Retracing some paths in Process Algebra

We use traced monoidal categories to give a precise general version of "geometry of interaction". We give a number of examples of both "particle-style" and "wave-style" instances of this construction. We relate these ideas to semantics of computation.

[1]  Rajagopal Nagarajan,et al.  Specification Structures and Propositions-as-Types for Concurrency , 1996, Banff Higher Order Workshop.

[2]  G. M. Kelly,et al.  Coherence for compact closed categories , 1980 .

[3]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[4]  Cliff B. Jones A pi-Calculus Semantics for an Object-Based Design Notation , 1993, CONCUR.

[5]  Robin Milner Functions as Processes , 1990, ICALP.

[6]  Frank Dederichs,et al.  Assumption/Commitment Rules for Networks of Asynchronously Communicating Agents , 1993 .

[7]  Martín Abadi,et al.  A Logical View of Composition , 1993, Theor. Comput. Sci..

[8]  Cliff B. Jones,et al.  Some Practical Problems and Their Influence on Semantics , 1996, ESOP.

[9]  Ross Street,et al.  Traced monoidal categories , 1996 .

[10]  Gordon D. Plotkin,et al.  A Powerdomain Construction , 1976, SIAM J. Comput..

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

[12]  Richard Southwell The Imperial College , 1949 .

[13]  Radu Grosu,et al.  A Model for Mobile Point-to-Point Data-flow Networks without Channel Sharing , 1996, AMAST.

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

[15]  Martín Abadi,et al.  A logical view of composition and refinement , 1991, POPL '91.

[16]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[17]  Samson Abramsky,et al.  Games and full abstraction for the lazy /spl lambda/-calculus , 1995, Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science.

[18]  Michael A. Arbib,et al.  The Pattern-of-Calls Expansion Is the Canonical Fixpoint for Recursive Definitions , 1982, JACM.

[19]  Samson Abramsky Semantics of Interaction (Abstract) , 1996, CAAP.

[20]  Radha Jagadeesan,et al.  New Foundations for the Geometry of Interaction , 1994, Inf. Comput..

[21]  Michael Barr,et al.  Algebraically compact functors , 1992 .

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

[23]  Radha Jagadeesan,et al.  Full Abstraction for PCF , 1994, Inf. Comput..

[24]  Guy McCusker Games and Full Abstraction for a Functional Metalanguage with Recursive Types , 1998, Distinguished Dissertations.

[25]  Zoltán Ésik,et al.  Iteration Theories , 1993, EATCS Monographs on Theoretical Computer Science.

[26]  R. D. Tennent Denotational semantics , 1995, LICS 1995.

[27]  Hans Bekic,et al.  Towards a Mathematical Theory of Processes , 1984, Programming Languages and Their Definition.

[28]  Robin Milner,et al.  Control structures , 1995, Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science.

[29]  Jean-Yves Girard,et al.  Geometry of Interaction 1: Interpretation of System F , 1989 .

[30]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[31]  Cliff B. Jones,et al.  Process algebraic foundations for an object-based design notation , 1993 .

[32]  Rajagopal Nagarajan,et al.  Interaction categories and the foundations of typed concurrent programming , 1996, NATO ASI DPD.

[33]  Samson Abramsky,et al.  Proofs as Processes , 1992, Theor. Comput. Sci..

[34]  Radha Jagadeesan,et al.  Games and Full Completeness for Multiplicative Linear Logic , 1994, J. Symb. Log..

[35]  Robin Milner,et al.  Processes: A Mathematical Model of Computing Agents , 1975 .

[36]  Uday S. Reddy,et al.  Global state considered unnecessary: An introduction to object-based semantics , 1996, LISP Symb. Comput..

[37]  Samson Abramsky Interaction categories (extended abstract) , 1994, FME 1994.

[38]  Guy McCusker,et al.  Games and Full Abstraction for the Lazy-calculusSamson , 1995 .

[39]  Samson Abramsky Interaction categories and communicating sequential processes , 1994 .

[40]  John C. Reynolds,et al.  The essence of ALGOL , 1997 .

[41]  Glynn Winskel,et al.  Synchronization Trees , 1984, Theor. Comput. Sci..