Legacy Issue Number: 15987
Source: Model Driven Solutions ( Ed Seidewitz)
Specification: Semantics of a Foundational Subset for Executable UML Models, FTF Beta 3 (ptc/10-03-14)
UML 2.4 has introduced a new Real primitive type. This should be supported by a new package of primitive functions in the fUML Foundational Model Library.
Reported: FUML 1.0 — Wed, 26 Jan 2011 05:00 GMT
Disposition: Resolved — FUML 1.1
The UML 2.4.1 Infrastructure specification states that “A real is a primitive type representing the mathematical concept of real” and that “An instance of Real is an element in the infinite set of real numbers.” However, some care needs to be taken in defining the fUML execution semantics of the Real type and supporting primitive functions, so that it is possible for a real implementation to conform to those semantics.
The UML specification also says that “An instance of Integer is an element in the (infinite) set of integers ”. And the base semantics for buml:Integer in Subclause 10.3.1.2 of the fUML 1.0 specification does, indeed, include the mathematical axioms necessary to define this infinite set. However, Subclause 9.1 includes the permission that “ a conforming implementation may limit the supported values [of Integer] to a finite set.”
Similarly, fUML should allow conforming implementations to limit the supported values of Real to a finite set. However, for Real numbers, this means more than just limiting the upper and lower bounds of the supported range of Real numbers. It also means dealing with the fact that Real numbers can only be represented to finite precision in an actual implementation.
Generally, programming languages provide floating-point representations that approximate Real numbers. However, this is an implementation representation, and the most commonly used standard reference on floating-point numbers, IEEE 754, is a standard for the implementation of floating-point computation.
For fUML, it is necessary to provide a precise semantic specification for Real numbers that is implementation independent but that provides clear criteria for the conformance of actual implementations. This should allow implementations based on a floating-point standard such as IEEE 754 but also allow implementations using, e.g., fixed-point computation or exact rational number computation.
This can be achieved in three steps.
1. Axioms for the Real type need to be added to the fUML base semantics in Clause 10.
2. Criteria are needed in Clause 9 for conformance to the Real type as it is to be provided in the fUML Foundational Model Library. The set of Real numbers includes values that cannot be represented in finite precision (e.g., irrational numbers and those rational numbers with infinite repeating digit representations in the base being used). So, some permission is needed to allow for the conformance of implementations using, e.g., finite-precision floating-point representations. In addition, IEEE 754 requires some additional special values be represented in the floating-point formats it defines. Since it is expected that it will be common that the fUML Real type will be implemented using a floating-point representation based on IEEE 754, it is necessary to allow for the inclusion of such values in an implementation of Real.
3. Criteria are needed in Clause 9 for conformance to the semantics of the primitive functions for Real to be provided in the Foundational Model Library. The specification of the primitive functions for Real in the Foundational Model Library will define the exact real number result of applying those functions. It is then necessary to define how these exact results may be represented in a conforming implementation that takes advantage of some or all of the permissions allowed relative to the representation of Real numbers.
This resolution also presumes the resolution of Issue 15986, “fUML 1.1 should be based on UML 2.4”. For simplicity, all revisions related to the new Real type have been included here. This includes changes to Clause 7 Abstract Syntax, Clause 8 Execution Model and Annex A Java to UML Activity Mapping, as well as the changes to Clauses 9 and 10 discussed above.
Updated: Fri, 6 Mar 2015 20:58 GMT