A New Roadmap on Linking Theories of Programming

Formal methods advocate the crucial role played by the algebra of programs in specification and implementation of programs. Study leads to the conclusion that both the top-down approach (with denotational model as its origin) and the bottom-up approach (a journey started from operational model) can meet in the middle with a program algebra. This paper proposes a new approach on linking theories of programming. Given a program algebra, we construct a test operator taking a test case and the testing program as its arguments. The operator yields a collection of observations of the test outcomes. The denotational model of a program can be derived as a binary relation which relates the test cases with their outcomes. An operational model is considered as consistent if its step relation is consistent with the algebraic semantics.