A Coalgebraic Foundation for Linear Time Semantics

We present a coalgebraic approach to trace equivalence semantics based on lifting behaviour endofunctors for deterministic action to Kleisli categories of monads for non-deterministic choice. In Set, this gives a category with ordinary transition systems as objects and with morphisms characterised in terms of a linear notion of bisimulation. The final object in this category is the canonical abstract model for trace equivalence and can be obtained by extending the final coalgebra of the deterministic action behaviour to the Kleisli category of the non-empty powerset monad. The corresponding final coalgebra semantics is fully abstract with respect to trace equivalence.

[1]  Michael Barr,et al.  Terminal Coalgebras in Well-Founded Set Theory , 1993, Theor. Comput. Sci..

[2]  Mogens Nielsen,et al.  Open Maps (at) Work , 1995 .

[3]  Albert R. Meyer,et al.  Bisimulation can't be traced , 1988, POPL '88.

[4]  Gordon D. Plotkin,et al.  The category-theoretic solution of recursive domain equations , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[5]  Daniele Turi,et al.  Categorical Modelling of Structural Operational Rules: Case Studies , 1997, Category Theory and Computer Science.

[6]  Matthew Hennessy,et al.  Full Abstraction for a Simple Parallel Programming Language , 1979, MFCS.

[7]  Jan J. M. M. Rutten,et al.  Initial Algebra and Final Coalgebra Semantics for Concurrency , 1993, REX School/Symposium.

[8]  Jan Rutten,et al.  On the foundations of final coalgebra semantics: non-well-founded sets, partial orders, metric spaces , 1998, Mathematical Structures in Computer Science.

[9]  Philip S. Mulry,et al.  Lifting Theorems for Kleisli Categories , 1993, MFPS.

[10]  Peter Aczel,et al.  A Final Coalgebra Theorem , 1989, Category Theory and Computer Science.

[11]  James Worrell,et al.  An axiomatics for categories of transition systems as coalgebras , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[12]  Jirí Adámek,et al.  On the Greatest Fixed Point of a Set Functor , 1995, Theor. Comput. Sci..

[13]  Jan A. Bergstra,et al.  Linear Time and Branching Time Semantics for Recursion with Merge , 1983, Theor. Comput. Sci..

[14]  Glynn Winskel,et al.  Bisimulation and open maps , 1993, [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science.

[15]  Jan Friso Groote,et al.  Structured Operational Semantics and Bisimulation as a Congruence , 1992, Inf. Comput..

[16]  Peter Aczel,et al.  Non-well-founded sets , 1988, CSLI lecture notes series.

[17]  John-Jules Ch. Meyer,et al.  Metric semantics for concurrency , 1988, BIT.

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

[19]  K. Mani Chandy,et al.  Current trends in programming methodology , 1977 .

[20]  Davide Sangiorgi,et al.  On the bisimulation proof method , 1998, Mathematical Structures in Computer Science.

[21]  P. Freyd.  Algebraically complete categories , 1991 .

[22]  Jan J. M. M. Rutten,et al.  On the Foundations of Final Coalgebra Semantics , 1998, Mathematical Structures in Computer Science.

[23]  Daniele Turi,et al.  Axiomatic domain theory in categories of partial maps , 1998 .

[24]  Wan Fokkink,et al.  Ntyft/Ntyxt Rules Reduce to Ntree Rules , 1996, Inf. Comput..

[25]  Gordon D. Plotkin,et al.  Towards a mathematical operational semantics , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.