HOCore in Coq

We consider a recent publication on higher-order process calculi [12] and describe how its main results have been formalized in the Coq proof assistant. We highlight a number of important technical issues that we have uncovered in the original publication. We believe that these issues are not unique to the paper under consideration and require particular care to be avoided.

[1]  Brian Huffman,et al.  A New Foundation for Nominal Isabelle , 2010, ITP.

[2]  Damien Pous,et al.  An Efficient Coq Tactic for Deciding Kleene Algebras , 2010, ITP.

[3]  Daniel Hirschkoff A Full Formalisation of pi-Calculus Theory in the Calculus of Constructions , 1997, TPHOLs.

[4]  Georges Gonthier A computer-checked proof of the Four Colour Theorem , 2005 .

[5]  Joachim Parrow,et al.  Higher-order psi-calculi , 2014, Math. Struct. Comput. Sci..

[6]  Furio Honsell,et al.  pi-calculus in (Co)inductive-type theory , 2001, Theor. Comput. Sci..

[7]  Damien Pous,et al.  Deciding Kleene Algebras in Coq , 2011, Log. Methods Comput. Sci..

[8]  Zining Cao More on Bisimulations for Higher Order pi-Calculus , 2006, FoSSaCS.

[9]  Christian Urban,et al.  Mechanizing the Metatheory of LF , 2008, 2008 23rd Annual IEEE Symposium on Logic in Computer Science.

[10]  Julian Rathke,et al.  Contextual equivalence for higher-order pi-calculus revisited , 2005, Log. Methods Comput. Sci..

[11]  Bent Thomsen,et al.  A calculus of higher order communicating systems , 1989, POPL '89.

[12]  Eduardo Giménez,et al.  A Tutorial on Recursive Types in Coq , 1998 .

[13]  Bent Thomsen,et al.  Plain CHOCS A second generation calculus for higher order processes , 2005, Acta Informatica.

[14]  Davide Sangiorgi pi-Calculus, Internal Mobility, and Agent-Passing Calculi , 1996, Theor. Comput. Sci..

[15]  D. Sangiorgi - calculus , internal mobility , and agent-passing calculi , 1995 .

[16]  Davide Sangiorgi,et al.  Bisimulation for Higher-Order Process Calculi , 1994, Inf. Comput..

[17]  Christian Urban,et al.  Nominal Techniques in Isabelle/HOL , 2005, Journal of Automated Reasoning.

[18]  Bent Thomsen,et al.  Calculi for higher order communicating systems , 1990 .

[19]  Randy Pollack,et al.  A Canonical Locally Named Representation of Binding , 2012, Journal of Automated Reasoning.

[20]  Unique decomposition of processes , 1990, Bull. EATCS.

[21]  Arthur Charguéraud,et al.  The Locally Nameless Representation , 2012, Journal of Automated Reasoning.

[22]  Cheng-Shang Chang Calculus , 2020, Bicycle or Unicycle?.

[23]  Dale Miller,et al.  Proof search specifications of bisimulation and modal logics for the π-calculus , 2008, TOCL.

[24]  Xavier Leroy,et al.  Formal verification of a realistic compiler , 2009, CACM.

[25]  Dale Miller,et al.  Proof Search Specifications for Bisimulation and Modal Logics for the pi-Calculus , 2008 .

[26]  Arthur Charguéraud,et al.  Engineering formal metatheory , 2008, POPL '08.

[27]  Cezary Kaliszyk,et al.  General Bindings and Alpha-Equivalence in Nominal Isabelle , 2012, Log. Methods Comput. Sci..

[28]  Joachim Parrow,et al.  Psi-Calculi in Isabelle , 2009, Journal of Automated Reasoning.

[29]  François Pottier,et al.  A fresh look at programming with names and binders , 2010, ICFP '10.

[30]  Christine Paulin-Mohring,et al.  The coq proof assistant reference manual , 2000 .

[31]  Jorge A. Pérez,et al.  On the Expressiveness and Decidability of Higher-Order Process Calculi , 2008, 2008 23rd Annual IEEE Symposium on Logic in Computer Science.

[32]  Zining Cao More on bisimulations for higher order π-calculus , 2012, Theor. Comput. Sci..

[33]  Erik Palmgren,et al.  Internalising modified realisability in constructive , 2005 .

[34]  Simon Boulier,et al.  Formalisation de HOCore en Coq , 2012 .

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