Ad/2010-08-01 Concrete Syntax for a uml action Language for Foundational uml (Alf) Second Revised Submission

6.2Templates

However, templates are particularly useful for modeling parameterized types, and they are, in fact, used in this way in the CollectionClasses model in the Alf Standard Model Library (see Subclause 11.6). But Alf text that uses types that are instantiations of such templates still needs to be mapped to fUML in order to provide its formal semantics. This requires a way to define the semantics of template binding in terms of constructs available in the fUML subset.

According to the UML Superstructure specification (Subclause 17.5.2 TemplateableElement, under Semantics), “The semantics of a [template] binding relationship is equivalent to the model elements that would result from copying the contents of the template into the bound element, replacing any elements exposed as a template parameter with the corresponding element(s) specified as actual parameters in this binding.” This section also states that “In a canonical model a bound element does not explicitly contain the model elements implied by expanding the templates it binds to, since those expansions are regarded as derived.” However, by actually carrying out the expansion, one can obtain an equivalent model that does not explicitly refer to the original template or the binding of its parameters. (This is analogous to the way other forms of derivation in the UML abstract syntax model are handled in fUML—see fUML Specification, Subclause 8.1.)

In order to make the explicit copy semantics of template binding more precise, an equivalent bound element may be constructed for any element with a template binding by the following steps.

1. 
   Copy the template associated with the template signature that is the target of the template binding. For the present purposes, a copy of a model element is an instance of the same metaclass as the original model element that has the same values as the original element for all non-composite properties (owned attributes and association ends) and copies (in the same sense) of the values from the original element for all composite properties.
   
2. 
   If the copy specializes any elements that are templates, then redirect the generalization relationships to equivalent bound elements for the general elements, using the same template binding. If the copy is an operation that has an associated method that is also a template, then replace that method with an equivalent bound element using the same template binding.
   

3. 
   For each element owned directly or indirectly by the copy, replace any reference to the parametered element of a template parameter of the copy with a reference to the actual element associated with the parameter in the template binding (if any). If an actual element has a template binding itself, then reference the equivalent bound element.
   
4. 
   Remove all template parameters that are referenced in the template binding from the template signature of the copy. If this would remove all template parameters from the template signature, then remove the template signature entirely.
   

• 
  The binding must specify an actual element for every template parameter of the template.
  
• 
  The element being bound must not have template parameters of its own.
  

For example, a set of integers may be notated in Alf as Set, using the standard template collection class Set and the standard primitive type Integer. If each occurrence in a model of the Alf text “Set” resulted in a different equivalent bound element, then an object created using one such occurrence would not be type compatible with, say, a formal parameter of an operation whose type is given by another such occurrence. Clearly this is not desirable.

Therefore, the template bindings within a model must be replaced as a whole using the following steps.

1. 
   Partition the set of all elements with template bindings in the model into disjoint subsets of elements with identical bindings. Two template bindings are considered identical if they have the same set of parameter substitutions. Two parameter substitutions are considered to be the same if they reference the same formal parameter and actual element.
   

2. 
   For each subset, create a single equivalent bound element (as defined above), starting with any one member of the subset.
   
3. 
   Replace any reference to any element in the model with a template binding with a reference to the equivalent bound element for its subset.
   

1. 
   Take the fully qualified name of each actual element in the template binding and replace all “::” separators with “$” characters. If the actual element is itself a template binding, then use the name of the equivalent bound element.
   
2. 
   Concatenate the modified names, separated by “_” (one underscore), and prepended and postpended with “__” (two underscores).
   
3. 
   Concatenate “$$”, the name of the target template of the template binding and the argument name list from 2 to produce the standard name of the equivalent bound element.