Machine function based control code algebras

Abstract

Machine functions have been introduced by Earley and Sturgis in [6] in order to provide a mathematical foundation of the use of the T-diagrams proposed by Bratman in [5]. Machine functions describe the operation of a machine at a very abstract level. A theory of hardware and software based on machine functions may be called a machine function theory, or alternatively when focusing on inputs and outputs for machine functions a control code algebra (CCA). In this paper we develop some control code algebras from first principles. Machine function types are designed specifically for various application such as program compilation, assembly, interpretation, managed interpretation and just-in-time compilation. Machine function dependent CCA’s are used to formalize the well-known compiler fixed point, the managed execution of JIT compiled text and the concept of a verifying compiler.