In the Language Description, in 7.4.9.4 Base Expressions, in the fourth bullet for, it states that "A construction expression is an invocation expression in which the invocation target is a classifier that is not a function." However, in the Abstract Syntax, in 8.3.4.8.5 InvocationExpression, the constraint checkInvocationxpressionConstructorBindingConnector considers a constructor expression to be an InvocationExpression that "does not have an ownedTyping that is a Behavior or an ownedSubsetting of a Feature that is typed by a Behavior, then it must own a BindingConnector between itself and its result parameter." Further, in the Semantics, in 8.4.4.9.4 Invocation Expressions, it states

An InvocationExpression may also have the form T(e1, e2, ...), where the invoked Type T is not a Function. If T is a Behavior other than a Function, then the InvocationExpression performs the Behavior, but has a null (empty) result value. If T is a Type that is not a Behavior, then the InvocationExpression acts as a constructor for an instance of the Type T.

Now, invoking a behavior and having it return a null value doesn't really seem very useful. It would actually be more useful if, consistent with the language description, "invoking" a non-function behavior was considered to be a constructor expression, evaluating to a performance of that behavior. This would, in particular, allow out parameters to be referenced from the instantiated performance. For example:

behavior B {in x; out y; out z;}
feature y1 = B(1).y;
feature b = B(2);
feature y2 = b.y;
feature z2 = b.z;

In the KerML semantics, 8.4.4.9.4 Invocation Expressions, the semantic equivalent model for an InvocationExpression used as a "constructor" for a type T (i.e., T(...)) is shown as having its result parameter redefined with a FeatureTyping relationship to T. However, there is no semantic constraint in the abstract syntax to enforce this. Note that this typing is important, because it is to be expected that the result of a constructor is of the type being constructed.

There is currently no validation rule/check constraint which enforces that when doing redefinitions, if redefined feature has isEnd=true, then redefining feature must also have isEnd=true;
Which opens modelers to errors, e.g. in the SysML spec,
ControlPerformances::DecisionPerformance::outgoingHBLink:: earlierOccurrence is not marked as "end" feature.

The mapping given in 9.2.17 from the MOF abstract syntax model to the reflective KerML in abstract syntax model is missing instructions for what to do if a property is ordered or non-unique. Therefore, appropriate annotations for these are missing from the normative KerML.kerml file.

In the KerML Specification, 8.2.4.3.1 Features, the production FeatureIdentification references the properties shortName and name. These should instead be declaredShortName and declaredName.

In 8.4.4.11 Feature Values Semantics, the following binding declaration appear in the second textual notation snippet:

member binding f = e.result featured by T;

and the fourth snippet:

member binding f = e.result featured by that.startShot;

These are both syntactically incorrect. The correct syntax is:

member binding b featured by T of f=e.result;

and

member binding b featured by that.startShot of f=e.result;

In 8.3.3.3.3 Feature, the constraint checkFeatureParameterRedefinition requires:

If a Feature is a parameter of an owningType that is a Behavior or Step, other than the result parameter (if any), then, for each direct supertype of its owningType that is also a Behavior or Step, it must redefine the parameter at the same position, if any.

However, in the textual BNF in 8.2.5.8.3 Base Expressions, a NamedArgumentList for an InvocationExpression is parsed with parameter redefinitions in the order of the argument list, not the original parameter list. Indeed, according to the description in 7.4.9.4 Base Expressions, named arguments may be "given in any order". But, if they are given in an order different than the original parameter order, this will violate checkFeatureParameterRedefinition. And then adding implied redefinitions to the InvocationExpression parameters, in the original parameter order, would potentially result each of the InvocationExpression parameters incorrectly redefining two different of the original parameters.

The description of the `checkFeatureParameterRedefinition` constraint is

If a Feature is a parameter of an owningType that is a Behavior or Step, other than the result parameter (if any), then, for each direct supertype of its owningType that is also a Behavior or Step, it must redefine the parameter at the same position, if any.

However, the OCL for the constraint does not exclude the result parameter as stated in the description.

In 8.3.3.3.3 Feature, the constraint checkFeatureParameterRedefinition requires:

If a Feature is a parameter of an owningType that is a Behavior or Step, other than the result parameter (if any), then, for each direct supertype of its owningType that is also a Behavior or Step, it must redefine the parameter at the same position, if any.

However, in the textual BNF in 8.2.5.8.3 Base Expressions, a NamedArgumentList for an InvocationExpression is parsed with parameter redefinitions in the order of the argument list, not the original parameter list. Indeed, according to the description in 7.4.9.4 Base Expressions, named arguments may be "given in any order". But, if they are given in an order different than the original parameter order, this will violate checkFeatureParameterRedefinition. And then adding implied redefinitions to the InvocationExpression parameters, in the original parameter order, would potentially result each of the InvocationExpression parameters incorrectly redefining two different of the original parameters.

Clause 7.3.4.2 (Feature Declaration) and 8.3.3.3.3 (Feature) say

Portion features are composite features where the values cannot exist without the whole, because they are the “same thing” as the whole. (For example, the portion of a person's life when they are a child cannot be added or removed from that person's life.)

isPortion : Boolean
Whether the values of this Feature are contained in the space and time of instances of the domain of the Feature and represent the same thing as those instances.

and Clause 9.2.4.1 (Occurrences Overview) includes an extended description of time and space modeling in occurrences. But the specification does not explain how to model things (objects and performances) at specific times or places, versus over time or space. For example, cars are driven by one person at a time, but potentially many people over time. How should these multiplicities be specified? See other examples in comments on KERML-204.

Clause 7.3.4.2 (Feature Declaration) and 8.3.3.3.3 (Feature) say

Portion features are composite features where the values cannot exist without the whole, because they are the “same thing” as the whole. (For example, the portion of a person's life when they are a child cannot be added or removed from that person's life.)

isPortion : Boolean
Whether the values of this Feature are contained in the space and time of instances of the domain of the Feature and represent the same thing as those instances.

and Clause 9.2.4.1 (Occurrences Overview) includes an extended description of time and space modeling in occurrences. But the specification does not explain how to model things (objects and performances) at specific times or places, versus over time or space. For example, cars are driven by one person at a time, but potentially many people over time. How should these multiplicities be specified? See other examples in comments on KERML-204.

SysML v2 includes syntax for enumeration definitions and usages. The semantics for enumerations are based on the general variation/variant semantics in SysML v2, which is itself based on KerML semantics. However, there currently is no syntax for enumerations in KerML. In particular, this leads to an awkward mapping in 9.2.17 KerML of MOF enumerations to KerML data types without specific syntax for enumeration.

Enumerations are the only modeling element in the CMOF subset of UML that does not have a clear mapping to a KerML element. Especially as KerML is considered further for use as the basis of other languages, including their reflective abstract syntaxes, it would be better if enumeration syntax was codified in KerML. This would also make it easier to incorporate enumerations consistently into SysML v2 and future KerML-based languages themselves.

Derived features (Feature::isDerived=true) are described as

Such a feature is typically expected to have a bound feature value expression that completely determines its value at all times.

Whether the values of this Feature can always be computed from the values of other Feature.

but this semantics is not model/mathed.

Derived features (Feature::isDerived=true) are described as

Such a feature is typically expected to have a bound feature value expression that completely determines its value at all times.

Whether the values of this Feature can always be computed from the values of other Feature.

but this semantics is not model/mathed.

KerML supports triggers on quantified time, but not quantified space, eg, that an object moves more than a specific distance, or comes within a specific distance of another, etc.

KerML supports triggers on quantified time, but not quantified space, eg, that an object moves more than a specific distance, or comes within a specific distance of another, etc.

SysML v2 includes syntax for enumeration definitions and usages. The semantics for enumerations are based on the general variation/variant semantics in SysML v2, which is itself based on KerML semantics. However, there currently is no syntax for enumerations in KerML. In particular, this leads to an awkward mapping in 9.2.17 KerML of MOF enumerations to KerML data types without specific syntax for enumeration.

Enumerations are the only modeling element in the CMOF subset of UML that does not have a clear mapping to a KerML element. Especially as KerML is considered further for use as the basis of other languages, including their reflective abstract syntaxes, it would be better if enumeration syntax was codified in KerML. This would also make it easier to incorporate enumerations consistently into SysML v2 and future KerML-based languages themselves.

The doc annotations of the datatypes in standard library Collections.kerml in machine readable document ad/23-02-05 are not aligned with the contents of subclause 9.3.3 of the KerML specification.

The documentation content should be made identical. The text in the KerML specification should be leading when drafting a resolution for this issue.

The doc annotations of the datatypes in standard library Collections.kerml in machine readable document ad/23-02-05 are not aligned with the contents of subclause 9.3.3 of the KerML specification.

The documentation content should be made identical. The text in the KerML specification should be leading when drafting a resolution for this issue.

7.3.4.1 (Features Overview) says

Values of a composite feature, on each instance of the feature's domain, cannot exist after the featuring instance ceases to exist.

and 8.3.3.3.3 (Feature) says

isComposite : Boolean
Whether the Feature is a composite feature of its featuringType. If so, the values of the Feature cannot exist after its featuring instance no longer does.

but the spec doesn't seem to say anywhere that the values cannot be values of any composite features on any other instance of the feature's domain ("single owner", "tree" property of composition), as typically expected.

In Clocks.kerml, the TimeOf function defines the timeContinuityConstraint, which states that (endShots of) immediate predecessors of an occurrence (i.e., those connected via a HappensJustBefore) must get the same timestamp (timeInstant in the model) as the start shot of the occurrence:

inv timeContinuityConstraint {
	doc
	/*
	 * If one Occurrence happens immediately before another, then the TimeOf 
	 * the end snapshot of the first Occurrence equals the TimeOf the second
	 * Occurrence.
	 */
	
	o.immediatePredecessors->forAll{in p : Occurrence; 
		TimeOf(p.endShot, clock) == timeInstant
	}
}	

Compare this to the documentation of HappensJustBefore, which states that "HappensJustBefore is HappensBefore asserting that there is no possibility of another occurrences[sic] happening in the time between the earlierOccurrence and laterOccurrence."

Considering that the intent of the libraries is not to constrain the time model and the format of timestamps, I checked this against three widely-used time models.

With continuous (dense) time, the current formulation of the timeContinuityConstraint might make sense, although it fails to capture that an infinite number of snapshots forming a HappensJustBefore chain may actually take non-zero time.

With discrete time, where a timestamp may be treated as a sequence number, for example, an Integer, the invariant may be too restrictive, as HappensJustBefore could apply to two snapshots that have successive sequence numbers, but have no other occurrence in between them. In fact, in a discrete time model, HappensJustBefore with the current definition degrades to HappensWhile because there is no notion of ordering between events with the same timestamp.

In super-dense time, where a clock is usually represented as a pair of a real value (timestamp) and an integer (sequence number to order events with the same timestamp), the invariant is again not very well defined because a pair with the same timestamp and smaller sequence number is generally considered to be (strictly) "less than".

Overall, I think the difference between HappensBefore and HappensJustBefore cannot be captured in the TimeOf function, but should rather be enforced on the succession graph induced by these relations as specified in the documentation of HappensJustBefore (but not formalized, as far as I am aware), independent of the timestamps. This would imply that the invariant should be removed from the library.

Alternatively, if the intent was to say there is no other possible value between the timestamp of the occurrence and that of its immediate predecessors (which degrades to the current definition with continuous time), the constraint could capture this better by asserting that there is no otherTimeInstant such that otherTimeInstant < timeInstant and TimeOf(p.endShot, clock) < otherTimeInstant. This would allow discrete clocks to assign successive timestamps to occurrences in a HappensJustBefore relation, forbid continuous clocks to assign different timestamps (as there is always another real number between any two), and force pairs in super-dense time to assign pairs with the same timestamp and either the same or successive sequence numbers.

In the KerML semantics, 8.4.4.9.4 Invocation Expressions, the semantic equivalent model for an InvocationExpression used as a "constructor" for a type T (i.e., T(...)) is shown as having its result parameter redefined with a FeatureTyping relationship to T. However, there is no semantic constraint in the abstract syntax to enforce this. Note that this typing is important, because it is to be expected that the result of a constructor is of the type being constructed.

In Clocks.kerml, the TimeOf function defines the timeContinuityConstraint, which states that (endShots of) immediate predecessors of an occurrence (i.e., those connected via a HappensJustBefore) must get the same timestamp (timeInstant in the model) as the start shot of the occurrence:

inv timeContinuityConstraint {
	doc
	/*
	 * If one Occurrence happens immediately before another, then the TimeOf 
	 * the end snapshot of the first Occurrence equals the TimeOf the second
	 * Occurrence.
	 */
	
	o.immediatePredecessors->forAll{in p : Occurrence; 
		TimeOf(p.endShot, clock) == timeInstant
	}
}	

Compare this to the documentation of HappensJustBefore, which states that "HappensJustBefore is HappensBefore asserting that there is no possibility of another occurrences[sic] happening in the time between the earlierOccurrence and laterOccurrence."

Considering that the intent of the libraries is not to constrain the time model and the format of timestamps, I checked this against three widely-used time models.

With continuous (dense) time, the current formulation of the timeContinuityConstraint might make sense, although it fails to capture that an infinite number of snapshots forming a HappensJustBefore chain may actually take non-zero time.

With discrete time, where a timestamp may be treated as a sequence number, for example, an Integer, the invariant may be too restrictive, as HappensJustBefore could apply to two snapshots that have successive sequence numbers, but have no other occurrence in between them. In fact, in a discrete time model, HappensJustBefore with the current definition degrades to HappensWhile because there is no notion of ordering between events with the same timestamp.

In super-dense time, where a clock is usually represented as a pair of a real value (timestamp) and an integer (sequence number to order events with the same timestamp), the invariant is again not very well defined because a pair with the same timestamp and smaller sequence number is generally considered to be (strictly) "less than".

Overall, I think the difference between HappensBefore and HappensJustBefore cannot be captured in the TimeOf function, but should rather be enforced on the succession graph induced by these relations as specified in the documentation of HappensJustBefore (but not formalized, as far as I am aware), independent of the timestamps. This would imply that the invariant should be removed from the library.

Alternatively, if the intent was to say there is no other possible value between the timestamp of the occurrence and that of its immediate predecessors (which degrades to the current definition with continuous time), the constraint could capture this better by asserting that there is no otherTimeInstant such that otherTimeInstant < timeInstant and TimeOf(p.endShot, clock) < otherTimeInstant. This would allow discrete clocks to assign successive timestamps to occurrences in a HappensJustBefore relation, forbid continuous clocks to assign different timestamps (as there is always another real number between any two), and force pairs in super-dense time to assign pairs with the same timestamp and either the same or successive sequence numbers.

7.3.4.1 (Features Overview) says

Values of a composite feature, on each instance of the feature's domain, cannot exist after the featuring instance ceases to exist.

and 8.3.3.3.3 (Feature) says

isComposite : Boolean
Whether the Feature is a composite feature of its featuringType. If so, the values of the Feature cannot exist after its featuring instance no longer does.

but the spec doesn't seem to say anywhere that the values cannot be values of any composite features on any other instance of the feature's domain ("single owner", "tree" property of composition), as typically expected.

Some (abstract and textual) syntax in Core has (informal) semantics requiring time, such as Feature::isComposite, ::isReadOnly, ::isPortion, as well as ::direction and ::isDerived, see 7.3.4.2 (Feature Declaration) and 8.3.3.3.3 (Feature), but Core does not include a time model.

Some (abstract and textual) syntax in Core has (informal) semantics requiring time, such as Feature::isComposite, ::isReadOnly, ::isPortion, as well as ::direction and ::isDerived, see 7.3.4.2 (Feature Declaration) and 8.3.3.3.3 (Feature), but Core does not include a time model.

The execution algorithm in Annex A should could more cases.

The execution algorithm in Annex A should could more cases.

The specification in subclause 10.2 lists the textual concrete syntax as one format for model interchange.

However, the textual concrete syntax does not include syntax for the elementId : UUID property of any element specified in such a model interchange. In general, this makes it impossible to derive the net semantic difference between model interchanges of a pair of revisions (or versions) of the same package represented in this format. The elementId identifiers are necessary to detect whether a change constitutes: (1) a newly created element, (2) an updated element (including a moved element), or (3) a deleted element. In general, it will only be possible to derive the net lexical difference. This limitation holds in particular for unnamed (i.e. anonymous) elements, as well as for elements with name and/or shortName changes.

It is therefore debatable whether the textual concrete syntax may be designated as a proper model interchange format.

This limitation of use of the textual concrete syntax as an interchange format should be explicitly addressed through one of the following:

1. Add an explanation of the limitation in the specification.
2. Add a facility in the textual concrete syntax to include representation of the elementId for any element. For usability reasons, implementations should provide a capability to show or hide the elementId snippets in the concrete textual notation editor widgets.

When redefining features, some metaproperties must be respecified even when they're intended to be the same as the redefined ones, while others don't. For example, feature type and multiplicity do not need to be respecified on a redefining feature when they are intended to be the same as the redefined feature, as I understand it, while direction does, even when it is intended to be the same as the redefined feature. Modelers must remember which feature metaproperties need to be respecified and which don't. The textual syntax would be easier to use if this were the same for all feature metaproperties, and more so if metaproperties could always be omitted in redefining features when they are intended to be the same as the redefined feature.

The specification in subclause 10.2 lists the textual concrete syntax as one format for model interchange.

However, the textual concrete syntax does not include syntax for the elementId : UUID property of any element specified in such a model interchange. In general, this makes it impossible to derive the net semantic difference between model interchanges of a pair of revisions (or versions) of the same package represented in this format. The elementId identifiers are necessary to detect whether a change constitutes: (1) a newly created element, (2) an updated element (including a moved element), or (3) a deleted element. In general, it will only be possible to derive the net lexical difference. This limitation holds in particular for unnamed (i.e. anonymous) elements, as well as for elements with name and/or shortName changes.

It is therefore debatable whether the textual concrete syntax may be designated as a proper model interchange format.

This limitation of use of the textual concrete syntax as an interchange format should be explicitly addressed through one of the following:

1. Add an explanation of the limitation in the specification.
2. Add a facility in the textual concrete syntax to include representation of the elementId for any element. For usability reasons, implementations should provide a capability to show or hide the elementId snippets in the concrete textual notation editor widgets.

Literal Values
inout
"Values of the Feature on each instance are determined either as in or out directions, or both."
In and out discuss 2 concepts of 'determination' of an instances value, and 'use' of an instances value
Is 'inout' ambiguous as to the features determination and use completely or still constrained?
Both 'in' and 'out' require opposite 'determination' than 'use', but can inout allow same 'determination' and 'use'?
To be more clear, can an inout feature be 'determined' 'externally' and 'used' 'externally'?
How is 'inout' different from not providing a directionality constraint?
How does directionality work with specializations like subsetting/redefinition, should there be constraints?

When redefining features, some metaproperties must be respecified even when they're intended to be the same as the redefined ones, while others don't. For example, feature type and multiplicity do not need to be respecified on a redefining feature when they are intended to be the same as the redefined feature, as I understand it, while direction does, even when it is intended to be the same as the redefined feature. Modelers must remember which feature metaproperties need to be respecified and which don't. The textual syntax would be easier to use if this were the same for all feature metaproperties, and more so if metaproperties could always be omitted in redefining features when they are intended to be the same as the redefined feature.

Literal Values
inout
"Values of the Feature on each instance are determined either as in or out directions, or both."
In and out discuss 2 concepts of 'determination' of an instances value, and 'use' of an instances value
Is 'inout' ambiguous as to the features determination and use completely or still constrained?
Both 'in' and 'out' require opposite 'determination' than 'use', but can inout allow same 'determination' and 'use'?
To be more clear, can an inout feature be 'determined' 'externally' and 'used' 'externally'?
How is 'inout' different from not providing a directionality constraint?
How does directionality work with specializations like subsetting/redefinition, should there be constraints?

The phrase "read only" is often enough taken to refer to features/properties that write actions (eg, FeatureWritePerformance) should not be applied to (see library errors in KERML-49, modeler misunderstandings in KERML-3 comments and UML constraint errors in UMLR-815), rather than having constant values, as intended.

The phrase "read only" is often enough taken to refer to features/properties that write actions (eg, FeatureWritePerformance) should not be applied to (see library errors in KERML-49, modeler misunderstandings in KERML-3 comments and UML constraint errors in UMLR-815), rather than having constant values, as intended.

Clause 7.4.5 (Associations), first two paragraphs after the references at the top describes how to declare associations and use of end features, but the

• only example of association end features is later when explaining the more advanced case of association specialization. The text references an earlier very brief description of end features in 7.3.4.2 (Feature Declaration), which points back to 7.4.5 for more information.

• third paragraph (the one starting "An association is also a relationship between the types") describes related types, but does not mention these are same as the end feature types, as specified by the deriveAssociationRelatedType constraint in 8.3.4.4.2 (Association).

Would helpful for 7.4.5 to include a simple example of association end features near the beginning where they are described, and to explain that related types are the same as end feature types.

Clause 8.3.3.1.10 (Type), includes inheritedMemberships as an operation with a text description, but no OCL.

Usecase: large corporation is working on a project, where also other suppliers deliver parts of the product architecture.

To avoid naming collisions in such constellations, it makes sense to use hierarchical package structures. If everyone just uses plain structures, we have potential conflicts with a duplicate declaration of namespaces.
As within large corporations hundreds of engineers can be working of one product class, which might be organized as namespaces, it makes sense to split the definition of multiple namespaces within the same parent namespace in different files to avoid merge conflicts

Example

package Vehicle{
   part engine : MyCorp::Automotive::Engine::SmallEngine;
   part gearFront : MyCorp::Automotive::Transmission::AT8Gear;
   part rearGear : SomeSupplier::Transmission::FancyGear;
}

Possible resolutions:
1) allow duplicate definitions of namespaces and implicitly merges the resulting trees, dangerous as it could happen unintended
2) allow to merge sub-trees of duplicate namespaces with a keyword
2a) all except one namespace declaration require an addendum keyword, injection of elements possible which might expose private information
2b) all namespaces must declare, that extension is possible

example

partial package CommonParent //declaration can be skipped, if nothing except namespace is declared
package CommonParent::GroupA{
  //some declarations
}
package CommonParent::GroupB{
  //some more declarations
}
package CommonParent::IntegrationLayer{} //should work as no explicitly declared namespace is duplicated
package CommonParent::GroupA::Backdoor {} //should generate an error as the explicitly declared namespace GroupA is duplicated

Usecase: large corporation is working on a project, where also other suppliers deliver parts of the product architecture.

To avoid naming collisions in such constellations, it makes sense to use hierarchical package structures. If everyone just uses plain structures, we have potential conflicts with a duplicate declaration of namespaces.
As within large corporations hundreds of engineers can be working of one product class, which might be organized as namespaces, it makes sense to split the definition of multiple namespaces within the same parent namespace in different files to avoid merge conflicts

Example

package Vehicle{
   part engine : MyCorp::Automotive::Engine::SmallEngine;
   part gearFront : MyCorp::Automotive::Transmission::AT8Gear;
   part rearGear : SomeSupplier::Transmission::FancyGear;
}

Possible resolutions:
1) allow duplicate definitions of namespaces and implicitly merges the resulting trees, dangerous as it could happen unintended
2) allow to merge sub-trees of duplicate namespaces with a keyword
2a) all except one namespace declaration require an addendum keyword, injection of elements possible which might expose private information
2b) all namespaces must declare, that extension is possible

example

partial package CommonParent //declaration can be skipped, if nothing except namespace is declared
package CommonParent::GroupA{
  //some declarations
}
package CommonParent::GroupB{
  //some more declarations
}
package CommonParent::IntegrationLayer{} //should work as no explicitly declared namespace is duplicated
package CommonParent::GroupA::Backdoor {} //should generate an error as the explicitly declared namespace GroupA is duplicated

Clause 7.4.5 (Associations), first two paragraphs after the references at the top describes how to declare associations and use of end features, but the

• only example of association end features is later when explaining the more advanced case of association specialization. The text references an earlier very brief description of end features in 7.3.4.2 (Feature Declaration), which points back to 7.4.5 for more information.

• third paragraph (the one starting "An association is also a relationship between the types") describes related types, but does not mention these are same as the end feature types, as specified by the deriveAssociationRelatedType constraint in 8.3.4.4.2 (Association).

Would helpful for 7.4.5 to include a simple example of association end features near the beginning where they are described, and to explain that related types are the same as end feature types.

Clause 8.3.3.1.10 (Type), includes inheritedMemberships as an operation with a text description, but no OCL.

Clause 9.2.10.1 (Transition Performances Overview) requires two connectors typed by associations, to constrain transitionLink and transitionLinkSource:

The Succession constrained by a TransitionPerformance is specified by a Connector between the Succession and its transitionStep, a unique Step typed by TransitionPerformance or a specialization of it, of the same Behavior as the Succession. This connector is
• typed by an Association defined to give a value to the transitionLink of TransitionPerformances,
• has connector end multiplicity 0..1 on the Succession end and 1 on the TransitionPerformance Step end.

The transitionStep above is also connected to the Succession's sourceFeature, because conditions on the Succession depend on each Occurrence of its sourceFeature separately, which TransitionPerformances identify as their transitionLinkSource. This connector is
• typed by an Association defined to give a value to the transitionLinkSource of TransitionPerformances.
• with connector end multiplicity 1 on both ends.

but

• succession could subset transitionStep.transitionLink (equivalent to a binding with optional multiplicity on succession end)

• bind succession's sourceFeature and its transitionStep.transitionLinkSource (1 to 1 end multiplicities)

giving the desired result without introducing new associations for each transitionStep. This would also align it with SysML's modeling pattern specified in TransitionUsage::checkTransitionUsageSuccessionBindingConnector and checkTransitionUsageSourceBindingConnector (after the latter is corrected as proposed in SYSML2-397).

Clause 9.2.10.1 (Transition Performances Overview) requires two connectors typed by associations, to constrain transitionLink and transitionLinkSource:

The Succession constrained by a TransitionPerformance is specified by a Connector between the Succession and its transitionStep, a unique Step typed by TransitionPerformance or a specialization of it, of the same Behavior as the Succession. This connector is
• typed by an Association defined to give a value to the transitionLink of TransitionPerformances,
• has connector end multiplicity 0..1 on the Succession end and 1 on the TransitionPerformance Step end.

The transitionStep above is also connected to the Succession's sourceFeature, because conditions on the Succession depend on each Occurrence of its sourceFeature separately, which TransitionPerformances identify as their transitionLinkSource. This connector is
• typed by an Association defined to give a value to the transitionLinkSource of TransitionPerformances.
• with connector end multiplicity 1 on both ends.

but

• succession could subset transitionStep.transitionLink (equivalent to a binding with optional multiplicity on succession end)

• bind succession's sourceFeature and its transitionStep.transitionLinkSource (1 to 1 end multiplicities)

giving the desired result without introducing new associations for each transitionStep. This would also align it with SysML's modeling pattern specified in TransitionUsage::checkTransitionUsageSuccessionBindingConnector and checkTransitionUsageSourceBindingConnector (after the latter is corrected as proposed in SYSML2-397).

There is currently no constraint that the typing of a subsetting feature conform to the typing of the subsetted feature. For example, the following is currently considered valid:

classifier A;
classifier B;

feature x : A;
feature y : B subsets x;

even if there is no specialization relationship between A and B. Currently, what happens is that y picks up the additions the additional type A due to the subsetting. So the above declaration for y is essentially equivalent to

feature y: B, A subsets x;

Now, unless A and B are declared as disjoint, it is possible that there are instances classified by both A and B, so that this joint typing of y isn't vacuous. Nevertheless, it seems more useful, for static type checking, to presume disjointness and to disallow the above subsetting unless B can be statically determined to specialize A.

This is relevant, in particular, for connectors, in which the related features are determined using reference subsetting. Consider the following:

assoc C {
   end a: A;
   end b: B;
}

feature a1: A;
feature b1: B;

connector c: C from a ::> b1 to b ::> a1;

Because of the above, this is currently allowed. But, as a result, this really seems to make the typing of association ends pretty much useless for connectors.

There is currently no constraint that the typing of a subsetting feature conform to the typing of the subsetted feature. For example, the following is currently considered valid:

classifier A;
classifier B;

feature x : A;
feature y : B subsets x;

even if there is no specialization relationship between A and B. Currently, what happens is that y picks up the additions the additional type A due to the subsetting. So the above declaration for y is essentially equivalent to

feature y: B, A subsets x;

Now, unless A and B are declared as disjoint, it is possible that there are instances classified by both A and B, so that this joint typing of y isn't vacuous. Nevertheless, it seems more useful, for static type checking, to presume disjointness and to disallow the above subsetting unless B can be statically determined to specialize A.

This is relevant, in particular, for connectors, in which the related features are determined using reference subsetting. Consider the following:

assoc C {
   end a: A;
   end b: B;
}

feature a1: A;
feature b1: B;

connector c: C from a ::> b1 to b ::> a1;

Because of the above, this is currently allowed. But, as a result, this really seems to make the typing of association ends pretty much useless for connectors.

The documentation for the validateAssociationStructureIntersection constraint is "If an Association is also a kind of Structure, then it must be an AssociationStructure." with the OCL

oclIsKindOf(Structure) = oclIsKindOf(AssociationStructure)

However, this is really a constraint on the abstract syntax, not user models. Since the current abstract syntax does not have any metaclass that is a subclass of both Structure and Association other than AssociationStructure, this constraint will always be true for every user model. (And, if the abstract syntax did include another subclass of both Structure and Association, then constraint would then be violated by every user model that used that construct!)

Clause 8.4.4.12.1 (Multiplicities, Semantics) says

The validateTypeOwnedMultiplicity constraint requires that a Type have at most one ownedMember that is a Multiplicity. If a Type has such an owned Multiplicity, then it is the typeWithMultiplicity of that Multiplicity. The value of the Multiplicity is then the cardinality of its typeWithMultiplicity and, therefore, the type (co-domain) of the Multiplicity restricts that cardinality.

If a Type does not have an owned Multiplicity, but has ownedSpecializations, then its cardinality is constrained by the Multiplicities for all of the general Types of those ownedSpecializations (i.e., its direct supertypes). In practice, this means that the effective Multiplicity of the Type is the most restrictive Multiplicity of its direct supertypes.

The above implies inherited multiplicities do not constrain cardinality of types that

• own a Multiplicity
• inherit them via unowned specializations

while the (math) semantics for specialization and multiplicity says they do (rule 1 in 8.4.3.2, Types Semantics, and rule 5 in 8.4.3.4, Features Semantics, respectively).

When a Feature has chainingFeatures, then it is sometimes useful to reference that last Feature in the chain in situations in which one would otherwise reference the owning Feature itself if there was no chain. For instance, in a graphical view, an edge with a chained Feature at an end will generally point to the last chainedFeature (possibly nested) rather than the chained Feature itself.

Currently, this means that it is necessary to check for a feature f whether f.chainingFeature is non-empty and, if so, use f.chainingFeature->last() instead of f. It would be more convenient to have a derived property of Feature (called, say, targetFeature) that would do this automatically, that is, be derived as

targetFeature = if chainingFeature.isEmpty() then self else chainingFeature->last() end if

Attributes
/owningType : Type {subsets type, redefines membershipOwningNamespace, type}

It is not "immediately" clear which 'type' metaproperty of which metaclass is the subsetted one, and which one is the redefined one. I think the semantics is meant to be that the redefines is for Featuring.type while the subsets is for the unnamed Association with the Type.featureMembership at it's other end.

KERML-22 already requests to name the Association, it should probably define the derivation rule for it's owned derived /type metaproperty... probably subsets membershipNamespace.. it may actually redefine membershipNamespace since only types can own FeatureMemberships

The documentation for the validateAssociationStructureIntersection constraint is "If an Association is also a kind of Structure, then it must be an AssociationStructure." with the OCL

oclIsKindOf(Structure) = oclIsKindOf(AssociationStructure)

However, this is really a constraint on the abstract syntax, not user models. Since the current abstract syntax does not have any metaclass that is a subclass of both Structure and Association other than AssociationStructure, this constraint will always be true for every user model. (And, if the abstract syntax did include another subclass of both Structure and Association, then constraint would then be violated by every user model that used that construct!)

The way KerML libraries are provided relies on textual notation files on which element declarations do not include the specification of their elementId property.

As consequence, if the elementId is actually generated by the tool, as written in the KerML specification (p226), it is very likely to have a different value from one computer to another and even from one loading to another on the same computer.

Hence, it is impossible to make sure it will "not change during the lifetime of the Element", as required by in the same paragraph of that specification.

Note: a similar issue will be raised on SysMLv2

Clause 8.4.4.12.1 (Multiplicities, Semantics) says

The validateTypeOwnedMultiplicity constraint requires that a Type have at most one ownedMember that is a Multiplicity. If a Type has such an owned Multiplicity, then it is the typeWithMultiplicity of that Multiplicity. The value of the Multiplicity is then the cardinality of its typeWithMultiplicity and, therefore, the type (co-domain) of the Multiplicity restricts that cardinality.

If a Type does not have an owned Multiplicity, but has ownedSpecializations, then its cardinality is constrained by the Multiplicities for all of the general Types of those ownedSpecializations (i.e., its direct supertypes). In practice, this means that the effective Multiplicity of the Type is the most restrictive Multiplicity of its direct supertypes.

The above implies inherited multiplicities do not constrain cardinality of types that

• own a Multiplicity
• inherit them via unowned specializations

while the (math) semantics for specialization and multiplicity says they do (rule 1 in 8.4.3.2, Types Semantics, and rule 5 in 8.4.3.4, Features Semantics, respectively).

When a Feature has chainingFeatures, then it is sometimes useful to reference that last Feature in the chain in situations in which one would otherwise reference the owning Feature itself if there was no chain. For instance, in a graphical view, an edge with a chained Feature at an end will generally point to the last chainedFeature (possibly nested) rather than the chained Feature itself.

Currently, this means that it is necessary to check for a feature f whether f.chainingFeature is non-empty and, if so, use f.chainingFeature->last() instead of f. It would be more convenient to have a derived property of Feature (called, say, targetFeature) that would do this automatically, that is, be derived as

targetFeature = if chainingFeature.isEmpty() then self else chainingFeature->last() end if

Attributes
/owningType : Type {subsets type, redefines membershipOwningNamespace, type}

It is not "immediately" clear which 'type' metaproperty of which metaclass is the subsetted one, and which one is the redefined one. I think the semantics is meant to be that the redefines is for Featuring.type while the subsets is for the unnamed Association with the Type.featureMembership at it's other end.

KERML-22 already requests to name the Association, it should probably define the derivation rule for it's owned derived /type metaproperty... probably subsets membershipNamespace.. it may actually redefine membershipNamespace since only types can own FeatureMemberships

The way KerML libraries are provided relies on textual notation files on which element declarations do not include the specification of their elementId property.

As consequence, if the elementId is actually generated by the tool, as written in the KerML specification (p226), it is very likely to have a different value from one computer to another and even from one loading to another on the same computer.

Hence, it is impossible to make sure it will "not change during the lifetime of the Element", as required by in the same paragraph of that specification.

Note: a similar issue will be raised on SysMLv2

In general, Feature::type can have more than one value, and there is no restriction on this for end Features. The Association::relatedType property is derived as all the types of all the associationEnds of the Association. However, Association::sourceType is derived to be just the first relatedType. But consider the following Association:

assoc A {
    end feature x : X1, X2;
    end feature y : Y1, Y2;
}

Even though this is a binary Association (it has exactly two ends), it has four relatedTypes: X1, X2, Y1 and Y2. As a binary Association, though, it (implicitly) specializes the library Association BinaryAssociation, with the first end redefining the source and the second end redefining the target. However, with the current derivation, the sourceType of A will be only X1, and the targetTypes will be X2, Y1 and Y2 – even though X2 is a type of the source end.

In 7.4.9.2 OperatorExpressions, in the bullet for "Classification expressions", it states:

The classification operators may also be used without a first operand, in which case the first operand is implicitly Anything::self (see 9.2.2.2.1). This is useful, in particular, when used as a test within an element filter condition expression (see 7.4.14).

In the concrete syntax, in 8.2.5.8.1 Operator Expressions, the production for ClassificationExpression does, indeed, allow the first operand to be optional. However, there is nothing stated there (or anywhere else in normative Clause 8) about the default for the first operand being Anything::self if it is not given explicitly, as stated in 7.4.9.2.

In 7.4.9.2 OperatorExpressions, in the bullet for "Classification expressions", it states:

The classification operators may also be used without a first operand, in which case the first operand is implicitly Anything::self (see 9.2.2.2.1). This is useful, in particular, when used as a test within an element filter condition expression (see 7.4.14).

In the concrete syntax, in 8.2.5.8.1 Operator Expressions, the production for ClassificationExpression does, indeed, allow the first operand to be optional. However, there is nothing stated there (or anywhere else in normative Clause 8) about the default for the first operand being Anything::self if it is not given explicitly, as stated in 7.4.9.2.

In general, Feature::type can have more than one value, and there is no restriction on this for end Features. The Association::relatedType property is derived as all the types of all the associationEnds of the Association. However, Association::sourceType is derived to be just the first relatedType. But consider the following Association:

assoc A {
    end feature x : X1, X2;
    end feature y : Y1, Y2;
}

Even though this is a binary Association (it has exactly two ends), it has four relatedTypes: X1, X2, Y1 and Y2. As a binary Association, though, it (implicitly) specializes the library Association BinaryAssociation, with the first end redefining the source and the second end redefining the target. However, with the current derivation, the sourceType of A will be only X1, and the targetTypes will be X2, Y1 and Y2 – even though X2 is a type of the source end.

[From Vince Molnar] Package-level features do not give featuring types, and some have lower multiplicity greater than zero, meaning everything in the universe (instances of Anything), including every data value, is required to give at least that number of values to them (see KERML-56). For example, the libraries include:

Clocks::universalClock[1] {...}
Observation::defaultMonitor[1] : ChangeMonitor[1] {...}
SpatialFrames::defaultFrame : SpatialFrame[1] {...}

Might be others. This one

Occurrences::earlierFirstIncomingTransferSort: IncomingTransferSort{... }

does not give a multiplicity, I couldn't find what this means (even for expressions), tho this particular feature is supposed to have exactly one value.

Clause 8.3.4.10.2 (FeatureValue) and 8.4.4.11 (Feature Values Semantics) say

A FeatureValue is a Membership that identifies a particular member Expression that provides the value of the Feature that owns the FeatureValue.

A FeatureValue is a kind of OwningMembership between a Feature and an Expression.

but does not require the model to specify when the expression is evaluated. Expressions (as steps) owned by some features are required to happen (be evaluated) during instances of the featuring types (domain) of that feature (see KERML-11), which might be too loose for some applications, while those owned other features are unconstrained, for example, their values could be the results of an expression evaluated before or after the instance of domain types exists. The results could vary over time if the expression reads values of other features. This seems to apply to all the combinations of default/initial feature values.

Clauses 7.4.8.1 (Functions Overview) and 8.4.4.8.2 (Expressions and Invariants) say

An invariant, though, is a boolean expression that must always evaluate to either true at all times or false at all times. By default, an invariant is asserted to always evaluate to true, while a negated invariant is asserted to always evaluate to false.

Expressions are kinds of Steps. The checkExpressionSpecialization constraint requires that Expressions specialize the base Expression Performances::evaluations (see 9.2.6.2.3), which is a specialization of Performances::performances.

the checkInvariantSpecialization constraint requires that Invariants specialize either the BooleanExpression Performances::trueEvaluations (see 9.2.6.2.2) or, if the Invariant is negated, the BooleanExpression Performances::falseEvaluations (see 9.2.6.2.2), both of which are specializations of Performances::booleanEvaluations.

where the Performance library defines

abstract expr trueEvaluations subsets booleanEvaluations { true }

abstract expr falseEvaluations subsets booleanEvaluations { false }

but do not require models to specify when invariant expressions are evaluated, which are the only times the results are required to be true/false. The conditions they test for might be present only when the invariants happen to be evaluated (see KERML-58 for more about this).

Clause 8.3.4.10.2 (FeatureValue) and 8.4.4.11 (Feature Values Semantics) say

A FeatureValue is a Membership that identifies a particular member Expression that provides the value of the Feature that owns the FeatureValue.

A FeatureValue is a kind of OwningMembership between a Feature and an Expression.

but does not require the model to specify when the expression is evaluated. Expressions (as steps) owned by some features are required to happen (be evaluated) during instances of the featuring types (domain) of that feature (see KERML-11), which might be too loose for some applications, while those owned other features are unconstrained, for example, their values could be the results of an expression evaluated before or after the instance of domain types exists. The results could vary over time if the expression reads values of other features. This seems to apply to all the combinations of default/initial feature values.

[From Vince Molnar] Package-level features do not give featuring types, and some have lower multiplicity greater than zero, meaning everything in the universe (instances of Anything), including every data value, is required to give at least that number of values to them (see KERML-56). For example, the libraries include:

Clocks::universalClock[1] {...}
Observation::defaultMonitor[1] : ChangeMonitor[1] {...}
SpatialFrames::defaultFrame : SpatialFrame[1] {...}

Might be others. This one

Occurrences::earlierFirstIncomingTransferSort: IncomingTransferSort{... }

does not give a multiplicity, I couldn't find what this means (even for expressions), tho this particular feature is supposed to have exactly one value.

Clauses 7.4.8.1 (Functions Overview) and 8.4.4.8.2 (Expressions and Invariants) say

An invariant, though, is a boolean expression that must always evaluate to either true at all times or false at all times. By default, an invariant is asserted to always evaluate to true, while a negated invariant is asserted to always evaluate to false.

Expressions are kinds of Steps. The checkExpressionSpecialization constraint requires that Expressions specialize the base Expression Performances::evaluations (see 9.2.6.2.3), which is a specialization of Performances::performances.

the checkInvariantSpecialization constraint requires that Invariants specialize either the BooleanExpression Performances::trueEvaluations (see 9.2.6.2.2) or, if the Invariant is negated, the BooleanExpression Performances::falseEvaluations (see 9.2.6.2.2), both of which are specializations of Performances::booleanEvaluations.

where the Performance library defines

abstract expr trueEvaluations subsets booleanEvaluations { true }

abstract expr falseEvaluations subsets booleanEvaluations { false }

but do not require models to specify when invariant expressions are evaluated, which are the only times the results are required to be true/false. The conditions they test for might be present only when the invariants happen to be evaluated (see KERML-58 for more about this).

The Type metaclass is concrete (like all the metaclasses in the abstract syntax), making it it syntactically valid to create a Type that is not a Classifier or a Feature. However, Clause 8.4.3.1.2 (Core Semantics Mathematical Preliminaries) requires the set of Types in a model to be the union of the set of Classifiers and Features. This means instances of Type in a model that are not Classifiers or Features are syntactically valid, but not given semantics (it's not possible to tell if instances of such types are valid or not).

Project interchange files (.kpar) were submitted for all model libraries. However, in all cases, these archives only included textual notation model interchange files (.kerml). There should also be normative model library project interchange files in which the models are formatted in XMI and JSON.

Clause 8.4.4.6.1 (Connectors, Semantics) says (see KERML-34 for term definitions)

the checkFeatureEndRedefinition constraint requires that the connectorEnds of a Connector redefine the associationEnds of its typing Associations. As a result, a Connector typed by an N-ary Association is essentially required to have the form (with implicit relatiojnships included):

connector a : A subsets Links::links {
end feature e1 redefines A::e1 references f1;
end feature e2 redefines A::e2 references f2;
...
end feature eN redefines A::eN references fN; }

where e1, e2, ..., eN are the names of associationEnds of the Association A, in the order they are defined in A, and the f1, f2, ..., fN are the relatedFeatures of the Connector. Multiplicities declared for connectorEnds have the same special semantics as for associationEnds (see 8.4.4.5).

while 8.3.3.3.8 (Redefinition), under Description (and similar wording in 7.3.4.5 Redefinition) says

Redefinition is a kind of Subsetting that requires the redefinedFeature and the redefiningFeature to have the same values (on each instance of the domain of the redefiningFeature). This means any restrictions on the redefiningFeature, such as type or multiplicity, also apply to the redefinedFeature (on each instance of the domain of the redefiningFeature), and vice versa.

preventing connector ends from giving a smaller lower multiplicity of the corresponding end of their (association) type. For example, people have exactly two parents, but a connector typed by that association might need to specify a [0..2] multiplicity on the parent end to reflect a particular purpose of identifying parents by that connector (such as "lives with").

This restriction is mentioned informally in Clause 8.4.4.6.2 (Binding Connectors):

Since both associationEnds of SelfLink have multiplicity 1..1, both connectorEnds of a BindingConnector do also.

even though some bindings in the libraries have optional connector end multiplicities (see KERML-27).

Clause 7 Language Description includes a large number of example models and snippets, in textual and graphical notation. However, no machine-readable interchange file was submitted for these models. Project interchange files should be provided for them, including textual notation, XMI and JSON versions.

Clause 7 Language Description includes a large number of example models and snippets, in textual and graphical notation. However, no machine-readable interchange file was submitted for these models. Project interchange files should be provided for them, including textual notation, XMI and JSON versions.

The Type metaclass is concrete (like all the metaclasses in the abstract syntax), making it it syntactically valid to create a Type that is not a Classifier or a Feature. However, Clause 8.4.3.1.2 (Core Semantics Mathematical Preliminaries) requires the set of Types in a model to be the union of the set of Classifiers and Features. This means instances of Type in a model that are not Classifiers or Features are syntactically valid, but not given semantics (it's not possible to tell if instances of such types are valid or not).

Project interchange files (.kpar) were submitted for all model libraries. However, in all cases, these archives only included textual notation model interchange files (.kerml). There should also be normative model library project interchange files in which the models are formatted in XMI and JSON.

Clause 8.4.4.6.1 (Connectors, Semantics) says (see KERML-34 for term definitions)

the checkFeatureEndRedefinition constraint requires that the connectorEnds of a Connector redefine the associationEnds of its typing Associations. As a result, a Connector typed by an N-ary Association is essentially required to have the form (with implicit relatiojnships included):

connector a : A subsets Links::links {
end feature e1 redefines A::e1 references f1;
end feature e2 redefines A::e2 references f2;
...
end feature eN redefines A::eN references fN; }

where e1, e2, ..., eN are the names of associationEnds of the Association A, in the order they are defined in A, and the f1, f2, ..., fN are the relatedFeatures of the Connector. Multiplicities declared for connectorEnds have the same special semantics as for associationEnds (see 8.4.4.5).

while 8.3.3.3.8 (Redefinition), under Description (and similar wording in 7.3.4.5 Redefinition) says

Redefinition is a kind of Subsetting that requires the redefinedFeature and the redefiningFeature to have the same values (on each instance of the domain of the redefiningFeature). This means any restrictions on the redefiningFeature, such as type or multiplicity, also apply to the redefinedFeature (on each instance of the domain of the redefiningFeature), and vice versa.

preventing connector ends from giving a smaller lower multiplicity of the corresponding end of their (association) type. For example, people have exactly two parents, but a connector typed by that association might need to specify a [0..2] multiplicity on the parent end to reflect a particular purpose of identifying parents by that connector (such as "lives with").

This restriction is mentioned informally in Clause 8.4.4.6.2 (Binding Connectors):

Since both associationEnds of SelfLink have multiplicity 1..1, both connectorEnds of a BindingConnector do also.

even though some bindings in the libraries have optional connector end multiplicities (see KERML-27).

Clauses 7.4.5 (Associations) and 8.4.4.5.1 (Associations) say

if an association end has a multiplicity specified other than 1..1, then this is interpreted as follows: For each association end, the multiplicity, ordering and uniqueness constraints specified for that end apply to each set of instance of the association that have the same (single) values for each of the other ends. For a binary association, this corresponds to the multiplicity resulting from "navigating" across the association given a value at one end of the association to the other end of the association.

If an associationEnd has a declared multiplicity other than 1..1, then this shall be interpreted as follows: For an Association with N associationEnds, consider the i-th associationEnd ei. The multiplicity, ordering and uniqueness constraints specified for ei apply to each set of instances of the Association that have the same (singleton) values for each of the N-1 associationEnds other than ei.

but this semantics is not math/modeled. In addition, the text above

• does not seem to consider instances of associated classes that do not participate in any links, because only refers to instances of links. In the Product Selection example, the cart in red on the bottom left of the first slide violates the linkedProduct "end" multiplicity 1..*, but the text above would not detect it because it does not participate in any link.
• Applies multiplicity, ordering and uniqueness to links (last sentence), which don't have these characteristics, rather than a feature with the values of ei from all the links.

The textual and abstract syntaxes (at least) for association end features do not relate to the corresponding ones in the associated classes (association ends in SysML1.x/UML sense, see KERML-34 for term definitions), leaving modelers and tool builders only non-standard ways of maintaining consistency between them. The libraries use a feature subsetting for this, but are not required to. For example, in Occurrences::HappensBefore, the earlier/laterOccurrence association end features subset the corresponding predecessors/successors features of the asssociated occurrence class by chaining through the other end feature:

assoc all HappensBefore specializes HappensLink, Without {
  end feature earlierOccurrence: Occurrence[0..*] ... subsets laterOccurrence.predecessors;
  end feature laterOccurrence: Occurrence[0..*] ... subsets earlierOccurrence.successors; }

abstract class Occurrence specializes Anything { ...
  feature predecessors: Occurrence[0..*] ... {...}
  feature successors: Occurrence[0..*] ... inverse of predecessors {...} }

End features can be multiply subset, and do not identify which subsetting maintains consistency with the corresponding features in the associated classes, preventing tool builders from depending on the subsetting pattern to identify the corresponding features of the associated classifiers, even if the pattern were required.

Some library types might be intended to be sufficient. For example, in Occurrences::Occurrence, the values of

feature spaceTimeCoincidentOccurrences: Occurrence[1..*] subsets timeCoincidentOccurrences, spaceEnclosedOccurrences ... { ...
  feature redefines thatOccurrence subsets largerSpace;
  feature redefines thisOccurrence subsets smallerSpace;
  connector :InsideOf from largerSpace references thatOccurrence [1]
                      to smallerSpace references thisOccurrence [1]; }

presumably should include all timeCoincident/spaceEnclosedOccurrences that meet the condition given by the connector, but the feature is not marked as sufficient. Might be others like this.

Some library types are sufficient, but do give give any conditions. For example, in Occurrences::Occurrence::

portion feature all portions: Occurrence[1..*] subsets spaceTimeEnclosedOccurrences { ... }

only has text documentation between the curly braces, leaving sufficiency to mean that portions and spaceTimeEnclosedOccurrences are equivalent. Might be others like this.

Performances::Performance and Objects::Object redefine self in the libraries, but Clauses 9.2.6.2.13 (Performance) and 9.2.5.2.7 (Object) are missing entries for these. Might be other self redefinitions missing also.

The textual and abstract syntaxes (at least) for association end features do not relate to the corresponding ones in the associated classes (association ends in SysML1.x/UML sense, see KERML-34 for term definitions), leaving modelers and tool builders only non-standard ways of maintaining consistency between them. The libraries use a feature subsetting for this, but are not required to. For example, in Occurrences::HappensBefore, the earlier/laterOccurrence association end features subset the corresponding predecessors/successors features of the asssociated occurrence class by chaining through the other end feature:

assoc all HappensBefore specializes HappensLink, Without {
  end feature earlierOccurrence: Occurrence[0..*] ... subsets laterOccurrence.predecessors;
  end feature laterOccurrence: Occurrence[0..*] ... subsets earlierOccurrence.successors; }

abstract class Occurrence specializes Anything { ...
  feature predecessors: Occurrence[0..*] ... {...}
  feature successors: Occurrence[0..*] ... inverse of predecessors {...} }

End features can be multiply subset, and do not identify which subsetting maintains consistency with the corresponding features in the associated classes, preventing tool builders from depending on the subsetting pattern to identify the corresponding features of the associated classifiers, even if the pattern were required.

Clauses 7.4.5 (Associations) and 8.4.4.5.1 (Associations) say

if an association end has a multiplicity specified other than 1..1, then this is interpreted as follows: For each association end, the multiplicity, ordering and uniqueness constraints specified for that end apply to each set of instance of the association that have the same (single) values for each of the other ends. For a binary association, this corresponds to the multiplicity resulting from "navigating" across the association given a value at one end of the association to the other end of the association.

If an associationEnd has a declared multiplicity other than 1..1, then this shall be interpreted as follows: For an Association with N associationEnds, consider the i-th associationEnd ei. The multiplicity, ordering and uniqueness constraints specified for ei apply to each set of instances of the Association that have the same (singleton) values for each of the N-1 associationEnds other than ei.

but this semantics is not math/modeled. In addition, the text above

• does not seem to consider instances of associated classes that do not participate in any links, because only refers to instances of links. In the Product Selection example, the cart in red on the bottom left of the first slide violates the linkedProduct "end" multiplicity 1..*, but the text above would not detect it because it does not participate in any link.
• Applies multiplicity, ordering and uniqueness to links (last sentence), which don't have these characteristics, rather than a feature with the values of ei from all the links.

Some library types might be intended to be sufficient. For example, in Occurrences::Occurrence, the values of

feature spaceTimeCoincidentOccurrences: Occurrence[1..*] subsets timeCoincidentOccurrences, spaceEnclosedOccurrences ... { ...
  feature redefines thatOccurrence subsets largerSpace;
  feature redefines thisOccurrence subsets smallerSpace;
  connector :InsideOf from largerSpace references thatOccurrence [1]
                      to smallerSpace references thisOccurrence [1]; }

presumably should include all timeCoincident/spaceEnclosedOccurrences that meet the condition given by the connector, but the feature is not marked as sufficient. Might be others like this.

Some library types are sufficient, but do give give any conditions. For example, in Occurrences::Occurrence::

portion feature all portions: Occurrence[1..*] subsets spaceTimeEnclosedOccurrences { ... }

only has text documentation between the curly braces, leaving sufficiency to mean that portions and spaceTimeEnclosedOccurrences are equivalent. Might be others like this.

Performances::Performance and Objects::Object redefine self in the libraries, but Clauses 9.2.6.2.13 (Performance) and 9.2.5.2.7 (Object) are missing entries for these. Might be other self redefinitions missing also.

The specification gives Feature::multiplicity, ordering, and uniqueness very different meanings for what it calls "end" features (see KERML-34 for definition of terms) than other features. This requires modelers and tool builders to create special cases in their minds and implementations to accommodate it. It also prevents

• connector ends from giving smaller lower multiplicity than their association ends (see KERML-55)
• participant features from specifying how many values they have (see KERML-35)
• multiplicities from being uniquely specified (see KERML-36).

Normally feature multiplicity restricts the number of values of a feature, but for association "end" features it restricts the number of values of the corresponding features of associated classifiers (association ends in SysML1.x/UML sense,(see KERML-34 for definition of terms) about terms), see excepts below. For example, in the Product Selection example, the info feature of association Selection has the usual semantics for multiplicity, but the "end" features linkedCart an linkedProduct do not. The same comments apply to end ordering and uniqueness.

Clause 7.4.5 (Associations) says

The semantics of multiplicity is different for end features from that for non-end features (as described in 7.3.4.2). The end features of an association determine the participants in the links that are instances of the association and, as such, effectively have multiplicity of "1" relative to the association. But, if an association end has a multiplicity specified other than 1..1, then this is interpreted as follows: For each association end, the multiplicity, ordering and uniqueness constraints specified for that end apply to each set of instance of the association that have the same (single) values for each of the other ends. For a binary association, this corresponds to the multiplicity resulting from "navigating" across the association given a value at one end of the association to the other end of the association.

Clause 8.4.4.5.1 (Associations) says

As endFeatures, the associationEnds of an Association are given a special semantics compared to other Features. Even if an associationEnd has a declared multiplicity other than 1..1, the associationEnd is required to effectively have multiplicity 1..1 as a participant in the Link. Note that the Feature Link::participant is declared readonly, meaning that the participants in a link cannot change once the link is created.

If an associationEnd has a declared multiplicity other than 1..1, then this shall be interpreted as follows: For an Association with N associationEnds, consider the i-th associationEnd ei. The multiplicity, ordering and uniqueness constraints specified for ei apply to each set of instances of the Association that have the same (singleton) values for each of the N-1 associationEnds other than ei.

Clause 8.3.3.3.3 (Feature) says

isEnd : Boolean
Whether or not the this Feature is an end Feature, requiring a different interpretation of the multiplicity of the Feature. An end Feature is always considered to map each domain instance to a single co-domain instance, whether or not a Multiplicity is given for it. If a Multiplicity is given for an end Feature, rather than giving the co-domain cardinality for the Feature as usual, it specifies a cardinality constraint for navigating across the endFeatures of the featuringType of the end Feature.

That is, if a Type has n endFeatures, then the Multiplicity of any one of those end Features constrains the cardinality of the set of values of that Feature when the values of the other n-1 end Features are held fixed.

KerML association end textual notation/abstract syntax give multiplicity, ordering, and uniqueness that can be redundantly stated on the corresponding features of associated classifiers (association ends in SysML1.x/UML sense, see KERML-34 about terms), eg, in Occurrences:

Occurrence::suboccurrences [1..*] {...}

HappensDuring {end shorterOccurrence [1..*] subsets longerOccurrence.suboccurrences;}

making it possible for multiplicities, ordering, and uniqueness to get out synch between the features, and potentially be inconsistent. See kerml-assoc-redundancy-issue-description-v2.pdf slides attached.

The specification says that association "end" features have exactly one value each (see KERML-34 for spec excerpts and definition of terms), but this semantics is not math/modeled.

The specification says that association "end" features have exactly one value each (see KERML-34 for spec excerpts and definition of terms), but this semantics is not math/modeled.

The specification gives Feature::multiplicity, ordering, and uniqueness very different meanings for what it calls "end" features (see KERML-34 for definition of terms) than other features. This requires modelers and tool builders to create special cases in their minds and implementations to accommodate it. It also prevents

• connector ends from giving smaller lower multiplicity than their association ends (see KERML-55)
• participant features from specifying how many values they have (see KERML-35)
• multiplicities from being uniquely specified (see KERML-36).

Normally feature multiplicity restricts the number of values of a feature, but for association "end" features it restricts the number of values of the corresponding features of associated classifiers (association ends in SysML1.x/UML sense,(see KERML-34 for definition of terms) about terms), see excepts below. For example, in the Product Selection example, the info feature of association Selection has the usual semantics for multiplicity, but the "end" features linkedCart an linkedProduct do not. The same comments apply to end ordering and uniqueness.

Clause 7.4.5 (Associations) says

The semantics of multiplicity is different for end features from that for non-end features (as described in 7.3.4.2). The end features of an association determine the participants in the links that are instances of the association and, as such, effectively have multiplicity of "1" relative to the association. But, if an association end has a multiplicity specified other than 1..1, then this is interpreted as follows: For each association end, the multiplicity, ordering and uniqueness constraints specified for that end apply to each set of instance of the association that have the same (single) values for each of the other ends. For a binary association, this corresponds to the multiplicity resulting from "navigating" across the association given a value at one end of the association to the other end of the association.

Clause 8.4.4.5.1 (Associations) says

As endFeatures, the associationEnds of an Association are given a special semantics compared to other Features. Even if an associationEnd has a declared multiplicity other than 1..1, the associationEnd is required to effectively have multiplicity 1..1 as a participant in the Link. Note that the Feature Link::participant is declared readonly, meaning that the participants in a link cannot change once the link is created.

If an associationEnd has a declared multiplicity other than 1..1, then this shall be interpreted as follows: For an Association with N associationEnds, consider the i-th associationEnd ei. The multiplicity, ordering and uniqueness constraints specified for ei apply to each set of instances of the Association that have the same (singleton) values for each of the N-1 associationEnds other than ei.

Clause 8.3.3.3.3 (Feature) says

isEnd : Boolean
Whether or not the this Feature is an end Feature, requiring a different interpretation of the multiplicity of the Feature. An end Feature is always considered to map each domain instance to a single co-domain instance, whether or not a Multiplicity is given for it. If a Multiplicity is given for an end Feature, rather than giving the co-domain cardinality for the Feature as usual, it specifies a cardinality constraint for navigating across the endFeatures of the featuringType of the end Feature.

That is, if a Type has n endFeatures, then the Multiplicity of any one of those end Features constrains the cardinality of the set of values of that Feature when the values of the other n-1 end Features are held fixed.

KerML association end textual notation/abstract syntax give multiplicity, ordering, and uniqueness that can be redundantly stated on the corresponding features of associated classifiers (association ends in SysML1.x/UML sense, see KERML-34 about terms), eg, in Occurrences:

Occurrence::suboccurrences [1..*] {...}

HappensDuring {end shorterOccurrence [1..*] subsets longerOccurrence.suboccurrences;}

making it possible for multiplicities, ordering, and uniqueness to get out synch between the features, and potentially be inconsistent. See kerml-assoc-redundancy-issue-description-v2.pdf slides attached.

The specification and models carry over the terms "association end" and "participant" from SysML 1.x, leaving the meaning of "participant" as it was, but changing the meaning of "association end" to be same as "participant", and providing no term equivalent to SysML 1.x "association end" (see below). This shift makes KerML/SysML 2 associations difficult to understand and discuss among current SysMLers (judging from experience during the submission process), and probably those new to SysML as well.

The specification term "association end" refers to what SySML 1.x calls a "participant" property, a property of links (instances of associations) that each identify exactly one of the things being linked by each link. The library element Link has a feature named "participant", with exactly the same meaning as in SysML 1.x, that generalizes "association end" features, such as the source and target features of BinaryLink. The term "association end" in SysML 1.x refers to properties (typically) of associated classes that on each instance of one associated class identify (potentially zero or multiple) instances of the other associated class that are linked by the association. KerML can model these kind of features, but does not give a name for them.

Clauses 7.4.5 (Associations) and 9.2.3.1 (Links Overview) say

Associations are classifiers that classify links between things (see 9.2.3.1) At least two owned features of an association must be end features (see 7.3.4.2), its association ends, which identify the things being linked by (at the "ends" of) each link (exactly one thing per end, which might be the same thing).

The end features of an association determine the participants in the links that are instances of the association and, as such, effectively have multiplicity of "1" relative to the association.

The participant Feature of Link is the most general associationEnd, identifying the things being linked by (at the "ends" of) each Link (exactly one thing per end, which might be the same things).

where Association::associationEnds identify participant features.

The above use of "association end" in the specifiation is reflected in the textual syntax for assocations by the keyword "end" identifying these participant features. Clause 8.4.4.5.1 (Associations) says:

n-aries have this form:

uassoc A specializes Links::Link {
end feature e1 subsets Links::Link::participant;
end feature e2 subsets Links::Link::participant;
...
end feature eN subsets Links::Link::participant; }

The Link instance for an Association is thus a tuple of participants, where each participant is a single value of an associationEnd of the Association.

The quoted text above is only about the equivalent of SysML 1.x participant properties, but might seem to current SysMLers to be about something equivalent to SysML 1.x association ends.

Clause 8.4.4.6.2 (Binding Connectors) says

binding f1 = f2;

is equivalent to

connector subsets Links::selfLinks {
  end feature thisThing redefines Links::SelfLink::thisThing references f1;
  end feature thatThing redefines Links::SelfLink::thatThing references f2; 

while the next clause, 8.4.4.6.3 (Successions) says

succession first f1 then f2;

is equivalent to

connector subsets Occurrences::happensBeforeLinks {
  end feature earlierOccurrence references f1
    redefines Occurrences::HappensBefore::earlierOccurrence;
  end feature laterOccurrence references f2
    redefines Occurrences::HappensBefore::laterOccurrence; }

The similarity between the clauses implies the first/then notation is short for successions with multiplicity 1..1 on both ends, but the text does not say it, if that's the intention, and should be clarified in any case.

Clause 8.4.4.6.2 (Binding Connectors) says

binding f1 = f2;

is equivalent to

connector subsets Links::selfLinks {
  end feature thisThing redefines Links::SelfLink::thisThing references f1;
  end feature thatThing redefines Links::SelfLink::thatThing references f2; 

while the next clause, 8.4.4.6.3 (Successions) says

succession first f1 then f2;

is equivalent to

connector subsets Occurrences::happensBeforeLinks {
  end feature earlierOccurrence references f1
    redefines Occurrences::HappensBefore::earlierOccurrence;
  end feature laterOccurrence references f2
    redefines Occurrences::HappensBefore::laterOccurrence; }

The similarity between the clauses implies the first/then notation is short for successions with multiplicity 1..1 on both ends, but the text does not say it, if that's the intention, and should be clarified in any case.

Background

Consider the flowing simple structure:

struct Car {
  feature carEngine : Engine[1];
  feature carWheels : Wheel[4];
  
  connector carDrive : Drive
    from carEngine to carWheels;
}

The feature multiplicities in this model require that each instance of Car have exactly one Engine and exactly four Wheels. The model also includes a usage of the following association:

assoc Drive {
  end feature driveEngine : Engine[0..1];
  end feature driveWheel : Wheel[2..4];
} 

The Drive end multiplicities require that every Engine is connected to 2 to 4 Wheels, while every Wheel is connected to at most 1 Engine. But each instance of the association Drive is a link between a single engine and a single wheel. The multiplicities of the end features of Drive are thus interpreted differently than those of the features of Car (but consistently with how UML and SysML v1 interpret association end multiplicity). Rather than constraining the values of the end features themselves, the end multiplicities constrain the number of links allowed when the value at one end is held fixed: if a value is given for the driveEngine, then there must be two to four Drive links from that driveEngine to different Wheels; if a value is given for the driveWheel, then there must be zero or one instances between that driveWheel and an Engine.

For example, consider the following usage of Car that explicitly binds all the Car features:

feature myCar : Car {
  feature :>> carEngine = myEngine;
  feature :>> carWheels =
    (leftFrontWheel, rightFrontWheel, leftRearWheel, rightRearWheel);
  
  connector :>> carDrive =
    ( Drive(myEngine, leftRearWheel),
      Drive(myEngine, rightRearWheel)
    );
}

The connector ends of the connector carDrive inherit their end multiplicities from the ends of the association Drive. The above model explicitly binds the carDrive connector to two Drive values:

1. a connection from myEngine to leftRearWheel

2. a connection from myEngine to rightRearWheel

This satisfies the multiplicity constraint for Drive, because the carEngine is linked to two Wheels (presuming leftRearWheel and rightRearWheel are different) and each carWheel is connected to at most one Engine.

Concern

While the semantic interpretation of the multiplicity of end features is different than that of non-end features, the same textual notation is used in both cases. This can be confusing, making it seem like, e.g., each instance of Drive has 0 or 1 driveEngine and 2 to 4 driveWheels, which would be the case for regular features but not for end features.

Proposal

Change the textual notation so that the multiplicity of an end feature is placed immediately after the end keyword, rather than in the usual place for a feature declaration. For example:

assoc Drive {
  end [0..1] feature driveEngine : Engine;
  end [2..4] feature driveWheel : Wheel;
}

This would not require a change in the abstract syntax.

Background

Consider the flowing simple structure:

struct Car {
  feature carEngine : Engine[1];
  feature carWheels : Wheel[4];
  
  connector carDrive : Drive
    from carEngine to carWheels;
}

The feature multiplicities in this model require that each instance of Car have exactly one Engine and exactly four Wheels. The model also includes a usage of the following association:

assoc Drive {
  end feature driveEngine : Engine[0..1];
  end feature driveWheel : Wheel[2..4];
} 

The Drive end multiplicities require that every Engine is connected to 2 to 4 Wheels, while every Wheel is connected to at most 1 Engine. But each instance of the association Drive is a link between a single engine and a single wheel. The multiplicities of the end features of Drive are thus interpreted differently than those of the features of Car (but consistently with how UML and SysML v1 interpret association end multiplicity). Rather than constraining the values of the end features themselves, the end multiplicities constrain the number of links allowed when the value at one end is held fixed: if a value is given for the driveEngine, then there must be two to four Drive links from that driveEngine to different Wheels; if a value is given for the driveWheel, then there must be zero or one instances between that driveWheel and an Engine.

For example, consider the following usage of Car that explicitly binds all the Car features:

feature myCar : Car {
  feature :>> carEngine = myEngine;
  feature :>> carWheels =
    (leftFrontWheel, rightFrontWheel, leftRearWheel, rightRearWheel);
  
  connector :>> carDrive =
    ( Drive(myEngine, leftRearWheel),
      Drive(myEngine, rightRearWheel)
    );
}

The connector ends of the connector carDrive inherit their end multiplicities from the ends of the association Drive. The above model explicitly binds the carDrive connector to two Drive values:

1. a connection from myEngine to leftRearWheel

2. a connection from myEngine to rightRearWheel

This satisfies the multiplicity constraint for Drive, because the carEngine is linked to two Wheels (presuming leftRearWheel and rightRearWheel are different) and each carWheel is connected to at most one Engine.

Concern

While the semantic interpretation of the multiplicity of end features is different than that of non-end features, the same textual notation is used in both cases. This can be confusing, making it seem like, e.g., each instance of Drive has 0 or 1 driveEngine and 2 to 4 driveWheels, which would be the case for regular features but not for end features.

Proposal

Change the textual notation so that the multiplicity of an end feature is placed immediately after the end keyword, rather than in the usual place for a feature declaration. For example:

assoc Drive {
  end [0..1] feature driveEngine : Engine;
  end [2..4] feature driveWheel : Wheel;
}

This would not require a change in the abstract syntax.

Clauses 8.4.4.6.2 (Binding Connectors) and 7.4.6.3 (Binding Connector Declaration) says they have end multiplicity 1..1 on both ends:

Binding connectors are binary connectors that require their source and target features to have the same values on each instance of their domain. They are typed by the library association SelfLink (which only links things in the modeled universe to themselves, see 9.2.3.1) and have end multiplicities of exactly 1. This requires a SelfLink to exist between each value of the source feature and exactly one value of the target feature, and vice-versa.

The connector ends of a binding connector always have multiplicity 1..1.

but there is no constraint for this on BindingConnector, which might be good because the libraries sometimes have optional mutiplicities, for example:

Occurrences:
  binding unionsOf.union[0..1] = self[1];
Transfers:
  private binding instant[0..1] of startShot[0..1] = endShot[0..1]
Control Performances:
  binding loopBack of untilDecision.elseClause[0..1] = whileDecision[1];

might be others.

SelfLink connectors with one optional end multiplicity are equivalent to feature subsetting (without the inheritance restrictions), rather than the typical meaning of "bind". Perhaps these should have a different textual keyword?

Clauses 8.4.4.6.2 (Binding Connectors) and 7.4.6.3 (Binding Connector Declaration) says they have end multiplicity 1..1 on both ends:

Binding connectors are binary connectors that require their source and target features to have the same values on each instance of their domain. They are typed by the library association SelfLink (which only links things in the modeled universe to themselves, see 9.2.3.1) and have end multiplicities of exactly 1. This requires a SelfLink to exist between each value of the source feature and exactly one value of the target feature, and vice-versa.

The connector ends of a binding connector always have multiplicity 1..1.

but there is no constraint for this on BindingConnector, which might be good because the libraries sometimes have optional mutiplicities, for example:

Occurrences:
  binding unionsOf.union[0..1] = self[1];
Transfers:
  private binding instant[0..1] of startShot[0..1] = endShot[0..1]
Control Performances:
  binding loopBack of untilDecision.elseClause[0..1] = whileDecision[1];

might be others.

SelfLink connectors with one optional end multiplicity are equivalent to feature subsetting (without the inheritance restrictions), rather than the typical meaning of "bind". Perhaps these should have a different textual keyword?

The specification and models carry over the terms "association end" and "participant" from SysML 1.x, leaving the meaning of "participant" as it was, but changing the meaning of "association end" to be same as "participant", and providing no term equivalent to SysML 1.x "association end" (see below). This shift makes KerML/SysML 2 associations difficult to understand and discuss among current SysMLers (judging from experience during the submission process), and probably those new to SysML as well.

The specification term "association end" refers to what SySML 1.x calls a "participant" property, a property of links (instances of associations) that each identify exactly one of the things being linked by each link. The library element Link has a feature named "participant", with exactly the same meaning as in SysML 1.x, that generalizes "association end" features, such as the source and target features of BinaryLink. The term "association end" in SysML 1.x refers to properties (typically) of associated classes that on each instance of one associated class identify (potentially zero or multiple) instances of the other associated class that are linked by the association. KerML can model these kind of features, but does not give a name for them.

Clauses 7.4.5 (Associations) and 9.2.3.1 (Links Overview) say

Associations are classifiers that classify links between things (see 9.2.3.1) At least two owned features of an association must be end features (see 7.3.4.2), its association ends, which identify the things being linked by (at the "ends" of) each link (exactly one thing per end, which might be the same thing).

The end features of an association determine the participants in the links that are instances of the association and, as such, effectively have multiplicity of "1" relative to the association.

The participant Feature of Link is the most general associationEnd, identifying the things being linked by (at the "ends" of) each Link (exactly one thing per end, which might be the same things).

where Association::associationEnds identify participant features.

The above use of "association end" in the specifiation is reflected in the textual syntax for assocations by the keyword "end" identifying these participant features. Clause 8.4.4.5.1 (Associations) says:

n-aries have this form:

uassoc A specializes Links::Link {
end feature e1 subsets Links::Link::participant;
end feature e2 subsets Links::Link::participant;
...
end feature eN subsets Links::Link::participant; }

The Link instance for an Association is thus a tuple of participants, where each participant is a single value of an associationEnd of the Association.

The quoted text above is only about the equivalent of SysML 1.x participant properties, but might seem to current SysMLers to be about something equivalent to SysML 1.x association ends.

Clause 9.2.9.1 (Control Performances Overview) says

Successions going out of Steps typed by DecisionPerformance or its specializations must:
• ...
• be included in a Feature of its featuringBehavior that unions (see 7.3.2.7) all the outgoing
Successions, and is bound to the outgoingHBLink of the Step (see 7.3.4.6 on feature chaining).

Successions coming into Steps typed by MergePerformance or its specializations must:
• ...
• subset a Feature of its featuringBehavior that unions all the incoming Successions, and is bound to the incomingHBLink of the Step.

but the Description sections of 9.2.9.2.1 (DecisionPerformance) and 9.2.9.2.7 (MergePerformance) say:

All such Successions must subset the outgoingHBLink feature of the source DecisionPerformance.

All such Successions must subset the incomingHBLink feature of the target MergePerformance.

respectively. These allow outgoing/incomingHBLink to have values that are not identified by outgoing/incoming successions when none of the successions is traversed. The pattern in the overview above introduces a feature unioning the successions and binds it to a chain through decision/merge to outgoing/incomingHBLink, ensuring the HB links are identified by the successions.

Clause 9.2.9.1 (Control Performances Overview) says

Successions going out of Steps typed by DecisionPerformance or its specializations must:
• ...
• be included in a Feature of its featuringBehavior that unions (see 7.3.2.7) all the outgoing
Successions, and is bound to the outgoingHBLink of the Step (see 7.3.4.6 on feature chaining).

Successions coming into Steps typed by MergePerformance or its specializations must:
• ...
• subset a Feature of its featuringBehavior that unions all the incoming Successions, and is bound to the incomingHBLink of the Step.

but the Description sections of 9.2.9.2.1 (DecisionPerformance) and 9.2.9.2.7 (MergePerformance) say:

All such Successions must subset the outgoingHBLink feature of the source DecisionPerformance.

All such Successions must subset the incomingHBLink feature of the target MergePerformance.

respectively. These allow outgoing/incomingHBLink to have values that are not identified by outgoing/incoming successions when none of the successions is traversed. The pattern in the overview above introduces a feature unioning the successions and binds it to a chain through decision/merge to outgoing/incomingHBLink, ensuring the HB links are identified by the successions.

Sufficient types are (Type::isSufficient=true) are described as

A type gives conditions for what things must be in or not in its extent (sufficient and necessary conditions, respectively).

... the type places additional sufficiency conditions on its instances corresponding to all the necessary conditions.

but this semantics is not math/modeled and the syntax cannot specify that only some necessary conditions are to correspond to sufficient ones.

Type unioning, intersecting, and differing are described as

Unioning, intersecting, and differencing are relationships between an owning type and a set of other types.
1. Unioning specifies that the owning type classifies everything that is classified by any of the unioned types.
2. Intersecting specifies that the owning type classifies everything that is classified by all of the intersecting types.
3. Differencing specifies that the owning type classifies everything that is classified by the first of the differenced types but not by any of the remaining types.

but this semantics is not math/modeled.

Sufficient types are (Type::isSufficient=true) are described as

A type gives conditions for what things must be in or not in its extent (sufficient and necessary conditions, respectively).

... the type places additional sufficiency conditions on its instances corresponding to all the necessary conditions.

but this semantics is not math/modeled and the syntax cannot specify that only some necessary conditions are to correspond to sufficient ones.

Type unioning, intersecting, and differing are described as

Unioning, intersecting, and differencing are relationships between an owning type and a set of other types.
1. Unioning specifies that the owning type classifies everything that is classified by any of the unioned types.
2. Intersecting specifies that the owning type classifies everything that is classified by all of the intersecting types.
3. Differencing specifies that the owning type classifies everything that is classified by the first of the differenced types but not by any of the remaining types.

but this semantics is not math/modeled.

Clause 8.4.4.7.2 (Steps, under Behavior Semantics) says

The checkStepSpecialization constraint requires that Steps specialize Performances::performances.

checkStepEnclosedPerformanceSpecialization and checkStepSubperformanceSpecialization constraints require that a Step whose owningType is a Behavior or another Step specialize Performances::Performance::enclosedPerformance or, if it is composite, Performances::Performance::subperformance.

checkStepOwnedPerformanceSpecialization constraint requires that a composite Step whose owningType is a Structure or a Feature typed by a Structure specialize Objects::Object::ownedPerformance.

where enclosedPerformances, subperformances, and ownedPerformances (in)directly subset timeEnclosedOccurrences, the values of which happen during the occurrences "having" the value.

The first constraint leaves open the possibility that steps might not happen during the occurrences they are steps of, bc Performances::performances is a step and subsets occurrences, rather than timeEnclosedOccurrences. This conflicts with the normal meaning of the term "step" (a terminology issue), which typically connotes (in library terms) performances that happen during the occurrences they are steps of.

The second constraint prevents the possibility above for steps owned by behaviors or other steps, while the third only prevents it for composite steps owned by structures.

The step keyword looks like it's sometimes used with other intentions than the constraints indicate. For example, in Observation.kerml:

behavior ObserveChange { ...
  step transfer : TransferBefore[1] ... {
    /* Then send changeSignal to changeObserver. */ ... } ... }

↑ Is it intended that observechange occurrences timeenclose the entire transfer (all the way to it's arrival at its target), as required by the second constraint?

struct ChangeMonitor { ...
  step startObservation { ... }
  step cancelObservation { ... }

↑ Is it intended that the values of start/CancelObservation can happen at other times than the ChangeMonitor occurrence referencing them, as allowed by the third constraint?

Transfers::
  step transfers: Transfer[0..*] nonunique subsets performances, binaryLinks { ... }
  step messageTransfers: MessageTransfer[0..*] nonunique subsets transfers { ... }
  step flowTransfers: FlowTransfer[0..*] nonunique subsets transfers { ... }
  step transfersBefore: TransferBefore[0..*] nonunique subsets transfers, happensBeforeLinks { ... }
  step flowTransfersBefore: FlowTransferBefore[0..*] nonunique subsets flowTransfers, transfersBefore { ... }

↑ These are features of (effectively) Anything, including structures and behaviors, so sometimes they'll be time enclosed and sometimes not. For example:

Occurrence::
  feature incomingTransfers: Transfers::Transfer[0..*] subsets Transfers::transfers { ... }
  feature outgoingTransfers: Transfers::Transfer[0..*] subsets Transfers::transfers { ... }

↑ will be time enclosed for transfers into/out of performances, but not objects, assuming the above are redefined as steps in behaviors or structures (or that features specialized from steps are also steps).

Clause 8.4.4.7.2 (Steps, under Behavior Semantics) says

The checkStepSpecialization constraint requires that Steps specialize Performances::performances.

checkStepEnclosedPerformanceSpecialization and checkStepSubperformanceSpecialization constraints require that a Step whose owningType is a Behavior or another Step specialize Performances::Performance::enclosedPerformance or, if it is composite, Performances::Performance::subperformance.

checkStepOwnedPerformanceSpecialization constraint requires that a composite Step whose owningType is a Structure or a Feature typed by a Structure specialize Objects::Object::ownedPerformance.

where enclosedPerformances, subperformances, and ownedPerformances (in)directly subset timeEnclosedOccurrences, the values of which happen during the occurrences "having" the value.

The first constraint leaves open the possibility that steps might not happen during the occurrences they are steps of, bc Performances::performances is a step and subsets occurrences, rather than timeEnclosedOccurrences. This conflicts with the normal meaning of the term "step" (a terminology issue), which typically connotes (in library terms) performances that happen during the occurrences they are steps of.

The second constraint prevents the possibility above for steps owned by behaviors or other steps, while the third only prevents it for composite steps owned by structures.

The step keyword looks like it's sometimes used with other intentions than the constraints indicate. For example, in Observation.kerml:

behavior ObserveChange { ...
  step transfer : TransferBefore[1] ... {
    /* Then send changeSignal to changeObserver. */ ... } ... }

↑ Is it intended that observechange occurrences timeenclose the entire transfer (all the way to it's arrival at its target), as required by the second constraint?

struct ChangeMonitor { ...
  step startObservation { ... }
  step cancelObservation { ... }

↑ Is it intended that the values of start/CancelObservation can happen at other times than the ChangeMonitor occurrence referencing them, as allowed by the third constraint?

Transfers::
  step transfers: Transfer[0..*] nonunique subsets performances, binaryLinks { ... }
  step messageTransfers: MessageTransfer[0..*] nonunique subsets transfers { ... }
  step flowTransfers: FlowTransfer[0..*] nonunique subsets transfers { ... }
  step transfersBefore: TransferBefore[0..*] nonunique subsets transfers, happensBeforeLinks { ... }
  step flowTransfersBefore: FlowTransferBefore[0..*] nonunique subsets flowTransfers, transfersBefore { ... }

↑ These are features of (effectively) Anything, including structures and behaviors, so sometimes they'll be time enclosed and sometimes not. For example:

Occurrence::
  feature incomingTransfers: Transfers::Transfer[0..*] subsets Transfers::transfers { ... }
  feature outgoingTransfers: Transfers::Transfer[0..*] subsets Transfers::transfers { ... }

↑ will be time enclosed for transfers into/out of performances, but not objects, assuming the above are redefined as steps in behaviors or structures (or that features specialized from steps are also steps).

Feature direction (Feature::direction:FeatureDirectionKind) is described as

in, out, inout: Specifies the direction of a feature, which determines what is allowed to change its values on instances of its domain:
-in: Things "outside" the instance. These features identify things input to an instance.
-out: The instance itself or things "inside" it. These features identify things output by an instance.
-inout: Both things "outside" and "inside" the instance. These features identify things that are both input to and output by an instance.

but this semantics is not math/modeled and depends on Kernel for instances changing over time.

Feature direction (Feature::direction:FeatureDirectionKind) is described as

in, out, inout: Specifies the direction of a feature, which determines what is allowed to change its values on instances of its domain:
-in: Things "outside" the instance. These features identify things input to an instance.
-out: The instance itself or things "inside" it. These features identify things output by an instance.
-inout: Both things "outside" and "inside" the instance. These features identify things that are both input to and output by an instance.

but this semantics is not math/modeled and depends on Kernel for instances changing over time.