Programs and Computable Functions

This chapter discusses programs and computable functions. Computability theory is based on a specific programming language. Certain letters are used as variables whose values are numbers. In particular, the letter X 1 , X 2 , X 3 are called the input variables of a programming language, Y is called the output variable, and Z 1 , Z 2 , Z 3 , etc. are called local variables. Thus from the outset, programming language must be regarded as a purely theoretical entity. The execution of the program has the effect of increasing the value of X by 2. In addition to variables, one will also need labels. GOTO L is not an instruction in programming language but as it is frequently used for an instruction, one can use it as an abbreviation for the program segment. Such an abbreviating pseudo instruction is called a macro and the program or program segment that it abbreviates is called its macro expansion. The use of these terms is obviously motivated by similarities with the notion of a macro instruction occurring in many programming languages.