A Calculus of Space, Time, and Causality: Its Algebra, Geometry, Logic

The calculus formalises human intuition and common sense about space, time, and causality in the natural world. Its intention is to assist in the design and implementation of programs, of programming languages, and of interworking by tool chains that support rational program development.

[1]  Peter W. O'Hearn,et al.  Separation Logic Semantics for Communicating Processes , 2008, FICS.

[2]  N. D. Gautam.  The validity of equations of complex algebras , 1957, Arch. Math. Log..

[3]  Georg Struth,et al.  Verifying Hybrid Systems with Modal Kleene Algebra , 2018, RAMiCS.

[4]  Georg Struth,et al.  Hybrid process algebra , 2005, J. Log. Algebraic Methods Program..

[5]  Georg Struth,et al.  Modal Kleene Algebra Applied to Program Correctness , 2016, FM.

[6]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[7]  Karem A. Sakallah,et al.  Symmetry and Satisfiability , 2021, Handbook of Satisfiability.

[8]  Simon Foster,et al.  Unifying Semantic Foundations for Automated Verification Tools in Isabelle/UTP , 2019, Sci. Comput. Program..

[9]  Ian J. Hayes,et al.  Concurrent Refinement Algebra and Rely Quotients , 2016, Arch. Formal Proofs.

[10]  Daniel Jackson,et al.  Alloy: a lightweight object modelling notation , 2002, TSEM.

[11]  Jim Woodcock,et al.  The Semantics of Circus , 2002, ZB.

[12]  A. Tarski.  A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[13]  Georg Struth,et al.  Probabilistic Concurrent Kleene Algebra , 2013, QAPL.

[14]  C. A. Petri.  Communication with automata , 1966 .

[15]  A. W. Roscoe,et al.  FDR3: a parallel refinement checker for CSP , 2015, International Journal on Software Tools for Technology Transfer.

[16]  H. M. Macneille,et al.  Partially ordered sets , 1937 .

[17]  Jim Woodcock,et al.  RoboChart: modelling and verification of the functional behaviour of robotic applications , 2019, Software & Systems Modeling.

[18]  C. A. R. Hoare,et al.  Algorithm 65: find , 1961, Commun. ACM.

[19]  Richard F. Paige,et al.  The Epsilon Transformation Language , 2008, ICMT@TOOLS.

[20]  Ralph-Johan Back.  A Method for Refining Atomicity in Parallel Algorithms , 1989, PARLE.

[21]  Ian P. Gent,et al.  Symmetry in Constraint Programming , 2006, Handbook of Constraint Programming.

[22]  Augusto Sampaio,et al.  Object-Orientation in the UTP , 2006, UTP.

[23]  C. A. R. Hoare,et al.  Algorithm 64: Quicksort , 1961, Commun. ACM.

[24]  Georg Struth,et al.  Kleene algebra with domain , 2003, TOCL.

[25]  Robert Colvin,et al.  A synchronous program algebra: a basis for reasoning about shared-memory and event-based concurrency , 2017, Formal Aspects of Computing.

[26]  Marta Z. Kwiatkowska,et al.  PRISM 4.0: Verification of Probabilistic Real-Time Systems , 2011, CAV.

[27]  Alfred Horn,et al.  On sentences which are true of direct unions of algebras , 1951, Journal of Symbolic Logic.

[28]  Augusto Sampaio,et al.  A Modular Theory of Object Orientation in Higher-Order UTP , 2014, FM.

[29]  Augusto Sampaio,et al.  Refactoring and representation independence for class hierarchies , 2012, Theor. Comput. Sci..

[30]  Augusto Sampaio,et al.  A Strategy for Compiling Classes, Inheritance, and Dynamic Binding , 2003, FME.

[31]  David L. Dill,et al.  Better verification through symmetry , 1996, Formal Methods Syst. Des..

[32]  Jim Woodcock,et al.  Cyber-Physical Systems Design: Formal Foundations, Methods and Integrated Tool Chains , 2015, 2015 IEEE/ACM 3rd FME Workshop on Formal Methods in Software Engineering.

[33]  Georg Struth,et al.  Internal axioms for domain semirings , 2011, Sci. Comput. Program..

[34]  Georg Struth,et al.  Completeness Theorems for Pomset Languages and Concurrent Kleene Algebras , 2017, ArXiv.

[35]  C. A. R. Hoare.  Theories of Programming: Top-Down and Bottom-Up and Meeting in the Middle , 1999, Correct System Design.

[36]  Vaughan R. Pratt.  Action Logic and Pure Induction , 1990, JELIA.

[37]  C. A. R. Hoare,et al.  The Weakest Prespecification , 1987, Information Processing Letters.

[38]  Augusto Sampaio,et al.  A Semantics for UML-RT Active Classes via Mapping into Circus , 2005, FMOODS.

[39]  Simon Foster,et al.  Unifying Theories of Programming in Isabelle , 2013, ICTAC Training School on Software Engineering.

[40]  Ian J. Hayes,et al.  Generalised rely-guarantee concurrency: an algebraic foundation , 2016, Formal Aspects of Computing.

[41]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[42]  Dexter Kozen,et al.  Kleene algebra with tests , 1997, TOPL.

[43]  John C. Reynolds,et al.  Separation logic: a logic for shared mutable data structures , 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science.

[44]  Georg Struth,et al.  Building program construction and verification tools from algebraic principles , 2015, Formal Aspects of Computing.

[45]  Jim Woodcock,et al.  A UTP semantics for Circus , 2009, Formal Aspects of Computing.

[46]  C. A. R. Hoare,et al.  An axiomatic basis for computer programming , 1969, CACM.

[47]  Michael W. Grieves,et al.  Digital Twin: Mitigating Unpredictable, Undesirable Emergent Behavior in Complex Systems , 2017 .

[48]  Augusto Sampaio,et al.  Laws of Object-Orientation with Reference Semantics , 2008, 2008 Sixth IEEE International Conference on Software Engineering and Formal Methods.

[49]  Jim Woodcock,et al.  FM’99 — Formal Methods , 1999, Lecture Notes in Computer Science.

[50]  Cristina Nita-Rotaru,et al.  Taking a long look at QUIC , 2019, Commun. ACM.

[51]  Georg Struth,et al.  Developments in concurrent Kleene algebra , 2014, J. Log. Algebraic Methods Program..

[52]  Simon Foster,et al.  Isabelle/UTP: A Mechanised Theory Engineering Framework , 2014, UTP.

[53]  Jeremy Avigad,et al.  The Lean Theorem Prover (System Description) , 2015, CADE.

[54]  Georg Struth,et al.  A Discrete Geometric Model of Concurrent Program Execution , 2016, UTP.

[55]  Peter W. O'Hearn,et al.  Separation logic , 2019, Commun. ACM.

[56]  Frank Budinsky,et al.  EMF: Eclipse Modeling Framework 2.0 , 2009 .

[57]  A. Prasad Sistla,et al.  Symmetry and model checking , 1996, Formal Methods Syst. Des..

[58]  Augusto Sampaio,et al.  Unifying classes and processes , 2005, Software & Systems Modeling.

[59]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[60]  Georg Struth,et al.  On Probabilistic Kleene Algebras, Automata and Simulations , 2011, RAMiCS.

[61]  Augusto Sampaio,et al.  A Complete Set of Object Modeling Laws for Alloy , 2009, SBMF.

[62]  Simon Foster,et al.  Calculational Verification of Reactive Programs with Reactive Relations and Kleene Algebra , 2018, RAMiCS.

[63]  Yves Bertot,et al.  Interactive Theorem Proving and Program Development: Coq'Art The Calculus of Inductive Constructions , 2010 .

[64]  C. A. R. Hoare,et al.  Logic, Algebra, and Geometry at the Foundation of Computer Science , 2019, FMTea.

[65]  Ulf Norell,et al.  A Brief Overview of Agda - A Functional Language with Dependent Types , 2009, TPHOLs.

[66]  Andreas Reuter,et al.  Transaction Processing: Concepts and Techniques , 1992 .

[67]  Andrzej Tarlecki,et al.  A Language of Specified Programs , 1985, Sci. Comput. Program..