Algebraic Processing of Programming Languages

Current methodology for compiler construction evolved from the need to release programmers form the burden of writing machine-language programs. This methodology does not assume a formal concept of a programming language and is not based on mathematical algorithms that model the behavior of a compiler. The side eeect is that compiler implementation is a diicult task and the correctness of a compiler usually is not proven mathematically. Moreover, a compiler may be based on assumptions about its source and target languages that are not necessarily acceptable for another compiler that has the same source and target languages. The consequence is that programs are not portable between platforms of machines and between generations of languages. In addition, while a conventional compiler freezes the notation that programmers can use to develop their programs the problem domain evolves and requires extensions that are not supported by the compiler. These problems are addressed by two directions of research in the current language processing technology. One direction enriches the programming environment provided by the conventional compilers with tools that optimize programs according to the architecture of the target machines. The other research direction focuses on a new methodology for programming language design and implementation that accommodates the existing programming tools and at the same time allows programmers to manufacture their own languages and compilers adapted to their own machines and problem domains. The rst research direction further complicates the compiler, which is already too complicated, and does not provide for language extensibility with the problem domain. The second research direction is based on mathematical concepts of programming language and programming language translation that are independent of the computer and computer user and could easily be mastered by programmers. The research reported in this paper ts within this framework. We rst introduce the formal concept of a programming language which captures all three components of a language, the semantics, the syntax, and their association into a communication tool, as mathematical constructs of universal algebra. This concept reveals the compositional structure of programming languages and allows us to look for a natural decomposition of programming languages into simpler objects such as language lexicon, language types, and language constructs. Each language component is however mathematically speciied and implemented and the speciications and implementations of these language components are further mathematically integrated into the speciication and implementation of the programming language they deene. We illustrate this approach of language …