Machine Code Programs are Predicates Too

I present an interpretation of machine language programs as boolean expressions Source language programs may also be so interpreted The correctness of a code generator can then be expressed as a simple re lationship between boolean expressions Code generators can then be calculated from their speci cation Introduction A predicate divides its domain in two In the speci cation of computational behaviour we wish to divide the set of all imaginable computations in two parts acceptable computations and unacceptable computations Predicates provide a convenient way of expressing this division In this paper we are interested in two kinds of computational behaviour the behaviour speci ed by high level language programs in terms of source level variables and the behaviour speci ed by machine language programs in terms of registers and memory By using predicate logic as a common framework to describe both forms of behaviour we can relate them and write down the logical relationship that should exist between the input and output programs of a compiler This relationship serves as a speci cation from which we can derive a code generator Except for the derivation of an example code generator all proofs and derivations have been omitted Where proofs are not straight forward an outline is presented Proofs of most of the theorems can be found in my thesis Norvell