Algebraic denotational semantics using parameterized abstract modules

Abstract

This paper describes a method for giving structured algebraic denotational definitions of programming language semantics. The basic idea is to use parameterized abstract data types to construct a directed acyclic graph of modules, such that each module corresponds to some of the language. A feature in this sense is sometimes a syntactic construction, and is sometimes a more basic language design decision. Our definitions are written in the executable algebraic specification language OBJT. Among the advantages of our approach are the following: it is relatively easier to understand the definitions because they are organized into modules and use flexible user-definable syntax; it is also relatively easy to modify or to extend the definitions, not only because of the modularity, but also because of the use of parameterization; it is possible to debug the definitions by executing test cases, which in this case are programs; the definitions are relatively compact; and they impose relatively little implementation bias. This paper illustrates these points with the definition of a modest programming language with integer and boolean expressions, blocks, iteration, conditional, input and output, and side-effect-only procedures, which can be assigned to variables and passed as parameters.