Countable nondeterminism and random assignment
Journal of the ACM (JACM)
Notes on logic and set theory
An axiomatic basis for computer programming
Communications of the ACM
A Discipline of Programming
Refinement Calculus: A Systematic Introduction
Refinement Calculus: A Systematic Introduction
Hoare Logics for Recursive Procedures and Unbounded Nondeterminism
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Exception Handling with Multi-Exit Statements
Programmiersprachen und Programmentwicklung, 6. Fachtagung des Fachausschusses Programmiersprachen der GI
Programming with Verification Conditions
IEEE Transactions on Software Engineering
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
ICATPN'06 Proceedings of the 27th international conference on Applications and Theory of Petri Nets and Other Models of Concurrency
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Invariant based programming is an approach where we start to construct a program by first identifying the basic situations (pre- and postconditions as well as invariants) that could arise during the execution of the algorithm. These situations are identified before any code is written. After that, we identify the transitions between the situations, which will give us the flow of control in the program. The transitions are verified at the time when they are constructed. The correctness of the program is thus established as part of constructing the program. The program structure in invariant based programs is determined by the information content of the situations, using nested invariant diagrams. The control structure is secondary to the situation structure, and will usually not be well-structured in the classical sense, i.e., it is not necessarily built out of single-entry single-exit program constructs. We study in this paper the semantics and proof rules for invariant-based programs. The total correctness of an invariant diagram is established by proving that each transition preserves the invariants and decreases a global variant. The proof rules for invariant-based programs are shown to be correct and complete with respect to an operational semantics. The proof of correctness and completeness introduces the weakest precondition semantics for invariant diagrams, and uses a special construction, based on well-ordered sets, of the least fixpoint of a monotonic function on a complete lattice. The results presented in this paper have been mechanically verified in the PVS theorem prover.