Traces of I/O-Automata in Isabelle/HOLCF

This paper presents a formalization of finite and infinite sequences in domain theory carried out in the theorem prover Isabelle. The results are used to model the metatheory of I/O automata; they are, however, applicable to any trace based model of parallelism which distinguishes internal and external actions. We make use of the logic HOLCF, an extension of HOL with domain theory and show how to move between HOL and HOLCF. This allows us to restrict the use of HOLCF to metatheoretic arguments while actual refinement proofs between I/O automata are carried out within the simpler logic HOL. In order to evaluate the formalization we prove the correctness of a generalized refinement concept in I/O automata.

[1]  Tobias Nipkow,et al.  Combining Model Checking and Deduction for I/O-Automata , 1995, TACAS.

[2]  Franz Regensburger,et al.  HOLCF: Higher Order Logic of Computable Functions , 1995, TPHOLs.

[3]  F. Vaandrager.  Forward and Backward Simulations Part I : Untimed Systems , 1993 .

[4]  Lawrence Charles Paulson,et al.  Isabelle: A Generic Theorem Prover , 1994 .

[5]  Martín Abadi,et al.  The Existence of Refinement Mappings , 1988, LICS.

[6]  Nancy A. Lynch,et al.  Liveness in Timed and Untimed Systems , 1994, Inf. Comput..

[7]  Stephen D. Brookes,et al.  Full abstraction for a shared variable parallel language , 1993, [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science.

[8]  Nancy A. Lynch,et al.  Forward and Backward Simulations: I. Untimed Systems , 1995, Inf. Comput..

[9]  Doron A. Peled,et al.  Formal Verification of a Partial-Order Reduction Technique for Model Checking , 1996, TACAS.

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

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

[12]  Nancy A. Lynch,et al.  Verifying timing properties of concurrent algorithms , 1994, FORTE.

[13]  M. Gordon,et al.  Introduction to HOL: a theorem proving environment for higher order logic , 1993 .

[14]  Lawrence C. Paulson,et al.  Co-induction and co-recursion in higher-order logic , 1993 .

[15]  Solomon Feferman.  Computation on Abstract Data Types: The Extensional Approach, with an Application to Streams , 1996, Ann. Pure Appl. Log..

[16]  Paul Loewenstein,et al.  A formal theory of simulations between infinite automata , 1992, Formal Methods Syst. Des..

[17]  Nancy A. Lynch,et al.  An introduction to input/output automata , 1989 .

[18]  Stephen D. Brookes.  Full Abstraction for a Shared-Variable Parallel Language , 1996, Inf. Comput..