Towards a theory of bisimulation for local names

A.M. Pitts and I.D.B. Stark (1998) have proposed the v-calculus as a language for investigating the interaction of unique name generation and higher-order functions. They developed a sound model based on logical relations, but left completeness as an open problem. In this paper, we develop a complete model based on bisimulation for a labelled transition system semantics. We show that bisimulation is complete, but not sound, for the v-calculus. We also show that by adding assignment to the v-calculus, bisimulation becomes sound and complete. The analysis used to obtain this result illuminates the difficulties involved in finding fully abstract models for v-calculus proper.

[1]  Robin Milner,et al.  A Calculus of Mobile Processes, II , 1992, Inf. Comput..

[2]  Gérard Berry,et al.  The chemical abstract machine , 1989, POPL '90.

[3]  I. Stark,et al.  Operational reasoning for functions with local state , 1999 .

[4]  Martín Abadi,et al.  A calculus for cryptographic protocols: the spi calculus , 1997, CCS '97.

[5]  Peter G. Harrison,et al.  Functional Programming , 1988 .

[6]  Matthew Hennessy,et al.  Algebraic theory of processes , 1988, MIT Press series in the foundations of computing.

[7]  Luca Cardelli,et al.  Mobile Ambients , 1998, FoSSaCS.

[8]  Davide Sangiorgi,et al.  Expressing mobility in process algebras : first-order and higher-order paradigms , 1993 .

[9]  Robin Milner,et al.  Definition of standard ML , 1990 .

[10]  Davide Sangiorgi,et al.  Techniques of \ weak bisimulation up to " , 1992 .

[11]  Andrew D. Gordon.  Nominal calculi for security and mobility , 1997 .

[12]  Eugene W. Stark,et al.  Operational semantics of a focusing debugger , 1995, MFPS.

[13]  Andrew M. Pitts,et al.  Observable Properties of Higher Order Functions that Dynamically Create Local Names, or What's new? , 1993, MFCS.

[14]  Matthias Felleisen,et al.  A Syntactic Approach to Type Soundness , 1994, Inf. Comput..

[15]  Eugenio Moggi,et al.  Notions of Computation and Monads , 1991, Inf. Comput..

[16]  Andrew D. Gordon.  Bisimilarity as a theory of functional programming , 1995, MFPS.

[17]  Matthew Hennessy,et al.  A theory of weak bisimulation for core CML , 1996, ICFP '96.

[18]  Robin Milner,et al.  A Calculus of Mobile Processes, II , 1992, Inf. Comput..

[19]  Ian David Bede Stark,et al.  Names and higher-order functions , 1994 .

[20]  Andrew D. Gordon,et al.  Notes on Nominal Calculi for Security and Mobility , 2000, FOSAD.

[21]  Carolyn L. Talcott,et al.  A Variable Typed Logic of Effects , 1995, Inf. Comput..

[22]  Robin Milner,et al.  The Problem of "Weak Bisimulation up to" , 1992, CONCUR.

[23]  John H. Reppy,et al.  Higher-Order Concurrency , 1992 .

[24]  Douglas J. Howe.  Equality in lazy computation systems , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[25]  I. Stark,et al.  On the Observable Properties of Higher Order Functions that Dynamically Create Local Names (Preliminary Report) , 1993 .