firstname)
children*
Person
age
firstname

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UnicityUnicity
coll -> isUnique ( expr )
True if all elements return a different value for exprTrue if all elements return a different value for expr
self.children -> isUnique ( firstname )
instead ofinstead of
self.children->forall( p1,p2 : Person |
p1 <> p2 implies p1.firstname <> e2.firstname)
Useful to define the notion of "imported key" for instance
children*
Person
age
firstname

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isUnique vs. {unique}isUnique vs. {unique}
self.children -> isUnique ( firstname )
children*
Person
age
firstname
{unique}

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Image of an expression: collectImage of an expression: collect
coll ->coll -> collectcollect( expr )( expr )
"image" of a function (map, apply, ...)
expr evaluated for each element
result in:
a Bag if coll is a Set or a Bag
a Sequence if coll is a Sequence or a OrderedSet
self.enfants->collect(age) = Bag{10,5,10,7}
self.employés->collect(salaire/10)->sum()
children*
Person
age
employees
*
Company Employee
salary

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Collect: Simplified Syntax!Collect: Simplified Syntax!
.. with a collectionwith a collection ↔↔ collectcollect
children*
Person
age
self.children.age
self.children->collect(age)

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Collect Possible Duplicates→Collect Possible Duplicates→
The result is a Bag or Sequence because of possible duplicatesThe result is a Bag or Sequence because of possible duplicates
To get a setTo get a set
self.children.age->asSet()
. shortcut very usefull to navigate!. shortcut very usefull to navigate!
self.children.children.cars
children*
Person
age
Cars
cars
**