Unifying Correctness Statements

Partial, total and general correctness and further models of sequential computations differ in their treatment of finite, infinite and aborting executions. Algebras structure this diversity of models to avoid the repeated development of similar theories and to clarify their range of application. We introduce algebras that uniformly describe correctness statements, correctness calculi, pre-post specifications and loop refinement rules in five kinds of computation models. This extends previous work that unifies iteration, recursion and program transformations for some of these models. Our new description includes a relativised domain operation, which ignores parts of a computation, and represents bound functions for claims of termination by sequences of tests. We verify all results in Isabelle heavily using its automated theorem provers.