An Algebraic Approach to Compiler Design

This work investigates the design of compilers for procedural languages, based on the algebraic laws which these languages satisfy. The particular strategy adopted is to reduce an arbitrary source program to a general "normal form", capable of representing an arbitrary target machine. This is acheived by a series of normal form reduction theorems which are proved algebraically from the more basic laws. The normal form and the related reduction theorems can then be instantiated to design compilers for distinct target machines. This constitutes the main novelty of the author's approach to compilation, together with the fact that the entire process is formalized within a single and uniform semantic framework of a procedural language and its algebraic laws. Furthermore, by mechanizing the approach using the OBJ3 term rewriting system it is shown that a prototype compiler is developed as a byproduct of its own proof of correctness.