An algebraic approach to compiler design

The general purpose of this thesis is to inve8tigate the design of compilers for procedu­ ralla.nguagea, based on the algebraic la.ws which these langua.ges sa.tisfy. The particular stra.tegy adopted is to reduce an arbitrary source progrQlIl to a nonna! form which de­ scribes precisely the beha.viour of the ta.rget machine. This is achieved by a. series of algebraic transformations which are proved from the more basic laws. The correctness of the oompiler follows from the correctness of each algebraic transforma.tion. The entire process is formalised within this single a.nd uniform semantic framework of a. procedural language a.nd its algebraic la.ws. But in order to atta.in abstraction and more reasoning power, the language comprises specification features, in addition to the programming constructs to be implemented. These features are used to define a very general normal fonn, capable of representing an arbitrary target machine. The normal form reduction theorems can therefore be reused. in the design of compilers which produce code for distinct target machines. A central notion is an ordering relation on programs: p r: q means that q is at least as good as p in the sense that it will meet every purpose and satisfy every specification satisfied by p. Furthermore, substitution of q for p in any context is an improvement (or at least will leave things unchanged when q is semantically equivalent to p). The compiling task is thereby simplified to finding a normal form that is not just the same but is allowed to be better than the original source code. Moreover, at all intermediate stages, we can postpone details of implementation until the most appropriate time to make the relevant design decisions. Dijkstra's guarded conuDand language is used to illustrate how a complete compiler can be developed, up to the level of instructions for a simple target ma.c.hine. Each feature of the language is dealt with by a separate reduction theorem, which is the basis for the modularity of the approach. We then show how more elaborate features such as procedures and recur5ion can be handled in complete isolation from the simpler features of the language. Although the emphasis is on the compilation of control strudures, we develop a scheme for compiling arrays. This is also an incremental extension in the sense that it has no effect on the features already implemented. A large subset of the theory is mechanised. as a collection of algebraic structures in the OBJ3 term rewriting system. The reduction theoreIllB are used as rewrite rolell to carry out compilation automatically. The overall structure of the original theory is preserved in the mechanisation. This is largely due to the powerful module system of OBJ3.