Circular Coinduction

Circular coinduction is a new technique for behavioral reasoning that extends coinduction to specifications with circularities. We show that a congruence criterion due to Bidoit and Hennicker follows easily from circular coinduction, and we give some natural examples of circular coinductive proofs. A notation, called BOBJ, appropriate for our style of behavioral specification is also sketched. Finally, everything is conducted in a general framework that in a sense is the gcd of previous behavioral frameworks.

[1]  B. Jacobs,et al.  A tutorial on (co)algebras and (co)induction , 1997 .

[2]  Peter Padawitz.  Towards the one-tiered design of data types and transition systems , 1997, WADT.

[3]  Grigore Rosu,et al.  Hiding More of Hidden Algebra , 1999, World Congress on Formal Methods.

[4]  Grigore Rosu,et al.  Circular coinductive rewriting , 2000, Proceedings ASE 2000. Fifteenth IEEE International Conference on Automated Software Engineering.

[5]  Samuel R. Buss,et al.  Incompleteness of Behavioral Logics , 2000, CMCS.

[6]  Grigore Rosu,et al.  An Overview of the Tatami Project , 2000 .

[7]  Michel Bidoit,et al.  Observational Logic , 1998, AMAST.

[8]  Alan Bundy,et al.  Using A Generalisation Critic to Find Bisimulations for Coinductive Proofs , 1997, CADE.

[9]  Joseph A. Goguen,et al.  Towards an Algebraic Semantics for the Object Paradigm , 1992, COMPASS/ADT.

[10]  Joseph A. Goguen,et al.  Types as theories , 1991 .

[11]  Gernot Salzer,et al.  Automated Deduction in Classical and Non-Classical Logics , 2002, Lecture Notes in Computer Science.

[12]  Grigore Rosu,et al.  Hidden Congruent Deduction , 1998, FTP.

[13]  Grigore Rosu,et al.  Distributed cooperative formal methods tools , 1997, Proceedings 12th IEEE International Conference Automated Software Engineering.