Semantics of meta-logic in an algebra of programs

Meta-programming is a powerful technique for extending and modifying the semantics of an existing object language. Along with the expressiveness, however, meta-programming puts forth some subtle semantic problems, among which the most critical is bound to the representation of object programs at the meta-level. We propose a semantic justification for a simple representation technique in the field of a generalised notion of meta-programming in logic. The generalisation consists in specifying the meta-programs with respect to object programs defined by program expressions. The expressions are defined via a rich suite of operations on logic programs. The technique allows one to build straightforward and concise meta-programs via the representation of object level variables by meta-level variables