Kernel ­ the Multiplicities Diagram


The Multiplicities diagram of the Kernel package is shown in Figure 10.

In order to locate the metaclasses that are referenced from this diagram,
· See "Classifier (from Kernel, Dependencies, PowerTypes)"
· See "Element (from Kernel)"
· See "ValueSpecification (from Kernel)"

MultiplicityElement  (from  Kernel)


A multiplicity is a definition of an inclusive interval of non-negative integers beginning with a lower bound and ending  with a (possibly infinite) upper bound. A multiplicity element embeds this information to specify the allowable cardinalities for an instantiation of this element.

Description

A MultiplicityElement is an abstract metaclass which includes optional attributes for defining the bounds of a multiplicity.

A MultiplicityElement also includes specifications of whether the values in an instantiation of this element must be unique or ordered.

Attributes


Associations


Constraints

These constraint must handle situations where the upper bound may be specified by an expression not computable in the model.

[1] A multiplicity must define at least one valid cardinality that is greater than zero.

upperBound()->notEmpty() implies upperBound() > 0

[2] The lower bound must be a non-negative integer literal.

lowerBound()->notEmpty() implies lowerBound() >= 0

[3] The upper bound must be greater than or equal to the lower bound.

(upperBound()->notEmpty() and lowerBound()->notEmpty()) implies upperBound() >= lowerBound()

[4] If a non-literal ValueSpecification is used for the lower or upper bound, then evaluating that specification must not have side effects.

Cannot be expressed in OCL.

[5] If a non-literal ValueSpecification is used for the lower or upper bound, then that specification must be a constant expression.

Cannot be expressed in OCL.

[6] The derived lower attribute must equal the lowerBound.

lower = lowerBound()

[7] The derived upper attribute must equal the upperBound.

upper = upperBound()

Additional Operations

[1] The query isMultivalued() checks whether this multiplicity has an upper bound greater than one.

MultiplicityElement::isMultivalued() : Boolean;
pre: upperBound()->notEmpty()
 isMultivalued = (upperBound() > 1)

[2] The query includesCardinality() checks whether the specified cardinality is valid for this multiplicity.

MultiplicityElement::includesCardinality(C : Integer) : Boolean;
pre: upperBound()->notEmpty() and lowerBound()->notEmpty()
includesCardinality = (lowerBound() <= C) and (upperBound() >= C)

[3] The query includesMultiplicity() checks whether this multiplicity includes all the cardinalities allowed by the specified multiplicity.

MultiplicityElement::includesMultiplicity(M : MultiplicityElement) : Boolean;
pre: self.upperBound()->notEmpty() and self.lowerBound()->notEmpty()
    and M.upperBound()->notEmpty() and M.lowerBound()->notEmpty()
includesMultiplicity = (self.lowerBound() <= M.lowerBound()) and (self.upperBound() >= M.upperBound())

[4] The query lowerBound() returns the lower bound of the multiplicity as an integer.

MultiplicityElement::lowerBound() : [Integer];
lowerBound = if lowerValue->isEmpty() then 1 else lowerValue.integerValue() endif

[5] The query upperBound() returns the upper bound of the multiplicity for a bounded multiplicity as an unlimited natural.

MultiplicityElement::upperBound() : [UnlimitedNatural];
upperBound = if upperValue->isEmpty() then 1 else upperValue.unlimitedValue() endif

Semantics

A multiplicity defines a set of integers that define valid cardinalities. Specifically, cardinality C is valid for multiplicity M if M.includesCardinality(C).

A multiplicity is specified as an interval of integers starting with the lower bound and ending with the (possibly infinite) upper bound.

If a MultiplicityElement specifies a multivalued multiplicity, then an instantiation of this element has a set of values. The multiplicity is a constraint on the number of values that may validly occur in that set.

If the MultiplicityElement is specified as ordered (i.e. isOrdered is true), then the set of values in an instantiation of this element is ordered. This ordering implies that there is a mapping from positive integers to the elements of the set of values. If a MultiplicityElement is not multivalued, then the value for isOrdered has no semantic effect.

If the MultiplicityElement is specified as unordered (i.e. isOrdered is false), then no assumptions can be made about the order of the values in an instantiation of this element.

If the MultiplicityElement is specified as unique (i.e. isUnique is true), then the set of values in an instantiation of this element must be unique. If a MultiplicityElement is not multivalued, then the value for isUnique has no semantic effect.

The lower and upper bounds for the multiplicity of a MultiplicityElement may be specified by value specifications, such as (side-effect free, constant) expressions.

Notation

The specific notation for a MultiplicityElement is defined by the concrete subclasses. In general, the notation will include a multiplicity specification is shown as a text string containing the bounds of the interval, and a notation for showing the optional ordering and uniqueness specifications.

The multiplicity bounds are typically shown in the format:

lower-bound..upper-bound

where lower-bound is an integer and upper-bound is an unlimited natural number. The star character (*) is used as part of a multiplicity specification to represent the unlimited (or infinite) upper bound.

If the Multiplicity is associated with an element whose notation is a text string (such as an attribute, etc.), the multiplicity string will be placed within square brackets ([]) as part of that text string. Figure 11 shows two multiplicity strings as part of attribute specifications within a class symbol.

If the Multiplicity is associated with an element that appears as a symbol (such as an association end), the multiplicity string is displayed without square brackets and may be placed near the symbol for the element. Figure 12 shows two multiplicity strings as part of the specification of two association ends.

The specific notation for the ordering and uniqueness specifications may vary depending on the specific subclass of MultiplicityElement. A general notation is to use a property string containing ordered or unordered to define the ordering, and unique or nonunique to define the uniqueness.

Presentation Options

If the lower bound is equal to the upper bound, then an alternate notation is to use the string containing just the upper bound. For example, "1" is semantically equivalent to "1..1".
A multiplicity with zero as the lower bound and an unspecified upper bound may use the alternative notation containing a single star "*" instead of "0..*".

The following BNF defines the syntax for a multiplicity string, including support for the presentation options.

multiplicity ::= <multiplicity_range> [ `{` <order_designator> `}' ]
multiplicity_range ::= [ lower `..' ] upper
lower ::= integer | value_specification
upper ::= unlimited_natural | `*' | value_specification
<order_designator> ::= ordered | unordered
<uniqueness_designator> ::= unique | nonunique

Examples


Type (from Kernel)

A type constrains the values represented by a typed element.

Description

A type serves as a constraint on the range of values represented by a typed element. Type is an abstract metaclass.

Attributes

No additional attributes.

Associations

No additional associations.

Constraints

No additional constraints.

Additional Operations

[1] The query conformsTo() gives true for a type that conforms to another. By default, two types do not conform to each other. This query is intended to be redefined for specific conformance situations.

conformsTo(other: Type): Boolean;
conformsTo = false

Semantics

A type represents a set of values. A typed element that has this type is constrained to represent values within this set.

Notation

No general notation.

TypedElement (from Kernel)

A typed element has a type.

Description

A typed element is an element that has a type that serves as a constraint on the range of values the element can represent.
Typed element is an abstract metaclass.

Attributes

No additional attributes.

Associations
Constraints

No additional constraints.

Semantics
Values represented by the element are constrained to be instances of the type. A typed element with no associated type may represent values of any type.

Notation

No general notation.