Formalization of the General Hoare Logic Laws

This paper presents a new approach to formalizing the general rules of the Hoare logic. Our way is based on formulas of the first-order predicate logic defined over the abstract state space of a virtual machine, i.e. so-called S-formulas. S-formulas are general tool for analyzing program semantics inasmuch as Hoare triples of total and partial correctness are not more than two S-formulas. The general rules of Hoare logic, such as the laws of consequence, conjunction, disjunction and negation can be derived using axioms and theorems of first-order predicate logic. Every proof is based on deriving the validity of some S-formula, so the procedure may be automated using automatic theorem provers. In this paper we will use Coq.