QUDV http://www.omg.org/spec/SysML/20150709/QUDV A_conversionBasedUnit_referenceUnit conversionBasedUnit * A_derivedQuantityKind_factor derivedQuantityKind * A_derivedUnit_factor derivedUnit A_dimension_factor dimension * A_generalQuantityKind_specificQuantityKind specific * A_generalUnit_specificUnit specific * A_includedSystemOfQuantities_systemOfQuantities systemOfQuantities * A_includedSystemOfUnits_systemOfUnits systemOfUnits * A_noQuantityKind_prefixedUnit prefixedUnit A_prefixedUnit_prefix prefixedUnit * A_quantityKindFactor_quantityKind quantityKindFactor * A_quantityKind_measurementUnit measurementUnit * A_systemOfQuantities_baseQuantityKind systemOfQuantities * A_systemOfQuantities_dimension systemOfQuantities * A_systemOfQuantities_quantityKind systemOfQuantities * A_systemOfUnits_baseUnit systemOfUnits * A_systemOfUnits_prefix systemOfUnits * A_systemOfUnits_systemOfQuantities systemOfUnits * A_systemOfUnits_unit systemOfUnits * A_unitFactor_unit unitFactor * A_usedSystemOfQuantities_systemOfQuantities systemOfQuantities * A_usedSystemOfUnits_systemOfUnits systemOfUnits * AffineConversionUnit invertible isInvertible = true OCL2.0 factor offset ConversionBasedUnit true isInvertible referenceUnit dependsOnUnits true A ConversionBasedUnit transitively depends on its referenceUnit and all of the Units that its referenceUnit depends on. result * body referenceUnit.dependsOnUnits()->including(referenceUnit)->asSet() OCL2.0 DerivedQuantityKind factor * dependsOnQuantityKinds true A DerivedQuantityKind transitively depends on its factors' QuantityKinds and all of the QuantityKinds that its factors' QuantityKinds depend on. result * body factor.quantityKind.dependsOnQuantityKinds()->flatten()->asSet()->union(factor.quantityKind->flatten()->asSet())->asSet() OCL2.0 DerivedUnit mustSpecifyQuantityKind Since a DerivedUnit is defined as a product factor of one or more other Units, it must specify explicitly its QuantityKinds. quantityKind <> null and quantityKind->notEmpty() OCL2.0 factor * hasReducedFactors If true, the UnitFactors specifying the product of powers of other measurement units that define the DerivedUnit cannot be simplified. If false, the DerivedUnit is non-reduced; some UnitFactors can be simplified. A non-reduced DerivedUnit can have as a general unit other DerivedUnits defined in terms of simplified UnitFactors, possibly in reduced form. true dependsOnUnits true A DerivedUnit transitively depends on its factors' Units and all of the Units that its factors' Units depend on. result * body factor.unit.dependsOnUnits()->flatten()->asSet()->union(factor.unit->flatten()->asSet())->asSet() OCL2.0 Dimension factor true * symbolicExpression Symbolic expression of the quantity dimension's product of powers, in terms of symbols of the kinds of quantity that represent the base kinds of quantity and their exponents. In tool implementations, the symbolicExpression may automatically derived from the associated factor set. GeneralConversionUnit expression expressionLanguageURI LinearConversionUnit invertible isInvertible = true OCL2.0 factor Prefix factor symbol PrefixedUnit PU1 The referenceUnit shall not be a PrefixedUnit, i.e.,it is not allowed to prefix an already prefixed measurement unit. In general the referenceUnit should be a SimpleUnit. not referenceUnit.oclIsTypeOf(PrefixedUnit) OCL2.0 noQuantityKind prefix QuantityKind true acyclic_quantity_kind_dependencies A QuantityKind cannot be defined in terms of itself. This follows from the quantity calculus used for expressing a derived QuantityKind in terms of base QuantityKinds chosen for a SystemOfQuantities by means of non-contradictory equations (See ISO 80000-1, 4.3). dependsOnQuantityKinds->excludes(self) OCL2.0 dependsOnQuantityKinds true true The set of all QuantityKinds that this QuantityKind directly or indirectly depends on according to its definition. * general * isNumberOfEntities If true, indicates that the QuantityKind represents a number of entities (see ISO 80000-1, 3.8, Note 4). isQuantityOfDimensionOne If true, indicates that the QuantityKind has dimension one (see ISO 80000-1, 3.8). dependsOnQuantityKinds Abstract operation specified in SpecializedQuantityKind, SimpleQuantityKind and DerivedQuantityKind to calculate the value of the derived property QuantityKind:/dependsOnQuantityKinds. result * QuantityKindFactor exponent quantityKind SimpleQuantityKind dependsOnQuantityKinds true A SimpleQuantityKind does not depend on any other QuantityKind. result * body Set(QuantityKind){} OCL2.0 SimpleUnit dependsOnUnits true A SimpleUnit, by definition, does not depend on any other Unit. result * body Set(Unit){} OCL2.0 SystemOfQuantities acyclicProvenance For a QuantityKind to have a provenance to a single SystemOfQuantities, the use and includes relationships among SystemOfQuantities must be acyclic. allAccessibleSystemOfQuantities()->excludes(self) OCL2.0 allBaseQuantitiesAreQuantities The set of all QuantityKinds in a given SystemOfQuantities can be partitioned into two disjoint, covering subsets: the set of base QuantityKinds (typically chosen to be mutually independent) and all its complement, the set of derived QuantityKinds, each of which can be expressed in terms of the base QuantityKinds (See ISO 80000-1, 4.3). allQuantityKinds()->includesAll(allBaseQuantityKinds()) OCL2.0 includedSystemOfQuantities_transitivelyDisjoint_usedSystemOfQuantities For a QuantityKind to have a provenance to a single SystemOfQuantities, includedSystemsOfQuantities must be transitively disjoint with usedSystemsOfQuantities allIncludedSystemOfQuantities()->intersection(self.oclAsSet()->closure(usedSystemOfQuantities))->isEmpty() OCL2.0 singleProvenance Every QuantityKind must be defined in only one SystemOfQuantities but it can be in the scope of several SystemOfQuantities. A given QuantityKind is in scope of a SystemOfQuantities either because it is defined or used in a SystemOfQuantities or because it is included from the scope of another SystemOfQuantities. includedSystemOfQuantities->collect(allQuantityKinds())->intersection(quantityKind)->isEmpty() OCL2.0 baseQuantityKind true * definitionURI description dimension true false true true * includedSystemOfQuantities * quantityKind true * symbol usedSystemOfQuantities * allAccessibleQuantityKinds true The query accessibleQuantityKinds() gives all the QuantityKinds directly defined in the SystemOfQuantities or transitively in any included or used SystemOfQuantities. result * body allAccessibleSystemOfQuantities()->collect(quantityKind)->flatten()->asSet() OCL2.0 allAccessibleSystemOfQuantities true The query allAccessibleSystemOfQuantities() gives all the SystemOfQuantities directly or transitively included or used. result * body self->closure(includedSystemOfQuantities->union(usedSystemOfQuantities))->asSet() OCL2.0 allBaseQuantityKinds true The query allBaseQuantityKinds() gives all the QuantityKinds directly adopted or transitively adopted from any included SystemOfQuantities as base QuantityKinds. result * body allIncludedSystemOfQuantities()->collect(baseQuantityKind)->flatten()->asSet()->union(baseQuantityKind)->asSet() OCL2.0 allIncludedSystemOfQuantities true The query allIncludedSystemOfQuantities() gives all the SystemOfQuantities directly or transitively included. result * body self->closure(includedSystemOfQuantities)->asSet() OCL2.0 allQuantityKinds true The query allQuantityKinds() gives all the QuantityKinds in scope of a SystemOfQuantities; that is, each QuantityKind is either directly defined in the SystemOfQuantities, selectively used from another SystemOfQuantities or part of the scope of all the QuantityKinds included from another SystemOfQuantities. result * body allIncludedSystemOfQuantities()->collect(quantityKind)->flatten()->asSet()->union(quantityKind)->asSet() OCL2.0 getDimension qk result SystemOfUnits SoU3_1 In a well-formed SystemOfUnits, all of the prefixes of PrefixedUnits are defined in the SystemOfUnits. allPrefixes()->includesAll(allUnits()->select(oclIsTypeOf(PrefixedUnit))->collect(oclAsType(PrefixedUnit).prefix)) OCL2.0 SoU3_2 All the dependent Units of a SystemOfUnits must be in the scope of that SystemOfUnits. allUnits()->includesAll(allUnits()->collect(dependsOnUnits())->flatten()->asSet()) OCL2.0 SoU3_3 All of the quantityKinds that are measurementUnits of Units in the SystemOfUnits are defined in the systemOfQuantities of that SystemOfUnits. getEffectiveSystemOfQuantities() = null or let aqk : Set(QuantityKind) = getEffectiveSystemOfQuantities().allQuantityKinds() in allUnits()->forAll(u | aqk->includesAll(getKindOfQuantitiesForMeasurementUnit(u))) OCL2.0 acyclicProvenance For a Unit to have a provenance to a single SystemOfUnits, the use and includes relationships among SystemOfUnits must be acyclic. allAccessibleSystemOfUnits()->excludes(self) OCL2.0 allBaseUnitsAreUnits The set of all Units in a given SystemOfUnits can be partitioned into two disjoint, covering subsets: the set of base Units (typically chosen to be mutually independent) and all its complement, the set of derived Units, each of which can be expressed in terms of the base Units (See ISO 80000-1, 6.4). allUnits()->includesAll(allBaseUnits()) OCL2.0 includedSystemOfUnits_transitivelyDisjoint_usedSystemOfUnits For a Unit to have a provenance to a single SystemOfUnits, all included systems of units must be transitively disjoint with all used systems of units. allIncludedSystemOfUnits()->intersection(self.oclAsSet()->closure(usedSystemOfUnits))->isEmpty() OCL2.0 singleProvenance Every Unit must be defined in only one SystemOfUnits but it can be in the scope of several SystemOfUnits. A given Unit is in scope of a SystemOfUnits either because it is defined or used in a SystemOfUnits or because it is included from the scope of another SystemOfUnits. includedSystemOfUnits->collect(allUnits())->intersection(unit)->isEmpty() OCL2.0 systemOfQuantitiesIncludesAllUnitsQuantityKinds For a Unit to have a provenance to a single SystemOfUnits, includedSystemsOfUnits must be transitively disjoint with usedSystemsOfUnits. let aqks : Set(QuantityKind) = getEffectiveSystemOfQuantities().allQuantityKinds() in allUnits()->forAll(u | getKindOfQuantitiesForMeasurementUnit(u)->intersection(aqks)->notEmpty()) OCL2.0 baseUnit true * definitionURI description includedSystemOfUnits * prefix true * symbol systemOfQuantities unit true * usedSystemOfUnits * allAccessibleSystemOfUnits true The query allAccessibleSystemOfUnits() gives all the SystemOfUnits directly or transitively included or used. result * body self->closure(includedSystemOfUnits->union(usedSystemOfUnits))->asSet() OCL2.0 allAccessibleUnits true The query accessibleUnits() gives all the Units directly defined in a SystemOfUnits or transitively in any included or used SystemOfUnits. result * body allAccessibleSystemOfUnits()->collect(unit)->flatten()->asSet() OCL2.0 allBaseQuantityKinds true The query allBaseQuantityKinds() gives all the QuantityKinds directly adopted or transitively adopted from any included SystemOfQuantities as base QuantityKinds in the effective SystemOfQuantities associated to a SystemOfUnits. result * result getEffectiveSystemOfQuantities().allBaseQuantityKinds()->flatten()->asSet() OCL2.0 allBaseUnits true The query allBaseUnits() gives all the Units directly adopted or transitively adopted from any included SystemOfUnits as base Units. result * body allIncludedSystemOfUnits()->collect(baseUnit)->flatten()->asSet()->union(baseUnit)->asSet() OCL2.0 allIncludedSystemOfUnits true The query allIncludedSystemOfUnits() gives all the SystemOfUnits directly or transitively included. result * body self->closure(includedSystemOfUnits->union(usedSystemOfUnits))->asSet() OCL2.0 allMeasurementUnitsDefinedForSomeQuantityKind true The predicate allMeasurementUnitsDefinedForSomeQuantityKind() determines whether, in a SystemOfUnits, every Unit must be defined, by convention, as a multiplicable reference for at least one QuantityKind (see ISO 80000-1, 3.9). result body allUnits()->forAll(quantityKind <> null) OCL2.0 allPrefixes true The query allPrefixes() gives all the Prefixes in scope of a SystemOfUnits; that is, each Prefix is either directly defined in the SystemOfUnits or in any accessible SystemOfUnits. result * body allAccessibleSystemOfUnits()->including(self)->collect(prefix)->flatten()->asSet() OCL2.0 allUnits true The query allUnits() gives all the Units in scope of a SystemOfUnits; that is, each Unit is either directly defined in the SystemOfUnits, selectively used from another SystemOfUnits or part of the scope of all the Units included from another SystemOfUnits. result * body allIncludedSystemOfUnits()->collect(unit)->flatten()->asSet()->union(unit)->asSet() OCL2.0 getAdoptedBaseUnitForMeasurementUnit true The query getAdoptedBaseUnitForMeasurementUnit() determines for a Unit u in scope of a SystemOfUnits the base Unit, if any, corresponding to u, which can be u itself if it is a baseUnit in that SystemOfUnits or its reference Unit if it is a base Unit and u is a PrefixUnit. result u body let abu : Set(Unit) = allBaseUnits() in if (abu->includes(u)) then u else if (u.oclIsKindOf(PrefixedUnit)) then abu->intersection(u.oclAsType(PrefixedUnit).referenceUnit->asSet())->any(true) else null endif endif OCL2.0 getAdoptedQuantityKindForAdoptedBaseUnitOfMeasurementUnit true The query getAdoptedQuantityKindForAdoptedBaseUnitOfMeasurementUnit() determines for a Unit u in scope of a SystemOfUnits the base QuantityKind, if any, corresponding to the base Unit of u. result * u body let bu : Unit = getAdoptedBaseUnitForMeasurementUnit(u) in if (bu = null) then Set{} else let qks : Set(QuantityKind) = getKindOfQuantitiesForMeasurementUnit(bu) in allBaseQuantityKinds()->intersection(qks) endif OCL2.0 knownPrimaryQuantityKind getEffectiveSystemOfQuantities().allBaseQuantityKinds()->includesAll(result) OCL2.0 baseUnitParameter allBaseUnits()->includes(u) OCL2.0 getEffectiveSystemOfQuantities true The query getEffectiveSystemOfQuantities() determines for a SystemOfUnits the SystemOfQuantities, if any, that it is directly or indirectly associated with via included SystemOfUnits. result body if systemOfQuantities = null then includedSystemOfUnits->collect(getEffectiveSystemOfQuantities())->flatten()->asSet()->any(true) else systemOfQuantities endif OCL2.0 atMostOneSystemOfQuantities systemOfQuantities = null implies includedSystemOfUnits->collect(getEffectiveSystemOfQuantities())->asSet()->size() <= 1 OCL2.0 getKindOfQuantitiesForMeasurementUnit true The query getKindOfQuantitiesForMeasurementUnit() determines for a Unit u in scope of a SystemOfUnits the set of QuantityKinds corresponding to u, if specified, or to the Units that u is defined in terms of, if any. result * u body if (u.oclIsKindOf(SimpleUnit)) then u.quantityKind->collect(oclAsType(QuantityKind))->asSet() else if (u.oclIsKindOf(DerivedUnit)) then let du : DerivedUnit = u.oclAsType(DerivedUnit) in if (du.quantityKind <> null) then du.quantityKind->collect(oclAsType(QuantityKind))->asSet() else getKindOfQuantitiesForMeasurementUnit(du.factor->any(true).unit) endif else if (u.oclIsKindOf(ConversionBasedUnit)) then let cu : ConversionBasedUnit = u.oclAsType(ConversionBasedUnit) in if (cu.oclIsKindOf(PrefixedUnit)) then getKindOfQuantitiesForMeasurementUnit(cu.referenceUnit) else if (cu.quantityKind <> null) then cu.quantityKind->collect(oclAsType(QuantityKind))->asSet() else getKindOfQuantitiesForMeasurementUnit(cu.referenceUnit) endif endif else Set(QuantityKind){} endif endif endif OCL2.0 getUnit name result body allUnits()->select(u | u.name = name)->any(true) OCL2.0 isCoherent result isCoherent du result Unit true acyclic_unit_dependencies A Unit cannot be defined in terms of itself. This follows from the requirement that, in a coherent SystemOfUnits, the Units of all derived QuantityKinds are expressed in terms of the base Units in accordance with the equations in the SystemOfQuantities (see ISO 80000-1, 6.4). dependsOnUnits->excludes(self) OCL2.0 dependsOnUnits true true The set of all Units that this Unit directly or indirectly depends on according to its definition. * general * isUnitCountOfEntities If true, indicates that the measurement unit represents a number of entities (see ISO 80000-1, 3.10, Note 3). isUnitForQuantityOfDimensionOne If true, indicates that the corresponding QuantityKind has dimension one (see ISO 80000-1, 3.8). quantityKind * dependsOnUnits Abstract operation specified in ConversionBasedUnit, SimpleUnit and DerivedUnit to calculate the value of the derived property Unit:/dependsOnUnits. result * UnitFactor exponent unit Rational denominator numerator equivalent r result plus r result times r result