ISO/TS 10303-1210:2004 Set theory


Application module: Set theory	ISO/TS 10303-1210:2004(E) © ISO

Cover page
Table of contents
Copyright
Foreword
Introduction
1 Scope
2 Normative references
3 Terms, definitions and abbreviations

4 Information requirements
4.1 Required AM ARM
4.2 ARM entity definitions
5 Module interpreted model
5.1 Mapping specification
5.2 MIM EXPRESS short listing

A MIM short names
B Information object registration
C ARM EXPRESS-G
D MIM EXPRESS-G
E Computer interpretable listings
Bibliography
Index

5.1 Mapping specification

In the following, "Application element" designates any entity data type defined in Clause 4, any of its explicit attributes and any subtype constraint. "MIM element" designates any entity data type defined in Clause 5.2 or imported with a USE FROM statement, from another EXPRESS schema, any of its attributes and any subtype constraint defined in Clause 5.2 or imported with a USE FROM statement.

This clause contains the mapping specification that defines how each application element of this part of ISO 10303 (see Clause 4) maps to one or more MIM elements (see Clause 5.2).

The mapping for each application element is specified in a separate subclause below. The mapping specification of an attribute of an ARM entity is a subclause of the clause that contains the mapping specification of this entity. Each mapping specification subclause contains up to five elements.

Title: The clause title contains:

the name of the considered ARM entity or subtype constraint, or
the name of the considered ARM entity atribute when this attribute refers to a type that is not an entity data type or a SELECT type that contains or may contain entity data types, or
a composite expression, <attribute name> to <referred type>, when this attribute refers to a type that is not an entity data type or a SELECT type that contains or may contain entity data types.

MIM element: This section contains, depending on the considered application element:

the name of one or more MIM entity data types;
the name of a MIM entity attribute, presented with the syntax <entity name>.<attribute name>, when the considered ARM attribute refers to a type that is not an entity data type or a SELECT type that contains or may contain entity data types;
the term PATH, when the considered ARM entity attribute refers to an entity data type or to a SELECT type that contains or may contain entity data types;
the term IDENTICAL MAPPING, when both application objects involved in an application assertion map to the same instance of a MIM entity data type;
the syntax /SUPERTYPE(<supertype name>)/, when the considered ARM entity is mapped as its supertype;
one or more constructs /SUBTYPE(<subtype name>)/, when the mapping of the considered ARM entity is the union of the mapping of its subtypes.

When the mapping of an application element involves more than one MIM element, each of these MIM elements is presented on a separate line in the mapping specification, enclosed between parentheses or brackets.

Source: This section contains:

the ISO standard number and part number in which the MIM element is defined, for those MIM elements that are defined in a common resource document;
the ISO standard number and part number of this part of ISO 10303, for those MIM elements that are defined in the MIM schema of this part.

This section is omitted when the keywords PATH or IDENTICAL MAPPING are used in the MIM element section.

Rules: This section contains the name of one or more global rules that apply to the population of the MIM entity data types listed in the MIM element section or in the reference path. When no rule applies, this section is omitted.

A reference to a global rule may be followed by a reference to the subclause in which the rule is defined.

Constraint: This section contains the name of one or more subtype constraints that apply to the population of the MIM entity data types listed in the MIM element section or in the reference path. When no subtype constraint applies, this section is omitted.

A reference to a subtype constraint may be followed by a reference to the subclause in which the subtype constraint is defined.

Reference path: This section contains:

the reference path to its supertypes in the common resources, for each MIM element created within this part of ISO 10303;
the specification of the relationships between MIM elements, when the mapping of an application element requires to relate instances of several MIM entity data types. In such a case, each line in the reference path documents the role of a MIM element relative to the referring MIM element or to the next referred MIM element.

For the expression of reference paths and of the constraints between MIM elements, the following notational conventions apply:

[]	enclosed section constrains multiple MIM elements or sections of the reference path are required to satisfy an information requirement;
()	enclosed section constrains multiple MIM elements or sections of the reference path are identified as alternatives within the mapping to satisfy an information requirement;
{}	enclosed section constrains the reference path to satisfy an information requirement;
<>	enclosed section constrains at one or more required reference path;
\|\|	enclosed section constrains the supertype entity;
->	the attribute, whose name precedes the -> symbol, references the entity or select type whose name follows the -> symbol;
<-	the entity or select type, whose name precedes the <- symbol, is referenced by the entity attribute whose name follows the <- symbol;
[i]	the attribute, whose name precedes the [i] symbol, is an aggregate; any element of that aggregate is referred to;
[n]	the attribute, whose name precedes the [n] symbol, is an ordered aggregate; member n of that aggregate is referred to;
=>	the entity, whose name precedes the => symbol, is a supertype of the entity whose name follows the => symbol;
<=	the entity, whose name precedes the <= symbol, is a subtype of the entity whose name follows the <= symbol;
=	the string, select, or enumeration type is constrained to a choice or value;
\	the reference path expression continues on the next line;
*	one or more instances of the relationship entity data type may be assembled in a relationship tree structure. The path between the relationship entity and the related entities, is enclosed with braces;
--	the text following is a comment or introduces a clause reference;
*>	the select or enumeration type, whose name precedes the > symbol, is extended into the select or enumeration type whose name follows the > symbol;
<*	the select or enumeration type, whose name precedes the <* symbol, is an extension of the select or enumeration type whose name follows the <* symbol.

The definition and use of mapping templates is not supported in the present version of the application modules. However, use of predefined templates /SUBTYPE/ and /SUPERTYPE/ is supported.

5.1.1 Complement

MIM element:	complement
Source:	ISO 10303-54

5.1.1.1 id

MIM element:	complement.id
Source:	ISO 10303-54

5.1.1.2 name

MIM element:	complement.name
Source:	ISO 10303-54

5.1.1.3 description

MIM element:	complement.description
Source:	ISO 10303-54

5.1.1.4 Complement to Class (as set_1)

MIM element:	PATH
Reference path:	complement complement.set_1 -> class

5.1.1.5 Complement to Class (as set_2)

MIM element:	PATH
Reference path:	complement complement.set_2 -> class

5.1.1.6 Complement to Class (as universe)

MIM element:	PATH
Reference path:	complement complement.universe -> class

5.1.2 Intersection

MIM element:	intersection
Source:	ISO 10303-54

5.1.2.1 id

MIM element:	intersection.id
Source:	ISO 10303-54

5.1.2.2 name

MIM element:	intersection.name
Source:	ISO 10303-54

5.1.2.3 description

MIM element:	intersection.description
Source:	ISO 10303-54

5.1.2.4 Intersection to Class (as operand)

MIM element:	PATH
Reference path:	intersection intersection.operand -> class

5.1.2.5 Intersection to Class (as resultant)

MIM element:	PATH
Reference path:	intersection intersection.resultant -> class

5.1.3 Power_set

MIM element:	power_set
Source:	ISO 10303-54

5.1.3.1 id

MIM element:	power_set.id
Source:	ISO 10303-54

5.1.3.2 name

MIM element:	power_set.name
Source:	ISO 10303-54

5.1.3.3 description

MIM element:	power_set.description
Source:	ISO 10303-54

5.1.3.4 Power_set to Class (as base)

MIM element:	PATH
Reference path:	power_set power_set.base -> class

5.1.3.5 Power_set to Class (as derived)

MIM element:	PATH
Reference path:	power_set power_set.derived -> class

5.1.4 Proper_subset

MIM element:	proper_subset
Source:	ISO 10303-54

5.1.4.1 id

MIM element:	subset.id
Source:	ISO 10303-54
Reference path:	proper_subset <= subset

5.1.4.2 name

MIM element:	subset.name
Source:	ISO 10303-54
Reference path:	proper_subset <= subset

5.1.4.3 description

MIM element:	subset.description
Source:	ISO 10303-54
Reference path:	proper_subset <= subset

5.1.4.4 Proper_subset to Class (as subset)

MIM element:	PATH
Reference path:	proper_subset proper_subset <= subset subset.subset -> class

5.1.4.5 Proper_subset to Class (as superset)

MIM element:	PATH
Reference path:	proper_subset proper_subset <= subset subset.superset -> class

5.1.5 Same_membership

MIM element:	same_membership
Source:	ISO 10303-54

5.1.5.1 id

MIM element:	same_membership.id
Source:	ISO 10303-54

5.1.5.2 name

MIM element:	same_membership.name
Source:	ISO 10303-54

5.1.5.3 description

MIM element:	same_membership.description
Source:	ISO 10303-54

5.1.5.4 Same_membership to Class (as set_1)

MIM element:	PATH
Reference path:	same_membership same_membership.set_1 -> class

5.1.5.5 Same_membership to Class (as set_2)

MIM element:	PATH
Reference path:	same_membership same_membership.set_2 -> class

5.1.6 Subset

MIM element:	subset
Source:	ISO 10303-54

5.1.6.1 id

MIM element:	subset.id
Source:	ISO 10303-54

5.1.6.2 name

MIM element:	subset.name
Source:	ISO 10303-54

5.1.6.3 description

MIM element:	subset.description
Source:	ISO 10303-54

5.1.6.4 Subset to Class (as subset)

MIM element:	PATH
Reference path:	subset subset.subset -> class

5.1.6.5 Subset to Class (as superset)

MIM element:	PATH
Reference path:	subset subset.superset -> class

5.1.7 Union

MIM element:	union
Source:	ISO 10303-54

5.1.7.1 id

MIM element:	union.id
Source:	ISO 10303-54

5.1.7.2 name

MIM element:	union.name
Source:	ISO 10303-54

5.1.7.3 description

MIM element:	union.description
Source:	ISO 10303-54

5.1.7.4 Union to Class (as operand)

MIM element:	PATH
Reference path:	union union.operand -> class

5.1.7.5 Union to Class (as resultant)

MIM element:	PATH
Reference path:	union union.resultant -> class