5 Module interpreted model

5.1 Mapping specification

• Components_of_scale
• Derivation_from_coordinate_system
• Derivation_from_uniaxial_scale
• Element_of_scale
• Scale
• Scale_encoding
• Scale_element
• Unit_of_measure

5.2 MIM EXPRESS short listing

*)
SCHEMA property_identification_mim;
  USE FROM external_reference_schema -- ISO 10303-41
    (externally_defined_item);
  USE FROM independent_property_definition_mim -- ISO 10303-1036
    (independent_property_definition);
  USE FROM property_space_mim -- ISO 10303-1080
    (property_space);
  USE FROM mathematical_identification_schema -- ISO 10303-5x
    (compound_maths_space_context,
    maths_space_context,
    maths_value_context,
    representation_context_defined_maths_space_context,
    unit_defined_maths_space_context);
  USE FROM distribution_mapping_schema -- ISO 10303-5x
    (maths_space_context_relationship;
(*

5.2.1 MIM EXPRESS types

None.

5.2.2 MIM EXPRESS entities

5.2.2.1 classification_of_scale_by_encoding

A classification_of_scale_by_encoding is a maths_space_context_relationship that indicates the encoding for a scale.

EXPRESS specification:

*)
ENTITY classification_of_scale_by_encoding
  SUBTYPE OF (maths_space_context_relationship);
  SELF\maths_space_context_relationship.related_context  :  scale;
  SELF\maths_space_context_relationship.relating_context  :  scale;
UNIQUE
  single_encoding_for_scale  :  
    SELF\maths_space_context_relationship.related_context ;
  END_ENTITY;
(*

Formal propositions:

single_encoding_for_scale: There shall not be more than one instance of classification_of_scale_by_encoding classifying a scale_context.

5.2.2.2 derivation_from_coordinate_system

A derivation_from_coordinate_system is a maths_space_context_relationship that is a Derivation_from_coordinate_system.

EXAMPLE - The relationship between the property_space 'my positions' and the maths_space 'real 3-tuple' is a scale that defines a coordinate system.

The relationship between the property_space 'stress tensor' and the maths_space 'real symmetric 3´3 matrices' with units of MPa is a tensor scale.

The relationship between the position scale and the tensor scale, that indicates the coordinate system for the tensor scale is derived from the position scale, is a derivation_from_coordinate_system.

EXPRESS specification:

*)
ENTITY derivation_from_coordinate_system
  SUBTYPE OF (maths_space_context_relationship);
  SELF\maths_space_context_relationship.related_context  :  scale;
  SELF\maths_space_context_relationship.relating_context  :  
    representation_context_defined_maths_space_context;
END_ENTITY;
(*

5.2.2.3 derivation_from_uniaxial_scale

A derivation_from_uniaxial_scale is a maths_space_context_relationship that is a Derivation_from_uniaxial_scale.

EXAMPLE - The relationship between the property_space 'uniaxial stress' and the maths_space 'the reals' with units of MPa is a uniaxial scale derived from a unit of measure.

The relationship between the property_space 'stress tensor' and the maths_space 'real symmetric 3´3 matrices' with units of MPa is a tensor scale.

The relationship between the uniaxial scale and the tensor scale, that indicates the units for the tensor scale are derived from the uniaxial scale, is a derivation_from_uniaxial_scale.

EXPRESS specification:

*)
ENTITY derivation_from_uniaxial_scale
  SUBTYPE OF (maths_space_context_relationship);
  SELF\maths_space_context_relationship.related_context  :  scale;
  SELF\maths_space_context_relationship.relating_context  :  unit_defined_maths_space_context;
END_ENTITY;
(*

5.2.2.4 derived_scale

A derived_scale_context is a scale and a compound_maths_space_context that is defined by a list of other instances of scale.

EXPRESS specification:

*)
ENTITY derived_scale
  SUBTYPE OF (compound_maths_space_context,
  scale);
  SELF\compound_maths_space_context.components  :  
      LIST [2,?] OF scale;
END_ENTITY;
(*

5.2.2.5 scale

A scale is a maths_space_context that is a Scale.

EXPRESS specification:

*)
ENTITY scale;
  SUBTYPE OF (maths_space_context);
  SELF\maths_space_context.physical_space  :  property_space;
END_ENTITY;
(*

5.2.2.6 scale_element

A scale_element is a maths_value_context that is a Scale_element.

EXPRESS specification:

*)
ENTITY scale_element;
  SUBTYPE OF (maths_value_context);

  SELF\maths_value_context.physical_value  :  
      independent_property_definition;
END_ENTITY;
(*

5.2.2.7 scale_encoding

A scale_encoding is a maths_space_context and an externally_defined_itemthat is a Scale_encoding.

EXPRESS specification:

*)
ENTITY scale_encoding
  SUBTYPE OF (maths_space_context,
  externally_defined_item);
UNIQUE
  single_instance_of_class  :  
    SELF\externally_defined_item.source, SELF\externally_defined_item.item_id;
WHERE
  valid_standard_class :
    IF (SELF\externally_defined_item.source = 'ISO/PDTS 10303-1085') THEN
        SELF\externally_defined_item.item_id IN 
          ['SE001', 'SE002', 'SE003', 'SE004', 'SE005', 'SE006',
           'SE007', 'SE008', 'SE009', 'SE010', 'SE011', 'SE012', 'SE013'];
    ELSE
      TRUE;
    END_IF;
END_ENTITY;
(*

Formal propositions:

single_instance_of_class: There shall not be more than one instance of scale_encoding with the same meaning.

valid_standard_class: Each instance of scale_encoding, that is reference data defined by this part of ISO 10303, shall make reference to a standard instance of Scale_encoding.

*)
END_SCHEMA;
(*