On Algebra of Program Correctness and Incorrectness

Modal Kleene Algebra Applied to Program Correctness

Modal Kleene algebras are relatives of dynamic logics that support program construction and verification by equational reasoning. We describe their application in implementing versatile program correctness components in interactive theorem provers such as Isabelle/HOL. Starting from a weakest precondition based component with a simple relational store model, we show how variants for Hoare logic...

Calculi for Program Incorrectness and Arithmetic

This thesis is about the development and usage of deductive methods in two main areas: (i) the deductive dis-verification of programs, i.e., how techniques for deductive verification of programs can be used to detect program defects, and (ii) reasoning modulo integer arithmetic, i.e., how to prove the validity (and, in special cases, satisfiability) of first-order formulae that involve integer ...

General Correctness Algebra

General correctness offers a finer semantics of programs than partial and total correctness. We give an algebraic account continuing and extending previous approaches. In particular, we propose axioms, correctness statements, a correctness calculus, specification constructs and a loop refinement rule. The Egli-Milner order is treated algebraically and we show how to obtain least fixpoints, used...

Modal Kleene Algebra and Partial Correctness

We enrich Kleene algebra by domain and codomain operators. These abstractions of relational notions give rise to four modal operators. The boxes and diamonds enjoy various symmetries via Galois connections and dualities. Lifting modal statements to modal operator semirings yields a further abstraction and thus a more elegant and concise “statefree” reasoning about modalities. We use this modal ...

Program Algebra and Thread Algebra