Circular expressions: elimination of static environments

Consider the connection between denotational semantics for a language with goto statements and flow diagrams for programs in such a language. The main point of interest is that the denotational semantics uses a recursively defined environment to give the meaning of labels, while a flow diagram merely has a jump to the appropriate program point. A simple reduction called “indirection elimination” strips away the environment from the denotational semantics and extracts an expression with cycles that is very close to the flow diagram of a program. The same idea applies to associating bodies with recursive procedures, or to any construct whose semantics is not wedded to the syntax. In addition to being a useful data structure and conceptual device, expressions with cycles are well defined mathematical objects—their semantics can be given by unfolding them into infinite structures that have been well studied. The practicality of the elimination of environments has been tested by constructing a trial implementation, which serves as the front end of a semantics directed compiler generator. The implementation takes a denotational semantics of a language and constructs a “black box” that maps programs in the language into an intermediate representation. The intermediate representation is a circular expression.