Reference Manual — FIRST PUBLIC DRAFT July 16 , 2003

Syntax CASL/Summary A The abstract syntax is central to the definition of a formal language. It stands between the concrete representations of documents, such as marks on paper or images on screens, and the abstract entities, semantic relations, and semantic functions used for defining their meaning. The abstract syntax has the following objectives: • to identify and separately name the abstract syntactic entities; • to simplify and unify underlying concepts, putting like things with like, and reducing unnecessary duplication. There are many possible ways of constructing an abstract syntax, and the choice of form is a matter of judgment, taking into account the somewhat conflicting aims of simplicity and economy of semantic definition. The abstract syntax is presented as a set of production rules in which each kind of entity is defined in terms of its sub-kinds: SOME-KIND ::= SUB-KIND-1 | ... | SUB-KIND-n or in terms of its constructor and components: SOME-CONSTRUCT ::= some-construct COMPONENT-1 ... COMPONENT-n The productions form a context-free grammar; algebraically, the nonterminal symbols of the grammar correspond to sorts (of trees), and the terminal symbols correspond to constructor operations. The notation COMPONENT* indicates repetition of COMPONENT any number of times; COMPONENT+ indicates repetition at least once. These repetitions can be replaced by auxiliary sorts and constructs, after which it is straightforward to transform the grammar into a Casl library of specifications using datatype declarations, see Part VI. This needs to be done. The context conditions for well-formedness of specifications are contextsensitive, and considered as part of semantics, see Part III. Many constructs can have comments and annotations attached to them (see Sect. 3.2), but these are not shown in the grammar. Maybe the optional annotations should be shown here? 112 II:5 Abstract Syntax