Circular expressions: Elimination of static environments

Abstract

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 (circular expression) 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. Circular expressions are offered as 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.