Modular Formalization of Reactive Modules in COQ

We present modular formalizations of the model specification language Reactive Modules and the temporal logic CTL* in the proof assistant Coq. In our formalizations, both shallow and deep embeddings of each language are given. The modularity of our formalizations allows proofs and theorems to be reused across different embeddings. We illustrate the advantages of our modular formalizations by proving the mutual exclusion property of the Bakery algorithm in different embeddings.

[1]  Donald Sanella.  What Does the Future Hold for Theoretical Computer Science , 1997 .

[2]  Robert S. Boyer,et al.  The Correctness Problem in Computer Science , 1982 .

[3]  Maribel Fernández,et al.  Curry-Style Types for Nominal Terms , 2006, TYPES.

[4]  Christoph Sprenger,et al.  A Verified Model Checker for the Modal µ-calculus in Coq , 1998, TACAS.

[5]  Ming-Hsien Tsai,et al.  Formalization of CTL* in Calculus of Inductive Constructions , 2006, ASIAN.

[6]  Panagiotis Manolios.  Mu-calculus model-checking , 2000 .

[7]  Seif Haridi,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

[8]  Rajeev Alur,et al.  A Temporal Logic of Nested Calls and Returns , 2004, TACAS.

[9]  David Aspinall,et al.  Formalising Java's Data Race Free Guarantee , 2007, TPHOLs.

[10]  Gertrud Bauer.  Some properties of CTL , 2003 .

[11]  Tobias Nipkow,et al.  I/Q Automata in Isabelle/HOL , 1994, TYPES.

[12]  Solange Coupet-Grimal,et al.  An Axiomatization of Linear Temporal Logic in the Calculus of Inductive Constructions , 2003, J. Log. Comput..

[13]  Panagiotis Manolios,et al.  Computer-aided reasoning : ACL2 case studies , 2000 .

[14]  Tobias Nipkow,et al.  Traces of I/O-Automata in Isabelle/HOLCF , 1997, TAPSOFT.

[15]  Olaf Müller,et al.  A verification environment for I-O-automata based on formalized meta-theory , 1998 .

[16]  Zhaohui Luo,et al.  Implementing a Model Checker for LEGO , 1997, FME.

[17]  Stuart Anderson,et al.  Diagrams and Programming Languages for Programmable Controllers , 1997, FME.

[18]  Leslie Lamport,et al.  The temporal logic of actions , 1994, TOPL.

[19]  Marino Miculan,et al.  On the Formalization of the Modal µ-Calculus in the Calculus of Inductive Constructions , 2001, Inf. Comput..

[20]  Christine Paulin-Mohring,et al.  Types for Proofs and Programs , 2008, Lecture Notes in Computer Science.

[21]  Olaf Müller,et al.  I/O Automata and Beyond: Temporal Logic and Abstraction in Isabelle , 1998, TPHOLs.

[22]  Thomas A. Henzinger,et al.  Reactive Modules , 1999, Formal Methods Syst. Des..

[23]  Tobias Nipkow,et al.  Isabelle tutorial and user’s manual , 1990 .