Two-level grammar as an implementable metalanguage for axiomatic semantics

Two-level grammars can define the syntax and the operational semantics of programming languages and these definitions are directly executable by interpretation. In this paper it is shown that axiomatic semantics can also be defined using a two-level grammar with the result being a partially automatic program verification system accomplished within the framework of a language definition. These results imply that a programming language can be defined operationally and axiomatically together in complementary definitions as advocated by Hoare and Lauer. Because two-level grammars are executable, these complementary definitions accomplish a system for interpreting and verifying programs.