Algebraic approaches to program semantics
Algebraic approaches to program semantics
Floyd-Hoare logic in iteration theories
Journal of the ACM (JACM)
Specification structures and propositions-as-types for concurrency
Proceedings of the VIII Banff Higher order workshop conference on Logics for concurrency : structure versus automata: structure versus automata
On Hoare logic and Kleene algebra with tests
ACM Transactions on Computational Logic (TOCL)
Ten Years of Hoare's Logic: A Survey—Part I
ACM Transactions on Programming Languages and Systems (TOPLAS)
An axiomatic basis for computer programming
Communications of the ACM
Separation Logic: A Logic for Shared Mutable Data Structures
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Local Reasoning about Programs that Alter Data Structures
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Complete Axioms for Categorical Fixed-Point Operators
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
A logical analysis of aliasing in imperative higher-order functions
Proceedings of the tenth ACM SIGPLAN international conference on Functional programming
Semantical consideration on floyo-hoare logic
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
A Hoare logic for single-input single-output continuous-time control systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Towards a typed geometry of interaction
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Hi-index | 0.00 |
We present an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. We first identify a particular class of functors – which we call ‘verification functors’ – between traced symmetric monoidal categories and subcategories of Preord (the category of preordered sets and monotone mappings). We then give an abstract definition of Hoare triples, parametrised by a verification functor, and prove a single soundness and completeness theorem for such triples. In the particular case of the traced symmetric monoidal category of while programs we get back Hoare’s original rules. We discuss how our framework handles extensions of the Hoare logic for while programs, e.g. the extension with pointer manipulations via separation logic. Finally, we give an example of how our theory can be used in the development of new Hoare logics: we present a new sound and complete set of Hoare-logic-like rules for the verification of linear dynamical systems, modelled via stream circuits.