Program derivation = rules + strategies

In a seminal paper Prof. Robert Kowalski advocated the paradigm Algorithm = Logic + Control which was intended to characterize program executions. Here we want to illustrate the corresponding paradigm Program Derivation = Rules + Strategies which is intended to characterize program derivations, rather than executions. During program execution, the Logic component guarantees that the computed results are correct, that is, they are true facts in the intended model of the given program, while the Control component ensures that those facts are derived in an efficient way. Likewise, during program derivation, the Rules component guarantees that the derived programs are correct and the Strategies component ensures that the derived programs are efficient. In this chapter we will consider the case of logic programs with locally stratified negation and we will focus on the following three important methodologies for program derivation: program transformation, program synthesis, and program verification. Based upon the Rules + Strategies approach, we will propose a unified method for applying these three programming methodologies. In particular, we will present: (i) a set of rules for program transformation which preserve the perfect model semantics and (ii) a general strategy for applying the transformation rules. We will also show that we can synthesize correct and efficient programs from first order specifications by: (i) converting an arbitrary first order formula into a logic program with locally stratified negation by using a variant of the Lloyd-Topor transformation, and then (ii) applying our transformation rules according to our general strategy. Finally, we will demonstrate that the rules and the strategy for program transformation and program synthesis can also be used for program verification, that is, for proving first order properties of systems described by logic programs with locally stratified negation.